SOVIET ATOMIC ENERGY - VOL. 38, NO. 6

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• Publication Date: December 1, 1975
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Russian OriginalVol. 3, No. 6, June, 1975
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December, 1975
244 ,L V 462-c-3-147
(73.'V1
ATEAZ 38(6) 469-570 (1975)
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HEPri1fl
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC?
? Physics Abstracts and Electrical and, Elec-
tronics Abstracts, Current Contents, and
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Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
thergiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artWork:\This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
EditoriarBoard of Atomnaya Energiya:
?
Editor: M. D. Millionshchikov
Deputy Director
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. Vlasov
A. A. Bochvar,
N. A. Dollezhar
( V. S. Fursov
I. N. Golovin
V. F. Kalinin
' A. K. Krasin
A. P. Zefirov
? V. V. Matveev
M. G. Meshcheryakov
P. N. Palei ' '
V. B. Shevchenko
V. I. Smirnov,
A. P. Vinogradov
Copyright C) 1975 Plenum Publishing Corporation, 227 West 17th Street, New York,
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
December, 1975
Volume 38, Number 6
June, 1975
ARTICLES
? Optimization of the Operating Conditions of Mass-Diffusion Cascade Installations
? V. A. Chuzhinov, N. I. Laguntsov, B. I. Nikolaev, and G. A. Sulaberidze
? Mathematical Simulation of the Extractive Reprocessing of Nuclear Fuel. 3. Redox
Reextraction Using Iron Salts ? A. M. Rozen, M. Ya. Zeltvenskii,
and I. V. Shilin
Two-Dimensional Diffusion Program HEXAGA II for Many-Group Calculations of
CONTENTS
Engl./Russ.
469 363
473'. 367
Hexagonal Lattices ? T. Apostolov and Z. Woznicki
479
372
Investigation of the Adiabatic Outflow of Water through Cylindrical Channels
? V. S. Aleshin, Yu. A. Kalaida, and V. V. Fisenko
483
375
? Oxidation of Tritium in Air under the Action of Intrinsic Radiation
? L. F. Belovodskii, V. K. Gaevoi, V. I. Grishmanovskii, and N. V. Nefedov
488
379
Experiments on the Synthesis of Neutron-Deficient Isotopes of Kurchatovium in
Reactions with Accelerated "Ti Ions ? Yu. Ts. Oganesyan, A. G. Demin,
A. S. Illinov, S. P. Trettyakova, A. A. Pleve, Yu. E. Penionzhkevich, M. P.Ivanov,
and Yu. P. Trettyakov
492
382
REVIEWS
? Problem of Environmental Protection in the Operation of Nuclear Power Stations
? N. G. Gusev
502
391
Contemporary Trends in Experimental Shielding Physics Research
? V. P. Mashkovich and S. G. Tsypin
510
398
Numerical Solutions of the Kinetic Equation for Reactor Shielding Problems
? T. A. Germogenova
513
401
BOOK REVIEWS
Yu. A. Egorova (editor). Problems of the Physics of Reactor Shielding ? Reviewedby
B. R. Bergeltson
518
405
ARTICLES
Problems of Secondary Gamma Radiation in Reactor Shields ? A. A. Abagyan,
T. A. Germogenova, A. A. Dubinin, V.1. Zhuravlev, V. A. Klimanov, E. I. Kostin,
V. P. Mashkovich, V. K. Sakharov, and V. A. Utkin
520
406
ABSTRACTS
Effect of Proton Irradiation on the Operation of a Scintillation Counter
? B. V. Gubinskii, E. M. Iovenko, V. A. Kuztmin, V. G. Mikutskii,
and V. N. Nikolaev
524
411
? Experimental Determination of the Temperature Dependence of the Thermal
Conductivity of Uranium Dioxide under Conditions of Reactor Irradiation
? B. V. Samsonov, Yu. G. Spiridonov, N. A. Fomin, and V. A. Tsykanov
525
412
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CONTENTS
(continued)
Engl./Russ.
Mechanical Strength of Uranium Field-Emitters ? A. L. Suvorov, G. M. Kukavadze,
D. M. Skorov, B. A. Kahn, A. F. Bobkov, V. A. Fedorchenko, B. V. Sharov,
and G. N. Shishkin
526
412
Dose Distribution in a Tissue-Equivalent Medium from a Plane Thin Isotropic Alpha-
Particle Source ? D. P. Osanov, V. P. Panova, Yu. N. Podsevalov,
and E. B. Ershov
527
413
Recovery of the Integrated Spectrum of Neutrons in the Energy Range 0.1-3 MeV by the
Extrapolation Method ? R. D. Vasil'ev, E. I. Grigoraev, G. B. Tarnovskii,
and V. P. Yaryna
528
414
Determination of Traces of Nitrogen in Pure Metals by Gamma Activation
? A. F. Gorenko, A. S. Zadvornyi, A. P. Klyucharev, and N. A. Skakun
529
415
Microscopic Distribution of Ionization Events in an Irradiated Medium as a Characteristic
of the Quality of Ionizing Radiation ? I. B. Keirim-Markus, A. K. Savinskii,
and I. V. Filyushkin
530
415
Allowance for Fluctuations in theIrradiationDose of Lungs by Highly Active Particles
? 0. M. Zaraev and B. N. Rakhmanov
531
416
LETTERS TO THE EDITOR
Calculation of Heterogeneous Nuclear Reactors by the Method of Inserted Elements
? I. S. Slesarev and A. M. Sirotkin
533
419
Transient Changes of the Thermoelectric Characteristics of Thermocouples by the
Action of Reactor Radiation ? V. P. Kornilov and E. . B. Pereslavtsev
536
420
Oxidation of Solid Solutions of Uranium and Niobium Monocarbides ? V. G. Vlasov,
V. A. Alabushev, and A. R. Beketov
539
422
Spectral Characteristics of the Background Noise in the Primary Loop of an Atomic
Generating Plant ? K. A. Adamenkov, V. I. Gorbachev, Yu. V. Zakharov,
V. P. Kruglov, S. A. Paraev, Yu. A. Reznikov, and R. F. Khasyanov
543
425
Pores in Helium-Saturated Nickel under Irradiation by Nickel Ions ? S. Ya. Lebedev,
S. D. Panin, and S. I. Rudnev
545
426
Scintillating Plastics with Improved Radiation Resistance ? V. M. Gorbachev,
V. V. Kuzyanov, Z. I. Peshkova, E. A. Rostovtseva, and N. A. Uvarov
547
427
Selecting the Operating Point in Resource Tests of Thermionic Converters
? V. I. Berzhatyi, A. S. Karnaukhov, and V. V. Sinyavskii
550
429
Neutron Resonances in 18lTa at 2-70 eV ? T. S. Belanova, A. G. Kolesov,
V. A. Poruchikov, S. M. Kalebin, and V. S. Artamonov
553
430
COMECON NEWS
Collaboration Daybook
555
432
BOOK REVIEWS
E. M. Filippov. Nuclear Geophysics ? Reviewed by J. A. Czubek
557
433
INFORMATION: CONFERENCES AND MEETINGS
Symposium of the International Agency on Atomic Energy Regarding the Choice of Areas
for Nuclear Installations ? N. P. Dergachev
a All-Union Scientific Conference on Shielding against Ionizing Radiations from Nuclear-
559
434
Industrial Installations ? V. P. Mashkovich
562
436
4 Fourth All-Union Conference on the Physics and Technology of High Vacuum
? G. L. Saksaganskii
565
437
BOOK REVIEWS
B. A. Ushakov, V. D. Nikitin, and I. Ya. Emelayanov. Foundations of Thermionic Energy
Conversion ? Reviewed by Yu. I. Skorik
568
439
The Russian press date (podpisano k pechati) of this issue was 5/28/1975.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLE S
OPTIMIZATION OF THE OPERATING CONDITIONS
OF MASS-DIFFUSION CASCADE INSTALLATIONS
V. A. Chuzhinov, N. I. Laguntsov, UDC 621.039.31
B. I. Nikolaev, and G. A. Sulaberidze
In the design and execution of practical cascade installations a calculation of the optimum operating
conditions of the separating devices is extremely vital. A correct choice of conditions enables the number
of such devices in the cascade and the energy capacity of production to be reduced for special external
working conditions.
When solving problems of the type encountered in separation practice, it is desirable in a number of
cases to use the method of mass diffusion; this has the advantages of servicing simplicity, fairly short
times of installation, compactness of apparatus, universality, and speed of operation, i.e., it enables iso-
topes of a variety of elements to be produced in the same apparatus in a very short time [1, 2]. How-
ever, the absence of published data as to methods of optimizing mass-diffusion apparatus, as distinct from
such classical methods of separation as thermal diffusion and distillation [3-8], makes it difficult to create
effective mass-diffusion separators.
This paper is devoted to questions of optimizing mass-diffusion units (columns or pumps) in cas-
cades. Since the creation and operation of practical separating installations involve the expenditure of
considerable material resources and electrical power, optimization of the cascade is best carried out by
reference to a criterion as fully as possible reflecting the economy of the method and the separating pro-
cess.
One such criterion is the net cost of the resultant product. An analytical expression for estimating
the net cost of an isotope mixture enriched with the valuable component may be obtained if we take account
of the main expenses incurred in the production of an isotope in the cascade (for example, one consisting
of mass-diffusion columns).
For simplicity, let us assume that all the columns in the cascade work in the same mode. The form
efficiency of the cascade 77, defined as the ratio of the separating power AUid of an ideal cascade having
specified values of individual flows and concentrations [F and cp in the feed, P and cp in the outgoing ma-
terials (product), and W and cw in the spent materials (waste)1, to the separating power AU of a real
cascade with the same flows and concentrations at the input and outputs, may be expressed in the following
form [4]:
1=
AU id 1
(PD (CA+ WO (cw)?Fa)(cp)1,
AU (//2/4K) lz
(1)
where H2/4K = SU is the specific separating power of the column, H and K are the coefficients of the trans-
fer equation for the column, / z is the total length of all the columns in the cascade, .t (c) = (2c-1) In [c
/(1?c)] is the separating potential.
From Eq. (1) we obtain an expression for the total length of the columns in a real cascade:
/x? (H/4K) [PO (cp)d- (cw) ? Fa) (CAI.
2
(2)
Since mass diffusion relates to irreversible methods of separation, we may consider that the energy
required by the cascade and the amount of cooling liquid employed are proportional to the length of the
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 363-366, June, 1975. Original article
submitted July 1, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
469
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2
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0 2 4 6 6 6
Fig. 1. Net cost and cost compo-
nents as functions of the vapor flow.
cascade. Using aK to denote the cost of unit length of the column,
we may write the capital expenditure 37K required for creating
the cascade in the form
YK = aK/I
(3)
If To is the period of service of the cascade, determined in ac-
cordance with established norms, while t is the time of operation
required to obtain a specified amount of product, the part of the
cost of the cascade which is transferable to the cost of the iso-
tope (amortization deductions) will be
Ya = aazt/To.
Since the power consumed by the cascade installation is
proportional to the total flow of vapor, its magnitude may be
defined as
Q
(4)
(5)
where q is the flow of vapor associated with unit length of the cascade, b is the energy consumed in creat-
ing unit vapor flow.
The specific flow of the vapor q may be expressed in terms of the working parameters of the column:
q = 22-cr2u = 2lEnDi0cr? (6)
Here r2 is the radius of the inner condenser of the column, u is the density of the vapor flow at the con-
densing surface, n is the molar density, Dio is the diffusion coefficient of the separated gas in the vapor
of the working liquid, a = ur2/nD to is a dimensionless parameter of the column, an analog of the Peclet dif-
fusion number.
Hence the energy needed in order to obtain a specified quantity of the isotope is
E 2abnD10oth,
and its cost may be written in the following form
YE 2atztEDioat/E,
where aE = baoE
(ace is the distribution cost of the unit of energy).
(7)
( 8)
In an analogous manner, for estimating the expenditure on cooling liquid we obtain the expression
yb= 2na6nD10ut/E, (9)
where ab is a coefficient allowing for the coolant expenses associated with unit flow of the vapor q.
Apart from these components, the net cost of the isotope must include the expenditure on the raw ma-
terial required to produce the specified amount of isotope yF = aF Ft, the expenditure of the wages of the
servicing personnel ywg awgt, and also the expenditure on repairing the cascade installation. The coeffi-
cients aF and awg represent the distribution cost of one unit of raw material and the wages per unit time
respectively. The cost of the capital and preventive repairs of the separating apparatus we define as a
part of the capital outlay; we allow for these in the expression for the net cost of the product by means of
a coefficient ki. The value of k1 depends on the complexity and specific characteristics of the apparatus
employed and is chosen on the basis of experience in the use of analogous installations.
Thus the expression for estimating the total cost of the product being manufactured (the isotope)
assumes the form
Y? [PO (C p) W (C ? (CF)1 [ (1?ki)
(H2/4K) 2anD jog abdaEFt-:- awg t.
To
(10)
Let us consider various possible cases of the use of this function.
If in a natural isotope mixture only one isotope is valuable, then, allowing for the balance equation
relating to the whole cascade
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P+W=P;
PCp+WCW=FCF>
we obtain the following expression for the net cost of the isotope from Eq. (10):
1 To
SPr (H2/4K) L F k Pim Cp?Cp oic wi Cp?Cwoic ir aR(1-1-ki)
cp?cw k CI??CW +231nDioa (aE-1-abd
Pt _1 L
aF CP?CW'
-
Cp?Cw P
For a specified geometry of the column the specific separating capacity 6U = H2/4K is determined
by the dimensionless flow of vapor y and by the circulation, the maximum value of which is in turn pro-
portional to u. Since the separating capacity (for a fixed flow of vapor) increases monotonically with in-
creasing circulation, tending toward a limiting value 61Jiirn, it is desirable to establish the value of the
circulation for which 6U is close to SUlim. Then the choice of operating conditions for the columns in the
cascade will be determined simply by the vapor flow.
Since the capital outlay is proportional to 1/SU and the power required to the quantity cr/oU, it follows
from Eq. (11) that the energy and apparatus optima for a cascade of mass-diffusion columns do not coin-
cide. Hence the operating conditions of the columns in the cascade have to be chosen in such a way that the
net cost of the resultant produce may be a minimum.
It is also useful to use the net-cost function (11) in order to optimize the cascade with respect to the
dimensions of the stripping section. For this purpose it is sufficient to find the minimum of Spr with
respect to the value of cw. In the particular case in which the net cost of the raw material is small, or
when the product obtained in the spent materials may be realized at the original (supply) price, there is no
need to consider the spent-materials section, and the expression for the net cost may be written in the
form:
where
s(I)(cp, cp) I_ aK (1 ?ki)
+271nDIOG (aE-Hab) _I+
Pr (H2/4K) To
cp) ?2cP)
(r)(c. cp)=-- (2c ? 1) ln c?c ?42c')
=
(12)
(13)
Also of interest is the case in which both isotopes of the separated mixtures are valuable. Then in
addition to the value of Cp we must specify the required concentration of the second isotope 1?cw, which
is enriched at the other end of the cascade. We may consider that the expenses incurred in producing each
isotope are proportional to the total length of the columns of the particular section in which the isotope
under consideration is enriched:
= yp YIV,
Yp (cp,
Yw Wcp(cw, co
(14)
(15)
where Yp and Yw are the expenses associated with the creation and exploitation of the enriched and spent
(waste) sections of the cascade respectively. The net cost of each isotope will in this case be determined
by an expression analogous to Eq. (12):
P4) (cp, Cp) Cp?Cw
SP P
Pr pt (11.214K)1 (cp, co +MD cr) {[(13 (c2')+ cc cc ?Fir ?1)(c"') cp?CW (1)(cF)..1
X [ To io E b
--L23-EnD 0 (a -} a d + cr?Civ 1-- --
2-iga (16)
CF?CW P
S"?
Pr ?
Cp?CW (Dm
WCD(Cw, CF) f r c,? (D(c.o+ W (CIV) Cp?CF
YW
Wt (H214K)ii PO (cp, +WO (cw, co I Cp?Cp
ab) + F cp?cp w
[ a (aE? a cr?cw+ a wg
al (1+ ki) 2anDio
_ T
(17)
By repeating the discussions outlined above we may obtain a function for the net cost of the isotopes
concentrated in a cascade of mass-diffusion (Hertz) pumps. In this case, in order to estimate the total
net cost of the product, we must replace the separating power H2/4K in Eq. (10) by the separating power
of the pump 61JH expressed in terms of its working and geometrical parameters [9,10]. The term allow-
ing for the energy expenses also changes slightly. For a cascade of mase-diffusion pumps with specified
geometry and working conditions Eq. (10) takes the form
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I [ )] ;, +ki) z
Y? t [Pao (cp) 4- O (civ) ? (4 a
)] nD
au 01 W T I e In q. 1 ?On
? a FFt awgt. (18)
Here Z is the area of the porous diaphragm, /e is the effective _diffusion length [10], lnq = u/e/nDio is the
Peclet diffusion number, en is the partition coefficient of the vapor flow, a'E k ak, an' are coefficients
allowing for the corresponding expenses. From Eq. (18) we may easily obtain the net-cost function for
various cases of transferring the total expenses to the isotopes produced.
Figure 1 shows the net cost of 99% I3CH4 calculated from Eq. (12) and also the components allowing
for the capital (SE) and energy (SE) expenditure on the creation and exploitation of the installation as func-
tions of the quantity a. The data required for the calculation were obtained during laboratory research into
mass-diffusion columns carried out earlier [1]. The values of SE, SE, and Spr are given in relative units.
The terms of Eq. (12) allowing for the wages of the servicing personnel and the cost of the original ma-
terials are omitted, since these have no effect on the appearance of the curves. We see from Fig. 1 that,
as a result of the noncoincidence of the optimal energy and capital outlays, the value of a corresponding
to the minimum net cost is smaller than the value of a corresponding to the maximum separating power
of the column.
By using the method proposed we may generalize the resultant net-cost function to other methods of
separation (thermal diffusion, gas diffusion, and so on). It is clear that in every specific case the optimiza-
tion parameters are to be chosen with due regard for the special features of the separating method and the
separating devices. The results may be used in designing mass-diffusion separating installations and also
when comparing the efficiency of methods used for separating various isotopes.
The authors wish to thank G. A. Tevzadze for discussing the work and also for valuable comments.
LITERATURE. CITED
1. B. I. Nikolaev et al., At. Energ., 23, No. 1, 62 (1967).
2. B. I. Nikolaev et al., Isotopenpraxis, 6, No. 11, 417 (1970).
3. K. Jones and W. Ferry, Separation of Isotopes by Thermal Diffusion [Russian translation], IL, Mos-
cow (1947).
4. A. M. Rozen, Theory of Isotope Separation in Columns [in Russian], Atomizdat, Moscow (1960).
5. G. D. Rabinovich, R. Ya. Gurevich, and G. I. Bobrova, Thermal Diffusion Separation of Liquid Mix-
tures [in Russian], Nauka i Tekhnika, Minsk (1971).
6. W. Rutherford et al., Rev. Sci. Instrum., 39, No. 1, 94 (1968).
7. M. P. Malkov et al., in: Transactions of the Second Geneva Conference, Vol. 10 [in Russian], Atom-
izdat Moscow (1969), p. 54.
8. Ya. D. Zel'venskii, A. A. Raitman, and A. P. Timashev, Khim. Prom., No. 7, 538 (1973).
9. G. F. Barvikh and R. Ya. Kucherov, in: Transactions of the All-Union Scientific-Technical Con-
ference on the Use of Radioactive and Stable Isotopes in the National Economy [in Russian], Izd.
AN SSSR, Moscow (1958), p. 120.
10. I. G. Gverdtsiteli, R. Ya. Kucherov, and V. K. Tskhakaya, in: Transactions of the Second Geneva
Conference, Vol. 10 [in Russian], Atomizdat, Moscow (1969), p. 69.
472
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MATHEMATICAL SIMULATION OF THE EXTRACTIVE
REPROCESSING OF NUCLEAR FUEL
3. REDOX REEXTRACTION USING IRON SALTS*
A. M. R9zen, M. Ya. Zel'venskii, UDC 621.039.59.001.57
and I. V. Shilin
Processes of separative reextraction play an important part in radiochemical technology; they are
used to separate plutonium and neptunium from each other and from uranium. However, the mathematical
extraction model developed in earlier treatments [1-4] is insufficient for describing these processes, since
it takes no account of the kinetics of redox reactions.
The aim of the present investigation was to develop a mathematical model and a computing algorithm
for the redox reextraction of neptunium and plutonium with due allowance for the kinetics of the chemical
reactions in the aqueous phase, and also to analyze the influence of the basic parameters of the process
on its efficiency, leading to a rational choice of the optimum conditions of operation. As redox reagent
we took the Fe2??Fe3+ system, for which a relatively large number of kinetic data have been published;
however, the algorithm developed in this connection is of a general character, and may be used for pro-
cesses involving other nonextracted redox reagents.
Kinetics of the Reduction of Plutonium and
Oxidation of Neptunium by Iron Salts
The reduction of plutonium (IV) by iron (II) proceeds in accordance with the reaction Pu4+ + Fe2+
Pu3+ + Fe3+, while the oxidation of neptunium (IV) by iron (III) obeys NO+ + Fe3+ + 2H20 Np04- + Fe2+
+ 4H+.
The kinetic equations of these reactions are
*Parts land 2, see At. Energ., 37, No. 3 (1974).
2
iilles
Reducing agent
Up MO." Pa Np
? NO, 4
2175-EET?zisg gent
Fig. 1. Arrangement of reextraction unit; 1) Flow of
original organic solution; 2) flow of extraction agent;
3) aqueous flow from the first extractor; 4) flow of
reextraction agent in the first and second extractors;
5) extract from the first extractor (also forming the
original solution for the second) and from the second
extractor; 6) reextract from the second extractor.
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 367-371, June, 1975. Original article sub-
mitted July 18, 1974; revision submitted January 3, 1975.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
473
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Losses of Np, Pu, %; U, g/liter
3 4 6 7
10-9 I t I I
45 qit 0,3
41 1,0 49 48 47 46
nnomin0 131 45
42 45 44 XHN
Fig. 2 Fig. 3
Fig. 2. Loss of valuable components (Pu and Np,% of the original content) as a function
of the ratio of the flows nnom/ n = L/Lnom for XHNO3 = 0.1M: 1)-4) losses of plutonium
from the organic phase of the first reextractor; 5)-8) losses of neptunium from the or-
ganic phases of the second reextractor; 9) losses of neptunium from the aqueous phase of
the first reextractor; 10) losses of plutonium from the organic phase of the first_reextrac-
tor for the ideal-displacement situation; 11)-14) losses of uranium from the aqueous
phase of the second reextractor. (The figures oncurves 1-10 give the contact time in the
mixing and settling chambers of the stage in min; those of 11-14 give the number of stages
in the uranium preextraction section.)
Fig. 3. Dependence of the neptunium and plutonium losses on the acidity of the reextrac-
tion agent: 1)-6) losses of neptunium from the aqueous phase of the first reextractor; 7)-
11) losses of plutonium from the organic phase of the first reextractor; 12-16) losses of
neptunium from the organic phase of the second reextractor. (Numbers on the curves
indicate the values of L/Lnom = nnomAL)
(Pu (III)] = I42 [Pu (IV)] ?k [Pu
at
d [Np (V)] --= ki?IP [Np (IV)] ? kn.[Np (V)].
at
By approximating the experimental data of [5-9] we obtain equations for the constants
icpu _ 1620 [Fe (II)] kpu kr' [Fe MIA
(1+2.0 [Nail) [H+1 ' 2 600 [11+1 '
= exp ( ? 0.36811 + 0.345) [Fe (III)]/[1113;
14113-= exp (0.506R+ 3.1) [Fe (II)] [11],
(3)
where ? = 3 [UO2 (NO3)2] + [HNO3] is the ionic strength; [NOn = 2 [UO2 (NO3)2] + [HNO3] is the concentration
of nitrate ions.
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Losses of Pu ? 102,%
477-
4,6-
2
1 2 3
Tset, min 0 2 4 6 8 /0 /2 14 Nre
Fig. 4 Fig. 5
Fig. 4. Influence of the time of contact in the settling chamber on the losses
of plutonium from the organic phase of the first reextractor (L/Lnom = 0.8;
XHNO = 0.2 M): 1) for ordinarymixer?settlers, Tmix = 1.5 min; 2) for
centrifugal extractors Tmix = 0.2 min.
Fig. 5. Dependence of the plutonium and neptunium losses on the number
of stages in the reextraction section of the first extractor (L/Lnom = 0.8;
XHNO3 = 0.2M): 1),2) neptunium and plutonium losses for a constant total
time of contact in the extractor Nre Tmix = 15 min and Tmix: reet = 1:2; 3)
plutonium losses on adding stages with a standard contact time (Tmix = 1.5
min, Tset
= 3.0 min).
Mathematical Description of the Process in Each
Stage, and Algorithm for Calculating the Distribution
of the Microcomponents with respect to the Various
Stages of the Extraction Apparatus under Steady-State
Conditions
We shall assume that the reextraction process does not amount to a slow chemical reaction, and that
its velocity, determined by mass-transfer processes, is fairly high; owing to the smallness of their dis-
tribution coefficients, the extractability of Pu(III) and Np(V) may be neglected. We shall consider that the
distribution coefficients of Pu(IV) and Np(IV) as microcomponents do not depend on their own concentration
but are determined by the concentration of uranium and nitric acid in the aqueous phase.
The mathematical description of the process at the i-th stage comprises the equations of material
balance (allowing for the structure of the flows) (a), the equations of extractive equilibrium (b), and the
kinetic equations of the redox reactions in the aqueous phase (c). The equations describing the process
are exactly the same for both plutonium and neptunium (the only difference lies in the numerical values of
the kinetic constants and the distribution coefficients) and take the following form:
for the mixing chamber of the stage
a) x5, i-i+ x5, i-t+ nYi+1
b)
c)
for the settling chamber of the stage
Xs, i- ?ns, i- =0;
? - ?
1/4, i = CCiX4, i;
dxs,
jX4, - I? k2, 1X5,
dt
a) xy, f + X- 5, f X4, f X5, =0;
b) ;4, i==U4,i;
dx5,
c) dt ?k1, x4, 1?k2,
(4)
(5)
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0,4
-NO3
a
Np
0 o Pc' 1 i
2 4 6 8 10 12 2 4 6 8 10 12
Number of stage Number of stage
Fig. 6
2 4 6 8 10 12
Number of stage
Fig. 7
2 4 6 8 10 12 14
Number of stage
Fig. 6. Distribution of the components with respect to the stages of the first extractor in the aque-
ous and organic phases (a and b respectively).
Fig. 7. Distribution of the components with respect to the stages of the second extractor in the
aqueous and organic phases (a and b respectively).
where n is the ratio of the flows of the organic and aqueous phases, a is the distribution coefficient of
Pu(IV) or Np(IV), x4 is the concentration of Pu(IV) or Np(IV), x5 is that of Pu(III) or Np(V) in the aqueous
phase, y4 is the concentration of Pu(IV) or Np(IV) in the organic phase. The index i means that the quantity
relates to the yield in the i-th stage; intermediate values (at the outlet of the mixing chamber) are denoted
by a stroke over the symbol.
The system (4), (5) reduces to a matrix equation describing the step as a whole:
44, 1+1
X5, i
1
A2/nct1A9 ? A4 ? 1)/nA9
(Aso + (1?A8)A6A2/A 9)/ai 0 44 (A8 ? 1)/(A6 ? 1)
(A7 -I- A8A6A 2/A9)/Cti 0 ,48A4/A9
X4,
X5,
SI
y4, i
r,,t
X5, i-i
(6)
_
Here A7 =k7, i +k21; A2 =1 + ain; A3 = ki,i/A2 +k2,1; A4 = e-A3Tmix and A5 = e -A1Tset for the ideal dis-
placement situation; A4 = (1 + A3Tmix)-1 and A5 = (1 4- AlTsetr I for the ideal mixing situation; A6 = kl,t
(1 ?A4)/(k1, t + k2, jA2); A7 = ki, i (1?A5)/Ai; Ag = (k2, jA5 + ki,i)/Ai; A9 = 1?A6; A10 = 1?A7, where Tmix
and Tset are the times spent by the aqueous phase in the mixing and settling chambers of the stage.
For the whole extractor the expression analogous to (6) is
0
24, Out
X5, out
SNSN-i ? ? ?
Yinno
ne
0
0
?SN.
o o
ne
0 1 0
0 0 1
Sly, ? . . Si
Y4, Mt
0
0
(7)
where ne and nre are the ratios of the flows in the extraction and reextraction sections of the apparatus,
no is the ratio of the flow of the reprocessed organic solution to the flow of the aqueous phase, NI is the
number of stages in the whole extractor, with due allowance for the fictitious stage of feeding in the solu-
tion to be reprocessed, which has the number NI + 1.
In shortened form Eq. (7) appears thus:
whence
476
0
x4, out
X5, out
?Q-FR
qt
42
43
Tit
r21
r23
out
r2irsi
Y out= r11x4, out =42? qi x5, out = q3
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(8)
(9)
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Thus the algorithm for calculating the distribution of neptunium and plutonium over the various stages
of the apparatus consists of the following; 1) calculation of the distribution of the macrocomponents, namely,
uranium and nitric acid (for the methods of calculation see [4], which also gives the equilibrium equations);
2) calculation of the kinetic constants of the reactions by means of Eq. (5) and of the distribution coeffi-
cients (see [4]) at each stage; 3) construction of the matrices Si in accordance with Eq. (6); 4) determination
of the matrix R and the column Q in accordance with Eqs. (7) and (8); 5) calculation of the neptunium and
plutonium concentrations in the flows of the aqueous and organic phases emerging from the extractor by
means of Eq. (9); 6) successive calculation of the neptunium and plutonium concentrations in the two phases
at each stage by means of Eq. (6), using the already prepared matrices Si.
Calculations of the Redox Reextraction Process
Using the Minsk-32 computer we calculated a reextraction system consisting of two extractors
(Fig. 1); the reduction and reextraction of plutonium took place in the first extractor, and the oxidation and
reextraction of neptunium in the second. The aim of the calculations was to study the influence of the ratio
of the flows, the acidity of the aqueous phase, the number of stages, and the time spent in the mixing and
settling chambers on the extraction of the valuable components. We also determined the range of condi-
tions for both extractors in which the losses of uranium, plutonium, and neptunium were lowest.
For the first extractor we took no = 8.0; re 1.5; "re = no + ne = 9.5 as nominal conditions. The
original organic solution contained 0.38 M uranium and 0.17 M HNO3. The concentration of plutonium and
neptunium in this solution was taken as unity. Into the preextraction section we fed a 30% solution of tri-
butylphosphate (TBP) in synthine; reextraction was effected with 0.1 M HNO3 containing 0.04 g-ion/liter
Fe(H) with an admixture of 10% Fe(III) (produced by self-oxidation). Into the second reextractor we fed
the organic flow from the first reextractor (at 80% of the nominal rating in the latter according to the ratio
of the flows), containing 0.32 M uranium, 0.0333 M HNO3, 0.83444 arbitrary units of Np, and 1.7 .10-4
arbitrary units of Pu. The nominal ratios of the flows were no = 11.875; ne = 1.125; nre = 13.0 The re-
extracting 0.1 M HNO3 contained 0.04 g-ion/liter Fe(III).
The ratio of the flows in the two reextractors was varied by varying the flow of the aqueous phase
L[n
nnomAL/Lnom)].
We see from Fig. 2 that an increase in the ratio of the flow increases the losses of the components
from the organic phase (plutonium in the first extractor, neptunium in the second), but reduces the losses
from the aqueous phase (neptunium in the first and uranium in the second). Whereas in the first reextrac-
tor the uranium concentration in the reextract is no greater than 1.5 mg/liter for any of the operating
conditions calculated, in the second reextractor a three-stage preextraction section fails to provide an
acceptable (10 mg/liter) degree of purity of the reextract with respect to uranium (Fig. 2, curve 11), and
the number of stages must be increased from four to six (Fig. 2, curves 12-14).
Increasing the acidity of the reextraction agent increases the losses of the components from the
aqueous phase (Fig. 3); hence it is desirable to conduct the whole process at a low acidity.
The time spent in the stage has a substantial influence on the losses of neptunium and plutonium
(Fig. 2), and due allowance for the kinetics of the redox reactions must therefore never be neglected. This
may at first glance appear paradoxical, since the velocity constants are high and the relaxation time of the
process (to = 1/k) should be short (for example, in the case of XHNO3 = 1 M and [Fe(II)] = 0.04 g-ion/liter;
= 16.2 min-I and to = 1/kPu = 0.06 min, while Tmix = 1.5 min,i.e., 25 times greater than to). How-
ever, one characteristic of the process in the two-phase system is a transition of the plutonium (neptunium)
to a state of reduction (oxidation) on passing into the aqueous phase from the organic phase, in accordance
with its distribution coefficient; the velocity constant then falls by a factor of (1 + an), while the relaxation
time correspondingly increases. This leads to a considerable retardation of the redox processes in the
extractive stage by comparison with the same process in the aqueous phase.
The calculations also showed that, despite the occurrence of redox reactions in the mixing and
settling chambers, the role of the latter was insignificant owing to the absence of mass transfer in these
chambers even for small values of Tmix (Fig. 4).
Influence of the Number of Stages. We found (Fig. 5, curves 1 and 2) that for a constant total time
of contact in the apparatus (NreTmix = const) it was advantageous to have more stages with a shorter con-
tact time in each. Increasing the number of reextraction stages while preserving their standard dimensions
naturally reduces the losses of the components (curve 3).
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Structure of the Flows. A comparison between the results of calculations relating to the operating
conditions of the process for the case of ideal displacement and ideal mixing (Fig. 2, curves 2 and 10) once
again [2] indicates the considerable advantage of using piston-type flow rather than ideal mixing.
The range of acceptable operating conditions is determined by the completeness of the plutonium,
neptunium, and uranium separation required. Since many parameters of the process act in contradictory
ways on the losses of these components, this range is comparatively narrow. For the first reextractor the
best arrangement is that corresponding to 80% nominal (flow ratios no = 10.0; ne = 1.875; "re = 11.875)
with a reextraction-agent acidity of no greater than 0.2 M. Under these conditions the plutonium losses
are no greater than 0.05%, and the neptunium losses no greater than 1%. A shift in the direction of lower
values of n leads to an increase in the losses of neptunium with the aqueous phase, while higher values of
n lead to an increase in the losses of plutonium with the organic flow passing into the second reextractor.
(The distribution of the components with respect to the stages in this condition is indicated in 'Fi6.) In
order to widen the range of acceptable conditions it is essential to enlarge the reextraction section of the
apparatus.
The second reextractor should have at least four stages in the uranium preextraction section, the
best working condition being that corresponding to 60% nominal (ratios of the flows no = 19.8; ne = 1.87;
nre = 21.7). For an XHNO3 no greater than 0.5 M the neptunium losses then fall below 1.10-3% and the
amount of uranium in the reextract is no greater than 10 mg/liter. (The distribution of the components
with respect to the stages in this situation is indicated in Fig. 7.) Increasing the preextraction section to
six stages leads to a considerable expansion of the range of acceptable conditions, which is then only
restricted by upper limits of no = 30.0 and ne = 2.8; the losses of neptunium are no greater than 5.104%.
We note that the ratios of the flows corresponding to the nominal operating mode of the first re-
extractor (as well as values lower than these), together with a reextraction-agent acidity of no greater than
0.2 M, ensure an almost complete transition of the neptunium and plutonium into the aqueous phase in one
extractor (the amount of uranium in this section will then lie below -1 mg/liter). Thus depending on the
technological requirements either individual or combined separation of Pu and-Np from U may be achieved.
Influence of Temperature. Since the activation energies for the reduction of plutonium and oxidation
of neptunium (19.7 and 35.2 kcal/mole respectively [7]) are comparatively high, the velocity constants
increase sharply with temperature, i.e., increasing the temperature reduces the losses of plutonium and
neptunium, or alternatively reduces the contact-time (calculation shows, for example, that on conducting
the process in centrifugal extractors, in which Tmix = 5-10 sec, to should be raised to - 40?C).
LITERATURE CITED
1. A. M. Rozen et al., Third Geneva Conference, Paper No. 346 (1964).
2. A. M. Rozen et al., in: Liquid Extraction [in Russian], Khimiya, Leningrad (1969), p. 5.
3. A. M. Rozen, Yu. V. Reshet'ko, and M. Ya. Zelivenskii, in: Transactions of the Comecon Symposium
on Research in the Reprocessing of Irradiated Fuel, Vol. 1 [in Russian], Czechoslovakian Atomic
Energy Commission, Prague (1972), p. 118.
4. A. M. Rozen, Yu. V. Reshettko, and M. Ya. Zellvenskii, At. Energ., 37, No. 3, 187 (1974).
5. T. Newton et al., J. Phys. Chem., 64, 244 (1960).
6. J. Huizenga and L. Magnusson, J. Amer. Chem. Soc., 73, 3902 (1951).
7. V. S. Koltunov, Kinetics of Redox Reactions of Uranium, Neptunium, and Plutonium in Aqueous
Solution [in Russian], Atomizdat, Moscow (1965).
8. G. Best, J. Inorg. and NucL Chem., 12, 136 (1959).
9. M. Germain, ibid., 32, 245 (1970).
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TWO-DIMENSIONAL DIFFUSION PROGRAM
HEXAGA II FOR MANY-GROUP CALCULATIONS
OF HEXAGONAL LATTICES
T. Apostolov and Z. Woznicki UDC 621.039.51
The HEXAGA II program uses a uniform triangular difference mesh employed for the calcula-
tions for various reactors of basically the water-moderated water-cooled type. The programiswritten
in FORTRAN IV for the systems SYBER-70 and EC-1040. HEXAGA II enables one to solve diffusion equa-
tions in the approximation from two to ten groups with allowance for diffusion of neutrons from high to low
energy groups. Neutron scattering accompanied by an increase of energy is taken into account when the
model is usedwith two or more thermal groups. The first variant of the program calculated the neutron
fluxes at 5000 points of the reactor lattice, and for the subsequent variants this number increases to 10,000
and more.
The many-grouped model of neutron diffusion is a search for a solution of the system of adjoint
elliptic second-order partial differential equations
? div [Dg grad Og] Egavg ? 2 zg'-gog' Fe-gog', g=1, 2, ..
g'=1
gr*g
(all the notation in (1) is standard and given in [1]).
The extraction cross section for the given group, Eg, is represented by the equation
Eg = 15 ? 2
g'*g
Equation (1) is augmented by the boundary conditions on the surface of the reactor:
Dg acag czg0g =0
On
(the derivative is along the outer normal to the boundary of the region).
Equations (1) and (2) are solved by the source-iteration method. For the numerical solution of the
problem in the group, one uses a finite-difference approximation in the triangular lattice. Thus, finite-
difference equations are obtained and these can be represented for each group by a system of linear equa-
tions:
(1)
(2)
/10=c,
(3)
where A is a nondegenerate matrix of coefficients; 4. is the required vector of the solution for the given
group; c is the known source vector, whose components take into account the processes of fission and
scattering for the given group. For the solution of such linear systems, factorization iterative methods
have been developed, for example, the method of Buleev [2], OLIPHANT [3, 41, STONE [5,6], DUPONT [7],
and others. In [8], factorization iterative methods called two-pass iteration methods were developed.
The essence of such a method, used in the HEXAGA II program to solve a system of linear equa-
tions [2], is as follows.
Institute of Nuclear Research and Nuclear Energy, Sofia, Bulgaria. Institute of Nuclear Research,
Swierk, Poland. Translated from Atomnaya gnergiya, Vol. 38, No. 6, pp. 372-374, June, 1975. Original
article submitted February 28, 1974; revision submitted November 12, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
479
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
AVAM &VA\
IVA EWA
AV1YAYAYAWA\
I I
#AVAVAVAWAA
YAYAWAYMMAY
V VA I IA WAY/
//AWN
A kVA IlrAv
vox/ I FAVA r
V
WA I
AV L'M YA1
A A WA1 MVA
VA 1 I MVAI
* Avean
NA %VA I I IN
V vNAWA IAT
VIVA I MVO!
WAVAV/
V
Fig. 1. Dtfferent arrangements of the hexagonal lattice relative to the central axis of
the reactor.
We represent the matrix A in the form
A=K?L?U,
where K = diag(kii) 0 is a diagonal matrix in which kii > 0 for all 1 s i s n; L = (1ii) 0 is the lower
triangular matrix in which /ii = 0 for all i s j; U = ?/0 is the upper triangular matrix in which uii = 0
for all i j and
(4)
Mil + Uji )
for all 1 i n, and for at least one i there is a rigorous equation which guarantees nonnegativity of the
matrix A and the existence of A-1 0.
The matrix A can be represented as
A=K?PA?(L+H)?(U+Q)-1-PA+11?Q,
(5)
where P A = diag(pii) 0, in which pH.? 0 for all 1 < i s n; H = (hij) 0 is the lower triangular matrix in
which h?? = 0 for all i 5 j; Q = (qii) ? 0 is the upper triangular matrix in which ? = 0 for all j. ?
ij
Further, one assumes
K >PA >0, ?
where kit > pii > 0 for all 1 s i s n. Then
DA=K?PA?>.0
is a nonnegative diagonal matrix in which DA-1 0 for all 1 i 5 n.
After transformations, we obtain
A=DA.?(L+H)?(U+Q)+PA+11-1-Q-
In what follows, we use the equation
DA? (L H)?(U-FQ)
= [I?(L + H)I:4] DAV ? (U-I-Q)]
?(L- H) (U Q).
The nonnegative matrix (L + H)D7A!(U + Q) can be expressed by the sum
+ H>rrAl + Ri +TA+Hid-Qi,
where R1 = diag [(L + H) D (U + Q)].
If we choose matrices PA, H, and Q such that PA = R1,H =111, and Q = Q1, then
A= M NA,
[I?D-A1(U + Q)] and NA = TA, and
where MA = 1-1?(L + H)D-1
480
Nil >0 andNA >0.
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(6)
(7)
(8)
(9)
(10)
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It is known from Varga's theorem [9] that the iteration matrix
= r A
has spectral radius p(MNA) < 1 and the iterative method
Oh' ? M.74INA4:Di />0
(where j is the number of the iteration) converges for the solution of a system of linear equations for all
vectors
In the practical use of the two-pass iteration methods one uses recursive formulas for some auxiliary
vector p, after whose calculation the vector ,t(J +1) is determined.
In our case the vector 413(J +1) is expressed in the form
= [/?D; (U ())1"--,
x [I ?(L ?H) T AcDo
+11 (U + Q)1-' D7.1' [I? (L +11) D2]-, c.
where j 0.
After multiplication of (12) by the matrix [I?D-11: (U + Q)], we obtain
=DA1 ((ti +0 Oh' ? II) D;i1-1 (T AO(' c)}.
We introduce the vector p(i +1) :
10-o= [I? (L + H) DAT, (TAD" c).
After multiplication of (14) by the matrix [I?(L + H)1)-11, we obtain
10-0= (L li) D0+1) T A4:1)01) c;
_D [(u +0 (Do -I)
(12)
(13)
(14)
(15)
This approach is none other than the elimination method of Gauss and is equivalent in this case to the
sweep method for three-diagonal matrices. To accelerate the convergence, the method of upper relaxation
can be used.
In [8] this method is compared with the Gauss?Seidel method and it is shown that
where L1 is the iteration matrix in the Gauss?Seidel method:
Li? (I ?
(16)
(17)
In the determination of the region of the solution in the program it is borne in mind that the majority
of reactors with hexagonal lattice of the core have angular symmetry (every 120?). Such an approach is
used in reactors of the water-moderated water-cooled type. Figure 1 shows three arrangements of the
hexagonal lattice relative to the central axis of the reactor. The neutron fluxes at arbitrary but symmetric
points in the regions I, II, and III also have the same values. Thus, to describe the lattice one need consider
only one of the regions and it is not necessary to determine the logarithmic boundary conditions on the axes X
and V, whose values are obtained from the symmetry condition. It is only necessary to determine the logarithmic
conditions on the boundaries parallel to the X and V axes lying within the core, on its boundary or outside it. One
also considers a variant using logarithmic conditions on four boundaries of the region (Figs. 2 and 3).
In one of the program variants, the regions may have the form of a parallelogram (see Fig. 2; such
a form of the region is used in the program PDQ-7); in others, they can have the form of a hexagon (see
Fig. 3), which simplifies the problem and makes the use of programs convenient.
Besides the described lattice form, one also considers a combined configuration of hexagonal and
oblique-angled polygons, and also a combined configuration of hexagonal lattices and lattices with (r, 0)
geometry. The combination of such lattices enables one to represent more accurately the actual geometry
and the material properties of the reactor lattice. However, the programming of the problem is then
much more complicated.
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0
411411=
410111
S.A=1157#
AI
11116/41/AvirMAI
41FMAvilIrainvIrIr
irAmmirilioritioril
IMMINVIIMAIM
IrffiririONFIRIIMir
IFAIMMAMIDVAII
V
Fig. 2. Regions of the reactor having the
the form of a parallelogram.
ININIAVAIPLWIIVW
MA I FA IMINI IM V
MOMAVIM
011121/4.1FAINNWAVAVIN
NA I IA III !AV/ kVA MAI
0411110 VAVA I MA I VA
1141 I PIM I IP IMAISMI I NW
PA 0110/41 121 VA 112
V
Fig. 3. Hexagonal form of reactor regions.
Two-pass iterative methods were used in the two-dimensional programs EWA II [4,6] and AGA II to
make a calculation for reactors with rectangular lattice on the GIER computer. The results show that the
rate of convergence of these methods is 5-10 times faster than methods based on the Gauss?Seidel com-
putational model.
It is to be expected that the use of two-pass iteration methods of solution of the diffusion equations for
a hexagonal lattice will increase the rate of convergence compared with the case of a rectangular lattice.
However, to confirm this conjecture concrete results are necessary; these are expected very shortly.
It should be pointed out that the number of arithmetic operations for one point in one group and one
iteration when one uses the two-pass method and the method of upper relaxation (of the HEXAGA II pro-
gram) exceeds ten operations of multiplication and ten operations of addition. When the Gauss?Seidel
method is used, there are eight operations of multiplication and eight of addition.
It is assumed that if a two-dimensional program is used for cylindrical and flat (y, z) geometry (30
groups and 4000 points), it will be possible to calculate the group geometric parameters B2z needed for
HEXAGA II. The algorithm EWA II is based on the modified two-pass iteration method. The program is
written in FORTRAN IV for the IBM-360/40 computer.
LITERATURE CITED
1. G. Habettler and M. Martino, in; Proc. Symp. on Appl. Math., Amer. Math. Soc., Providence, Rhode
Island, 11, 127 (1961).
2. N. Buleev, Matem. Sb., 51, 227 (1960).
3. T. Oliphant, Quart. Appl. Math., 20, 257 (1962).
4. T. Oliphant, ibid., 19, 221 (1961).
5. H. Stone, Trans. Amer. Nucl. Soc., 13, 180 (1970).
6. H. Stone, SIAM J. Number. Anal., 5, 530 (1968).
7. T. Dupont, ibid., 753.
8. Z. Woznicki, Doctoral Dissertation, Computing Center CYFRONET, Institute of Nuclear Research,
Swierk (1973).
9. R. Varga, Matrix Iterative Analysis, Prentice Hall (1962).
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INVESTIGATION OF THE ADIABATIC OUTFLOW
OF WATER THROUGH CYLINDRICAL CHANNELS
V. S. Aleshin, Yu. A. Kalaida, UDC 621.039.001.5
and V. V. Fisenko
Partial evaporation of the fluid along the channel length occurs during the outflow of saturated and
underheated water with high initial parameters through a cylindrical channel with pointed entrance edges, and
the stream is two-phasal at the exit from the channel. A large number of papers, including the surveys
[1,2], is devoted to the investigation of the adiabatic flow of saturated water. However, up to now there
have been no reliable methods of estimating the weight discharge for a broad range of initial parameters
and the total picture of the flow of evaporating water in cylindrical channels has been studied inadequately.
This is explained by the complexity of the heat and mass exchange processes between the liquid and vapor
phases flowing in the channel and by the influence of various factors (the initial parameters, the //d ratio,
where / is the channel length and d is its diameter, the counter-pressure at the exit, etc.) on the outflow
processes.
The results of investigating the outflow of hot water through cylindrical channels of 5 and 9.53 mm
diameter with pointed entrance edges and an //d ratio between 0.5 and 18 are examined in this paper as the
pressure PI changes ahead of the outflow channel between 25 and 150 kg/cm2 and the water underheating
Ats is 0-100?C up to saturation.
2 3 4 5
50 100 150 200
P1. kg/cm2
Fig. 1 Fi g. 2
Fig. 1. Schematic diagram of the apparatus: 1) disposal section; 2) valves to
produce counterpressure; 3) probe; 4) outflow valve; 5) quick-shutoff valve; 6)
hot-water chamber; 7) high-pressure air system.
Fig. 2. Dependence of the stream discharge on the initial pressure for different
Ats (d = 5 mm, //d = 0.5): 1) discharge of cold water at t = 18?C; 2) rated dis-
charge of dry saturated vapor; 3) rated discharge of saturated water (x = 0).
Atomnaya Energiya, Vol. 38, No. 6, pp. 375-378, June, 1975. Original article submitted April 30,
1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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pl;t, /////////y/////7///0_
200
197
15 t151 4 ,55
-20 0 20 40 60 80 1,mm 3 9 lid
Fig. 3 Fig. 4
Fig. 3. Change in medium parameters (p and t) along the channel length
for d = 9.53 mm, //d = 9.55, 6ts = 20?C for different initial pressures pi,
kg/cm2: 1) 100; 2) 75; 3) 50; 4) 25.
Fig. 4. Change in parameters of the medium (p and t) along the channel
length for pi = 75 kg/cm2,Lt = 20?C, d = 9.53 mm for different //d:
1) //d = 9.55; 2) //d = 6; 3) lid =3; 4) //d = 0.5.
270
260
231
195
\
4,t, \
v////////// ///////////
////%
The experimental apparatus (Fig. 1) consists of a 350 liter (hot water) chamber to obtain hot water
at pressures to 150 kg/cm2 and a temperature to 350?C; an outflow section of telescope type, which permits
altering the working channel without disassembly of the apparatus; a tank for disposal of-the-outflowing
medium through a throttling unit under a layer of water; a high-pressure air system to maintain a given pressure
ahead of the outflow section and to assure its constancy during the outflow process.
The hot water chamber was filled with water purified in special filters, and the water was deaerated
before each test. The cold water hydraulic characteristics were recorded for each of the channels before
the tests.
The error in measuring the temperature and pressure in the hot water chamber, at the entrance to
the outflow channel, and at its exit was no higher than ?5%.
The stream static pressure and temperature along the outflow channel length were measured by
using a probe. The impulse hole to determine the pressure and the microthermocbuple imbedded in the
probe permitted a record of both the continuous diagram along the channel length, and the parameters at
fixed points.
The discharge of the outflowing medium was measured with a flowmeter with a continuous recorder
tape, which is important in investigations of the critical flow modes.
Weight Discharge of Water. To determine the influence of the initial pressure pi, the degree of
underheating of the water below boiling Ms, and the //d ratio on the weight discharge characteristics, a
series of tests was conducted in which only one of the factors listed above was altered while the other
conditions remained equal. Presented in Fig. 2 is a graph of the dependence of the ratio between the weight
discharge and the channel cross-sectional area on the pressure ahead of the entrance to the outflow sec-
tion for a channel with //d = 0.5 (the dashes show the assumed weight discharge at an initial pressure above
150 kg/cm2). It follows from Fig. 2 that the experimental discharge characteristics almost agree with the
hydraulic characteristics up to a 70-75 kg/cm2 pressure for any degree of underheating. The vapor for-
mation in the stream becomes so intense at pressures above 75 kg/cm2 and a 0-50?C degree of underheat-
ing that the presence of the vapor phase noticeably diminishes the stream density and reduces the weight
discharge.
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80
70
60
50
449
30
20
10
20 40 60 80 100
Pep. kg/cm2
Fig. 5
Fig. 5. Dependence of grel and p2 on the
= 7.26, Ate = 20?C and different pi, kg/cm2; 1) 100; 2) 75; 3) 50; 4) 25.
Fig. 6. Dependence of e = p2/pi on //d, Ate, and pi.
I 1t s0
s
451
444
1
8
42 90
100
41
46
At 0
45
??,
b
60
70
4
180
90
4
qv
It iiti t 'III
2 4 6 8 150 125 100 80 60
Lid p, kg/cm2
Fig. 6
counterpressure pep for d = 6.4 mm, //d
20
Analogous graphs have been obtained for weight discharges for other //dratios(0.5; 2.0; 3.0; 4.0; 5.0;
6.0; 9.0; 18.0). It follows from the graphs that a deviation of the experimental from the hydraulic curves
sets in at a lower pressure as //d increases. Thus, for //d >6-8 the diminution in discharge starts at
pr-=,' 25 kg/cm2 as compared with the hydraulic value.
Pressure and Temperature Distribution. The temperature and pressure along the channel axis were
measured by displacement of a probe. The investigations were carried out in 9.53 mm channels for an
//d between 0.5 and 9.55. More than 100 combined diagrams were obtained. Some are presented in Figs.
3 and 4. Analysis of the test curves shows that three characteristic sections are formed along the channel
length in channels with //d > 6-8. An abrupt pressure drop below the saturation pressure corresponding
to the initial temperature is observed in the first section in the area of the entrance edge, and intensive
vapor formation occurs, whereupon the temperature of the medium drops. A certain lag in the temperature
drop as compared with the pressure reduction as the water moves (particularly for saturated water) indi-
cates its possible overheating and a metastability of the process in progress. Then the velocity of the
stream motion diminishes as the stream broadens beyong the leading edge, the pressure rises and the
process of vapor condensation is observed, as the rise in stream temperature indicates.
The nature of the pressure drop depends on the initial temperature. The higher the stream tem-
perature, the smaller the fraction of the pressure drop at the entrance section and the greater the fraction
at the exit of the channel.
Let us note that the phenomenon of a sharp pressure drop and its subsequent rise at the leading edge
has not been observed in researches performed earlier either because of the low initial parameters
(a pressure less than 25 kg/cm2) or of the absence of a continuous record of the pressure and temperature
along the channel length.
Depending on the initial values of pi and ti, either a recovered hydraulic stream of saturated water
at a temperature corresponding to the initial temperature (for Ate > 20?C) or a two-phase stabilized stream
with a temperature somewhat lower than the initial value (for Ats < 20?C) flows in the second section, the
section of stabilized parameters. As the underheating is reduced, the vapor content increases in the
stream and reaches a maximum at the outflow of the saturated water. The lower the initial water tem-
perature, the closer will the stabilized parameters section be to the exit section. The vapor formation
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process starts again in the third section of the channel as the stream approaches the exit edge; the stream
temperature also drops as the pressure drops. The pressure drops to p2 in the exit section, a value greater
than atmospheric and dependent on the initial parameters. Thus, for example, as pi rises from 25 to 100
kg/cm2 at Ats = 20?C the pressure p2 grows from 14 to 57 kg/cm2, and the pressure ratio a = p2/pi remains
practically constant. A steady, equilibrium two-phase stream for which a r-z1 0.55 flows out of the channel.
As the underheating increases because of the diminution in the vapor phase content in the stream, the
quantity a drops. Thus, for Ats = 59?C, a is reduced to 0.334.
Shown in Fig. 4 is the nature of the change in the stream p and t along the channel length as a function
of //d for saturated water flowing out at an initial pressure of 75 kg/cm2. The nature of the process in
long channels with //d > 6-8 is described above. Diminution in the channel length is accompanied by the
growth in metastability of the stream, by a rise in its density, and by an increase in the weight discharge.
Thus, for //d = 0.5 the stream turns out to be overheated 45?C in the exit section. The pressure at the
exit from the channel drops more sharply in short channels. It is characteristic that there may be a sec-
tion with stabilized parameters even in short channels with //d = 3.0.
It also follows from Fig. 4 that the pressure drop along the channel length is accompanied by an
abrupt reduction in temperature, and therefore, by a continuous vapor formation process.
Investigation of the Critical Modes. A series of tests was conducted in channels of 6.4 mm diameter
with //d = 0.5-7.26 and Ats = 0-100?C to investigate the critical flow modes of boiling water. The initial
pressure varied between 25 and 150 kg/cm2. Processing the test results permitted construction of depen-
dences of the relative discharge grel = gep/go (go is the discharge for a stream outflow into the atmosphere,
and gcp is the discharge at a variable counterpressure pep) and of the pressure p2 at the exit section on
the counterpressure. One of the graphs is presented in Fig. 5. It follows therefrom that the passage over
to the critical mode occurs more smoothly as boiling water flows out, the pressure at the exit edge p2
tends to some constant value for a continuously diminishing counterpressure pep. The time of the onset
of the flow crisis agrees with the time of build-up of a constant pressure in the exit section of the channel
(the beginning of the critical flow mode is shown by dashes). This indicates that the critical channel section
coincides with the exit, and the steady pressure ratio p2/pi is critical.
The dependences 132 = f (pcp) and grel =f (pep) obtained permit establishment of three characteristic
boiling water flow domains in the channel (the domain boundaries are shown for an initial pressure of pi
= 100 kg/cm2).
1. The critical mode domain (A). The weight discharge is a maximum in this domain and is in-
dependent of the counterpressure.
2. The near-critical domain (B). As the counterpressure increases in this domain the pressure in
the exit section rises monotonely, remaining greater than pep. The discharge decreases in-
significantly.
3. The third domain (C) is provisionally called the domain of the pseudohydraulic flow mode. It
sets in at the time the pressure in the exit section equals the counterpressure and is retained
down to total equalization of the pressure (pep = pi). The discharge decreases sharply in this
domain and is zero for pep =
Tests conducted with unchanged pi = 75 kg/cm2 and Ats = 0-100?C showed that the crisis in the dis-
charge sets in atlowercounterpressures as Ats increases, i.e., e =P2/PI diminishes.
Processing the numerous experimental results permits construction of a nomogram (Fig. 6) of the
dependence of a on the initial pressure, the degree of underheating of the water to the saturation state, and
the relative channel length. The dashes show the sequence in determining a for a given //d ratio and initial
Ats and pi.
The following dependences can be recommended to determine the specific weight discharges by
generalizing the test results.
1) For //d > 0, Ats 3.
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000
o)
8 0 8 coo 0
0 0 00 0
0
10 0? 1 0
C60
oPo
6b00
0
I
80
?
0?Q0
1 0
20
401
a
0,02
t, sec
Fi
g.
6
/2 t, sec
240 Z60 280
Energy of ions, MeV
Fig. 7
Fig. 6. Distribution of tracks of fragments of spontaneous fission in the reaction
of 207pb 50Ti: a) time cycle of measurements from 0.003 to 0.03 sec; b) from 1
to 13 sec.
Fig. 7. Integral functions of excitation (a) for the isotopes 131Pm (e) and 2?4111Pb
(C), formed in the reaction 2081T1Pb + --- and ?) results of a calculation
with parameter of diffuseness d = 0.44 -10-13 and d = 0.34 .10-13 cm, respectively
(the value of the remaining parameters are the same as in [12]). Integral functions
of excitation (b) for the spontaneously fissioning emitter with TT 2 "-=1 5 msec: ?)
calculated values of the excitation for the reactions ("Ti, 2n) an ("Ti, 4n) at d
= 0.34 -10-13 Cm.
It was shown earlier [12] that reactions with the emission of two neutrons are very sensitive to the
value of the minimum energy of excitation of the compound nucleus. The transition from 48Ti ions to "Ti
ions, according to our estimates, increases the cross section of 2n-reactions approximately 100-fold. In
view of this, a beam of accelerated "Ti ions was used in the experiments.
Production of Accelerated Titanium Ions
The calculated value of the barrier to interaction in the reaction 238Pb + "Ti is equal to 230-235 MeV
in the laboratory system of coordinates. The maximum energy of the beams of accelerated ions for the
300 cm cyclotron of the Laboratory of Nuclear Research, United Institute of Nuclear Research, is deter-
mined by the ratio Emax = 250 Z1 /AI, and for 50Ti+7 and 50Ti+4 is 245 and 320 MeV, respectively.
For the acceleration of "Ti ions in such a high charge state, we created a special ion source, in
which the enriched isotope "Ti in the form of the metal was used as the starting material.
The intensity of the isolated beam of 50Ti8 ions was 5 -1013-1011 particles/sec, while the intensity
of the internal beam of 50Ti+8 ions was 2 -1011 particles/sec. The energy of Ti+7 ions is only 10-15 MeV
greater than the barrier to interaction; therefore, the isolated beam was used to study the reactions pro-
ceeding with the emission of two neutrons, and the bulk of the experiments was conducted on the internal
beam of the cyclotron.
Experimental Procedure
In experiments with "Ar ions [12] it was shown that when isotopes of lead are used as the target,
there is practically no background associated with the spontaneous fission of side products of the reaction.
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6
- 18
144
148 152 156
Fig. 8
Fig. 8. Systematics of the periods of spontaneous fission
the isotopes 250102, 255104, and 256104.
Fig. 9. Illustrative representation of the barriers to fission for the isotopes Fm, 254102,
and 256KU. (The periods of spontaneous fission are given along the y axis.)
1 year
1 day
1 h
1 sec
1 msec
1 ?sec
1 nsec
160 N /44 152
Fig. 9
considering new data for
150
Therefore, for the synthesis of heavy elements by this method, a highly sensitive rapid method for the
detection of nuclei according to spontaneous fission can be successfully used.
In the experiments we used the distribution of 205Pb isotopes (content 97.8%, impurities 207Pb 1.6%
and 206Pb 0.6%); 207pb (content 83.4%, impurities 208Pb 14.3% and 206Pb 2.3%); 206Pb (content 90.4%, im-
purities 208Pb 6.7% and 207Pb 2.9%)?
The experimental setup for the recording of short-lived spontaneously fissioning nuclei is schemati-
cally presented in Fig. 4. The beam of 50Ti ions drops along a tangent to the surface of a hollow cylinder,
oriented vertically and rotating at a maximum angular velocity of 3000 rpm. By the method of atomiza-
tion, a layer of lead about 2 mg/cm2 thick, simultaneously serving as the target and the collector of recoil
nuclei, was applied on the side surface of the cylinder. As a result of the fact that the beam is incident at
a small angle to the surface of the cylinder, the layer of lead is an "infinitely" thick target, in which there
is an integration of the function of excitation from Bint to Emax.
The maximum energy of the internal beam of 50Ti ions was selected equal to 260 MeV (see the excita-
tion function in Fig. 3). The intensity and position of the beam of ions were monitored during the experi-
ment with a special device, situated outside the target. The integral flux of ions that passed through the
target was determined by an activation method according to the yield of the isotope 117In (T112 = 2.8 days),
formed in the bombardment of copper with titanium ions; for these purposes, a copper target ? 15? thick
with an area of 1 cm2 (-1% of the total area of the lead target) was situated on the side surface of the
cylinder.
Track detectors of spontaneous fission fragments of mica with a content of uranium and thorium
impurities < 10-7 g/g were positioned around the rotating target at a distance of 2 mm. Despite the fact
that the energy of the recoil is comparatively great (? 50 MeV) and corresponds to a range in lead of ? 6
mg/cm2, in view of the small angle of entrance into the target these nuclei are situated close to the sur-
face of the layer, and the efficiency of the recording of spontaneous fission fragments is about 50%.
Shields protecting the detectors from scattered ions and forced fission fragments, as well as the
special method of treatment of the detectors, entirely eliminated the background at a distance of only ?2
cm from the site of incidence of the beam.
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This method was tested in experiments [12] on the production of the isotopes 244Fm in the reaction
206, 207, 208pb (40 ? -, dA
xn)2?Fm, where it was shown that it can be successfully used for recording short-lived
spontaneously fissioning emitters, if their lifetime is greater than 3 msec and the cross section of their
formation exceeds 10-35 cm2.
Synthesis of the Isotopes 256Ku and255Ku
The isotope 258Ku can be obtained in the reaction 208Pb(50Ti, 2n). From the systematics of the proper-
ties (see Fig. 1) it follows that the lifetime of this isotope with respect to a decay ranges from 50 to 200
msec, whereas the partial period of relatively spontaneous fission is substantially greater on account of
?the stabilizing action of the subshell N = 152. Therefore, in the reaction of 206Pb + 56Ti, we can count on the
recording of spontaneous fission of the isotope 252102 (T112 c=.: 2 sec, 30% spontaneous fission), which is
formed in the a decay of the 256KU nuclei.
In the first experiment the rate of rotation of the cylinder was selected equal to 8 rpm, which per-
mitted recording of the spontaneous fission with T112 > 0.5 sec. In the case of irradiation of 20813b with an
integral flux of 8 -1015 56Ti ions, 12 tracks of spontaneous fission were observed, which is substantially less
than the expected value. This may be evidence that either the mechanism of the fusion reaction changes
substantially from 40Ar ions to 50Ti ions, or the properties of the isotope 256KU differ substantially from
those predicted.
To test the second hypothesis, the experiments were repeated at a rate of rotation of the cylinder of
1500 rpm. At an integral flux of 50Ti ions ?1015 particles, 70 tracks of spontaneous fission fragments, with
the time distribution presented in Fig. 5, were recorded.
Subsequent experiments were conducted with a target of 207Pb at a rate of rotation of the cylinder
1500 rpm. At an integral ion flux of ?1.2 -1015 particles, 53 spontaneous fission fragments were recorded
(Fig. 6a). Evidently the half-life is significantly greater than the selected time value, and therefore the
experiment was repeated at a lower rate of rotation (54 rpm). Here also an analogous picture of the dis-
tribution of tracks was obtained; therefore, in the third series of experiments the rate was lowered to 3.6 rpm
(Fig. 6b).
Thus, it follows from the experiments that in the formation of 207Pb by 50Ti ions, the formation of a
spontaneously fissioning emitter with a half-life of several seconds is observed.
Finally, in the last series of experiments we irradiated a target of 20613b. At an integral flux of
?0.4 -1016 ions, only four tracks were recorded, half of which, taking into account the data obtained earlier,
may be due to reactions on impurity isotopes 207Pb and 206Pb. In other words, in the combination of 2061,b
+ 50Ti, only the upper limit of formation of spontaneously fissioning nuclei can be determined.
All the experimental results are presented in Table 1. The error in the determination of the values
of the cross sections, according to our estimates, do not exceed a factor of two, whereas the relative error
is determined chiefly by the statistical accuracy and is ?30%.
Thus, from the aggregate of data obtained it follows that in the case of irradiation of targets of
separated lead isotopes with 50Ti ions, the formation of two spontaneously fissioning emitters with greatly
differing half-life: about 5 msec and several seconds, is observed.
The emitter with half-life 5 msec, observed in the reaction of 206Pb + 50Ti, cannot be assigned to
nuclei with atomic number Z < 104, since all the isotopes of element 102 are known up to N = 146 and do
not possess such properties [16], while for the odd isotopes of element 103 there is a strong prohibition of
spontaneous fission [17].
The maximum yield of this emitter is observed in the reaction with 208Pb; the effect decreases by
more than 10-fold with a target of 207Pb and is practically entirely absent for 206Pb.
Thus, analyzing the experimental cross sections of the reactions and the properties of the known
isotopes of kurchatovium and lighter elements, it can be assumed that the observed effect is due to decay
of the isotope 256Ku, which is formed in the reaction 208Pb(50Ti,2n)256Ku.
The question of the properties of the isotope of kurchatovium with N = 152, as will be evident from
the following, is of theoretical significance; therefore it is important to accurately identify the mass num-
ber of the emitter with half-life ?5 msec. Since there is a great prohibition of spontaneous fission for odd
isotopes, possible candidates are the even nuclei 256Ku and 258Ku, which are formed in reactions with the
emission of two and four neutrons, respectively.
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Despite the fact that the calculated values of the cross sections of reactions with the emission of two
and four neutrons differ substantially from one another (see Fig. 3), separate experiments were conducted
on the measurement of the integral function of excitation for the emitter with T1/2 ?=-,. 5 msec. Figure 7
presents the experimental values and the calculated dependences of the integral cross sections of forma-
tion of the isotope with half-life ?5 msec and the nuclei 151Pm (the fission fragments of the compound
nucleus) and 234mPb (products of a transfer reaction) in the irradiation of 238Pb by 53Ti ions. The depen-
dences presented in Fig. 7 additionally confirm the fact that the short-lived emitter is formed in a reaction
with the emission of two neutrons and is the isotope 253Ku.
Comparing the yield of short-lived and long-lived activity in the reaction of 238Pb + 53Ti, we can con-
clude that the isotope 256KU in the majority of the cases experiences spontaneous fission.
It should be noted that the experimental cross section of the reaction Pb(53Ti, 2n)Ku proved to be 10
times lower than the theoretical values (see Fig. 3). However, in a calculation of o-(x,n), the empirical
dependence of Sikkeland et al. [18], based on the assumption of an influence of the subshell N = 152 on the
value of I'll/I' f, was used for the ratio of the partial width rn/rf. And yet, as will be shown later, this
assumption is not substantiated for nuclei with Z 104. The exclusion of the influence of the subshell
N = 152 on the value of rn/rf leads to a significant decrease in the calculated cross sections, which
virtually eliminates the discrepancy noted above.
The long-lived emitter with half-life about 4 sec, in all probability, is the isotope 255KU, which is
formed with a maximum cross section in the reaction 237Pb(53Ti, 2n), and with lower probability in the
reaction 238Pb(53Ti, 3n), and is absent in the reaction 236Pb(53Ti, 1n).
However, we should note that the lifetime of this emitter proved close to the lifetime of the known
isotope 252102, which in this combination might be obtained in the reaction of the type of 237Pb(53Ti, aln)-
252102.
Let us consider separately the question of the probability of side processes in reactions with ions of
the type of "lir or 53Ti. At a maximum energy of the bombarding 53Ti ions equal to 260 MeV, the maximum
energy of excitation of the compound nucleus 257KU is ^'40 MeV. Estimates show that the threshold of the
reaction with evaporation of an a particle and one neutron is equal to ?260 MeV. Moreover, in this region
of nuclei the ratio of the partial width ra/ rn, like rp/r n, is small 10-2). Therefore, the contribution
of the processes occurring with the evaporation of charged particles from the compound nucleus is negli-
gible.
And yet, the process of direct emission of a particles, followed by evaporation of a neutron, as
occurred in reactions with light ions of carbon, nitrogen, and oxygen, is energetically possible. However,
as was shown in [19-21], the mechanism of such reactions depends substantially on the structure of the
bombarding ion. In the sequence from light ions to particles of the type of 43Ar and 53Ti, the probability
of the escape of direct a particles decreases hundreds and thousands of times.
Model experiments were conducted in which spontaneously fissioning nuclei of 244FM were obtained
in reactions in the irradiation of the isotopes 235T1 and 233T1 with 45Sc ions and of the isotopes 266Fb with
43Ar ions. As can be seen from Table 1, the ratio of the cross sections ?(a, 2n)/o- (2n) 0.03. From this
it can be concluded that the probability of formation of the isotope 252102 in the irradiation of 237Pb with 53Ti
ions is negligible.
From a comparison of the cross sections of formation of the isotopes 255Ku and 256KU it follows that
the odd isotope 255KU has comparable values of the half-life with respect to a decay and spontaneous fission.
Finally, the absence of an effect in the reactions of 23813b + "Ti may mean that the life-time of the even
isotope 254Ku is less than 3 msec.
DISCUSSION OF RESULTS
Let us consider the question of how the properties of the synthesized neutron-deficient isotopes of
kurchatovium agree with the known data on the stability of heavy nuclei with respect to spontaneous fis-
sion.
For the isotope 256Ku with N = 152, instead of the expected half-life, comprising tens and hundreds
of second, the experimental value was 103-104 times smaller.
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The position of this point in the systematics of spontaneous fission substantially changes the concept
of the stabilizing influence of the subshell N = 152 in the transition from Z = 102 to Z = 104. The depen-
dence of TSF for kurchatovium isotopes on the number of neutrons is evidence of a monotonic increase in
the lifetime of the even?even nuclei with increasing mass, without any significant variations in the region
of N = 152 (Fig. 8).
The lifetime of the odd nucleus 255KU is determined by the prohibition of spontaneous fission, which
in this case is ?103. Now it is not surprising that the isotope 260Ku has TSF 0.1 sec, and there is no
1/2
need to assume such high prohibitions (-107-1012) for the other odd isotopes of kurchatovium with mass
numbers 257 and 259, as was done in the form of Ghiorso et al. [6, 11]. From the systematics (see Fig. 8)
it is evident that for practically all the odd isotopes of kurchatovium, the prohibition of oddness leads to an
inhibition of spontaneous fission by 103-104-fold.
Since a substantial change in the half-life with respect to spontaneous fission (more than 10-fold) is
observed in the sequence from the isotope 254102 to the isotope 258Ku, it is natural to attempt to give an at
least qualitative explanation for the data obtained.
According to the modern concepts, in the region of transfermium elements the barrier to fission has
a complex structure, and the stability of the nuclei with respect to spontaneous fission is determined
chiefly by the contribution of the shell correction to the total energy of deformation of the nucleus.
Let us consider from this standpoint the isotopes of fermium, for which a strong influence on the
half-life TSF,/2 by the subshell N = 152 has been established experimentally. When N = 152, the barrier to
1
fission, calculated according to the method of Strutinskii [22], seems to consist of two barriers and takes
the form of a two-hump curve with two minima, corresponding to the ground state and isomeric state of
the nucleus. The lifetime of this nucleus with respect to spontaneous fission is determined by the integral
of motion on the entire path from the ground state to a point lying beyond the second barrier (Fig. 9).
With decreasing number of neutrons (transition to lighter isotopes of fermium), the value of the
second barrier will be lowered as a result of a decrease in the liquid drop energy of deformation of the
nucleus, which should lead to a decrease in the periods of spontaneous fission. In the limiting case, when
the ground state is higher than the second maximum, the value of T772 will be determined by the perme-
ability only of the first barrier. It can be assumed that as a result of this circumstance the transition from
252Fm to 244Fm will lead to a change of approximately 1012-fold in TSF.
1/2
And yet, as was shown in the work of Randrup et al. [23], the possibility remains that such a situa-
tion might arise in the movement from N = 152 toward heavier isotopes of fermium. In this case the super-
position of the shell correction and liquid drop energy of deformation may also lead to a substantial de-
crease in the second maximum and, as a result, sharply reduce the lifetime of the heavy isotopes with
respect to spontaneous fission. Actually, in the sequence from 252Fm to 258Fm, the value of TS' changes
1/2
approximately 1013-fold.
Now let us fix N = 152, and we shall measure the number of protons in the nucleus. With increasing
Z, the liquid drop portion of the energy of deformation will decrease, which leads to the same consequences
that were observed in the case of neutron-deficient isotopes of fermium discussed above. It can be as-
sumed that the greatest change in TSF, will occur at the moment when the lifetime of the nucleus is de-
1/2
termined chiefly by the permeability of the first barrier. The possibility remains that this situation exists
in the transition from 252Fm to 258Ku, since the half-life with respect to spontaneous fission changes ap-
proximately 1012-fold in this case.
If this assumption is correct, then further movement in the direction of large Z or variation of N
at set Z should not lead to such strong changes in TSF since the value of the first barrier, as it follows
1/2
from the calculations of [22], is comparatively insensitive to the nucleon composition of the nucleus. It
seems to us that this viewpoint is qualitatively confirmed by the latest calculations of Pauli and Leder-
gerber [24] and Moller and Nix [25,26]; however, the quantitative conclusions require a detailed theoretical
analysis, considering new data with respect to the properties of isotopes of kurchatovium and heavier
elements.
Such an interpretation of the experimental data means that for even?even isotopes of kurchatovium
the lifetime with respect to spontaneous fission is already determined practically entirely by shell effects.
This is analogous to what is expected for the region of ultraheavy elements, and it must be hoped that in
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the case of movement in the direction of the twice-magnetic nucleus with Z = 114, N = 182, a sharp in-
crease in TSF,/2 will actually be observed, as it follows from the theoretical predictions.
1
CONCLUSIONS
A number of conclusions can be drawn from the aggregate of experimental results.
The method of synthesis of transfermium elements in the irradiation of lead isotopes with ions with
mass AI 40 atomic units, investigated earlier [12] for the example of the reaction Pb("Ar, xn)Fm, is
also extremely effective using "Ti ions. The reactions Pb("Ar, 2n)Fm and Pb(50Ti, 2n)Ku have approxi-
mately equal cross sections, which might have been expected on the basis of theoretical estimates. This
permits us to hope that this method can be used successfully for the synthesis of heavier elements in the
reactions induced by 54Cr, 55Mn, and "Fe ions.
In all probability, the substantial changes in the systematics of the half-lives for even?even isotopes
of kurchatovium are associated with the structure of the barriers to fission of these nuclei. From this
standpoint, it seems important to investigate the properties of more neutron-deficient isotopes of kurchato-
vium, using, in particular, the reactions with2?4Pb, and to attempt to advance into the region of elements
with Z 106. On the other hand, a detailed theoretical analysis must be made of the data obtained on the
basis of the modern theory of nuclear fission, which, in our opinion, will aid in a more reliable prediction
of the properties of heavy and ultraheavy elements.
The authors are deeply grateful to Academician G. N. Flerov for his great support, constant aid, and
valuable suggestions at all stages of this work; we should like to thank V. M. Plotko and N. A. Danilova
for their great contribution to the development of the experimental method and their active participation
in the experiments, as well as K. I. Merkin and T. I. Rybakov for their painstaking work on the examination
of a large number of detectors of fission fragments. The authors are grateful to the operating group of the
U-300 accelerator, supervised by A. N. Filipson, for producing intense and stable beams of accelerated
ions. The enriched isotope "Ti was kindly provided by the State Isotope Reserve of the USSR, and the
authors are grateful to V. P. Bochin, V. S. Romanov, and S. A. Sel'yanov for aid in the preparation of
samples of this isotope for the ion source.
LITERATURE CITED
1. G. N. Flerov and I. Zvara, Report of the United Institute of Nuclear Research D7-6013 [in Russian],
Dubna (1971).
2. G. N. Flerov et al., At. inerg., 17, No. 4, 310(1964); Phys.Letters, 13, 73 (1964).
3. I. Zvara et al., Report of the United Institute of Nuclear Research P7-3783 [in Russian], Dubna
(1968); Radiokhimiya, 11, 163 (1969).
4. I. Zvara et al., Report of the United Institute of Nuclear Research D7-4542 [in Russian], Dubna
(1969); Radiokhimiya, 12, 565 (1970); J. Inorg. and Nucl. Chem., 32, 1885 (1970).
5. I. Zvara et al, Report of the United Institute of Nuclear Research D12-5845 [in Russian], Dubna
(1971); J. Inorg. and Nucl. Chem. Letters, 7, 1109 (1971).
6. A. Ghiorso, in: Proc. R. A. Welch Found. Conf. on Chemical Research, XIII. The Transuranium
Elements. The Mendeleev Centennial, Houston, Texas, 17-19 November (1949), p. 107.
7. A. Ghiorso et al., Phys. Rev. Letters, 22, 1317 (1949).
8. A. Ghiorso et al., Phys. Letters, 32B 95 (1970).
9. Yu. Ts. Oganesyan et al., At. Energ., 28, No. 5, 393 (1970).
10. M. J. Nurmia, Nuclear Chemistry Annual Report LBP-666, Berkeley (1971), p. 42.
11. A. Ghiorso and T. Sikkeland, Phys. Today, 20, No. 9, 25 (1967).
12. Yu. Ts. Oganesyan et al., Preprint of the United Institute of Nuclear Research D7-8194 [in Russian],
Dubna (1974).
13. W. Myers and W. Swiatecki, in: Proc. Intern. Symp.,"Why and How Should We Investigate Nuclides
for the Stability Line," Lysekil, Sweden (1966); Almquist and Wiksell, Stockholm (1968).
14. Yu. Ts. Oganesyan et al., Preprint of the United Institute of Nuclear Research P7-7863 [in Russian],
Dubna (1974).
15. A. S. Il'inov, Report of the United Institute of Nuclear Research P7-7108 [in Russian], Dubna (1973).
16. G. N. Flerov, At. Energ., 24, No. 1, 5 (1968); Ann. Phys., 2, 311 (1967).
17. G. N. Flerov et al., Report of the United Institute of Nuclear Research P7-4932 [in Russian], Dubna
(1970).
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18. T. Sikkeland, A. Ghiorso, and M. Nurmia, Phys. Rev., 172, 1232 (1968).
19. T. Galin et al., Preprint IPNO -RC-73-03, Orsay (1973).
20. L. Moretto et al., Preprint LBP-1966, Berkeley (1973).
21. A. G. Artyukh et al., Report of the United Institute of Nuclear Research P7-7189 [in Russian], Dubna
(1973).
22. M. Brack et al., Rev. Mod. Phys., 44, 320 (1972).
23. T. Randrup et al., Nucl. Phys., A217, 221 (1973).
24. H. Pauli and T. Ledergerber, in: Proc. 3rd. Symp. on Physics and Chemistry of Fission, Rochester,
Paper IAEA-SM-174/202 (1973).
25. P. Willer and J. Nix, ibid., Paper IAEA-SM-174/202 (1973).
26. P. Moller and J. Nix, Preprint LA-UR-74-417, Los Alamos (1974).
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REVIEWS
PROBLEM OF ENVIRONMENTAL PROTECTION IN
THE OPERATION OF NUCLEAR POWER STATIONS*
N. G. Gusev UDC 551.510.72
Protection of population and environment in the design and operation of nuclear industrial units is
becoming an important contemporary social problem. This review considers the need for the distribution
of established maximum doses over radiation sources and the need for estimates of collective and popula-
tion doses from all forms of nuclear energy.
Requirement for Distribution of Maximum
Population Doses
Scientists of all countries have concentrated their attention on the problem of protection against ioniz-
ing radiation from the very first steps in the peaceful use of atomic energy. As a result, the safest branch
of industry for personnel and population ? nuclear power ? was created in a short time.
The international Commission on Radiological Protection (ICRP) established maximum permissible
doses (MPD) which are considered safe for the occupational worker and the general population. National
regulations were based on these recommendations. In planning units for the nuclear industry, however,
the application of these regulations is complicated by a number of factors arising out of the extensive in-
troduction of nuclear energy into many fields of human activity. If one assumes that by the year 2000 the
*Reviews published in this issue are revised texts of papers read at the plenary session of the All-Union
Scientific Conference on Protection against Ionizing Radiation from Nuclear Installations (Moscow, 17-19
December, 1974).
TABLE 1. Distribution of Maximum Population Dose over Radiation
Sources, % of Total Maximum Dose
Radiation sourceSum
Gaseous and
aerosol wastes
Liquid and
solid wastes
.-
Water-cooled, water-moderated reactors (VVER)
4
2
6
Single-loop reactors (EtBMK)
5
3
8
Gas-cooled reactors
2
1
3
Thermal nuclear power stations
3
1
4
Fast reactors
2
1
3
Experimental reactors
3
2
5
Other types of reactors
4
2
6
Fuel reprocessing plants
10
8
18
Ores, hydrometallurgy, fuel elements
2
3
5
Radiochemistry, irradiators
1
1
2
Burial grounds for liquid and solid waste
1
3
4
Structural materials
?
?
5
Agricultural fertilizers
?
?
4
Accelerators, electron-beam tubes
?
1
Television sets
?
?
1
Reserve for other sources
?
?
25
Translated from Atomnaya nergiya, Vol. 38, No. 6, pp. 391-397, June, 1975. Original article sub-
mitted January 8, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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100
10
41
2
6
1950 1970 1980 1990 2000
Year
Fig. 1. Mean annual whole-body dose (USA); 1)
total dose; 2) natural radiation; 3) medical pro-
cedures; 4) global fallout; 5) various sources;
6) occupational irradiation; 7) nuclear power
stations and other sources of environmental
contamination.
TABLE 2. Maximum Annual Doses, rem electrical power from nuclear power stations over the
entire world will amount to 3000 GW, then from a rough
estimate there will be generated in that period from
nuclear power alone (in billions of curies) a mixture of
fission products amounting to ?40,000 (no holding time)
or 600 (after one year's holding time) including the long-
lived fission products (no holding time); 85Kr, 3; 89Sr,
400; 995r, 30; 13.1Cs, 35; 1311, 250; 1291, 10-5, etc. A large
*For thyroid gland in children, MPD = 1.5 rem/yr. amount of long-lived isotopes (3H, 14C, 54mn, Co,60 mos)
and transuranic elements will be formed. There will be
an increase in the number of other sources of artificialradiation and an ever increasing number of people
will be subject to their effects. Thus, of the two main principles for protection against radiation promul-
gated by the ICRP ? maintaining radiation doses at the lowest possible level (allowing for technological and
economic considerations) and a reduction in the number of irradiated individuals ? only the first is
actually achievable.
In this review, however, we raise the question not of further reduction in dose but of the need for
distribution of presently established MPD for the population with consideration of the partial contribution
from the separate kinds of radiation sources so that the total dose does not exceed the established maxi-
mum.
Category
Critical-organ group
Tr
in
iv
A . Staff personnel
5
15
30
75
B . Indiv iduals in the general
population
0,5
1,5
3*
7,5
C. General population
0,17
0,5
1
An analysis was made of a large number of reports on actual and predicted discharges, on levels
of environmental contamination, on exposure of the general population to various sources of ionizing radia-
tions, and on methods and approaches to the evaluation of population doses. Part of this material appears
in [1-171. Based on the analysis, an attempt is made in this review to pick out the most important radia-
tion sources (Table 1). The list of radiation sources given in Table 1 includes only the portion susceptible
to quantitative analysis.
Particularly complicated is the solution of the problem of population exposure for medical applica-
tion of x rays, mainly in x-ray diagnostics and stomatological procedures. According to [1], the mean
value of the genetically significant dose (GSD) from diagnostic procedures amounts to 20 mrad/yr. Since
the GSD is a weighted mean value including the relative birth rate and relative exposure for individuals
up to 30 years of age, the actual doses to the gonads, and even more to the bone marrow or abdominal
region, will be considerably higher. [By definition [1],
GSD
(NF F DF -1-1011 Wm 131"f )
,hW3, h h k .1,
j k
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TABLE 3. Maximum Doses Recommended for Individuals, mrem
/yr
Group
Isotope
Critical-organ group
III
Global genetically significant isotopes: 3H, 35S, 85Kr,
"3Xe, I34Cs, 137Cs
100
Global somatically significant isotopes: I4C, 1291, 1311,
89Sr, 9?Sr, 'Ce, 238-241Pu, 241Am
400
900
Local isotopes' propagated over a radius > 10 km
170
500
1000
The same for a radius < 10 km
500
1500
3000T
'we arbitrarily call isotopes not in Groups K and L local.
tFor the thyroid gland in children, MPD = 1500 mrem/yr.
where j and k are the type of irradiation and age; F and M denote female and male; N1 is the number of
individuals receiving the dose D1 rad/yr to the gonads; W is the expected number of children per person.
All calculations are carried out up to 30 years of age.]
The individual radiation doses for the population of the United States from various radiation sources
[2] are shown in Fig. 1 as estimated for the period 1960-2000. The comparison was made with respect to
whole-body doses except for the dose from medical procedures. In the calculation of the latter, the somatic
dose per capita resulting from irradiation of the abdominal region (abdominal dose) was used as the basis.
It is clear that this dose is about 90% of the total dose from artificial sources of irradiation and is at least
35% of the dose from all sources, including the dose from natural radiation. Being 2-3 times less than the
abdominal dose, the GSD exceeds the dose from any other artificial radiation sources.
It is necessary to plan MPD distribution with all radiation sources included and to pay particular
attention to the acceptance of technical and organizational solutions for the reduction of population exposure
during medical procedures. This form of radiation effect is not included in Table 1 but it must be taken
into account (just like exposure from contamination resulting from nuclear explosions) when considering
the social aspects of the use of nuclear energy.
There are also other sources which do not appear in Table 1. Among them are, for example, dis-
charges of natural radioactive materials introduced into the atmosphere by thermal and electric power
stations operating with mineral fuel [9,17], nuclear explosion for peaceful purposes, nuclear accidents,
exposure in aviation and astronautics when transporting nuclear fuel, etc. However, the reserve set aside
for them and also for new sources (25%) does not include the dose from medical procedures.
There are standards recommended by the ICRP and accepted in MRB-69 (Table 2).
The value MPD = 0.17 rem/yr for the general population (Group 1 critical organs) corresponds to a
GDS=5 rem in 30 years. Given below is the recommended distribution of this maximum dose in rem/per
30 years:
Staff
1.0
Individuals
0.5
Population
2
Reserve.
1.5
The GSD for the population is distributed in the following manner; 0.5 and 1.5 rem respectively from ex-
ternal and internal irradiation.
There is no distribution of the maximum somatically significant dose (SSD) with respect to the
various population categories. Evidently, the ICRP will make recommendations in time with respect to
this problem.
New difficulties arise in the development of standards with respect to irradiation. An immediate one
is the concept of "global" isotopes. This term arose after it became known that because of nuclear explo-
sions, global cpntamination of the biosphere (including the entire animal and vegetable worlds, the
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atmosphere, and the hydrosphere) by such artificial isotopes as 3H, 14C, "Kr, 89Sr, 90Sr, and 137Cs ocurred.
However, in nuclear power, 1291 is usually still assigned to the class of global isotopes although the pro-
pagation of this isotope over considerable distances by atmospheric flow is unlikely because of the high
weight ratio (6 kg/Ci). Nevertheless, a number of other isotopes which are present in atmospheric dis-
charges or liquid wastes from nuclear units should be included in the class of global isotopes under con-
ditions where there is a high density of nuclear-industry sources. Besides radiological properties (parti-
cularly high radiotoxicity), one should consider the total number of isotopes produced in an entire technical
cycle, the fraction reaching the environment, the physical and physicochemical characteristics of the iso-
topes, the capability of actively participating in biological processes (active metabolism), the possibility
of accumulation in soil or other media, the creation of an intensified 7-ray field at a given locality, etc.
The most important criterion for assigning one or another isotope (or source) to the global category is a
relatively large contribution to the collective or population dose. It is also necessary to take into account
the well-known requirement that for presently established MPD occupational workers make up no more
than 1.7%, and individuals in the population no more than 3.3%, of the entire population.
Table 3 gives MPD corresponding to 100% recommended for individuals in a population and also the
isotopes which should be considered global. The MPD for Group K isotopes (100 instead of 117 mrem) is
taken from the GSD distribution given above where a genetically significant MPD of 3.5 rem in 30 years is
assigned to all categories; the MPD for Group L is taken from Table 2 after subtraction of a dose of 100
mrem/yr resulting from genetically significant isotopes; the MPD for Groups M and N is also taken from
Table 2 for categories B and C respectively depending on the distance over which the isotopes may be pro-
pagated (usually, the greater the distance the greater the contribution to the collective dose). When using
Tables 1 or 3 in practice, one applies the generally accepted rule that the MPD to the entire body or to
individual groups of organs from a sum of isotopes (or from several types of ionizing radiation) must not
exceed the MPD from a single isotope.
Among other controversial questions are the uncertainty of including the contribution to the MPD
from radioactive wastes of other nuclear power stations or, generally, other nuclear industrial units, the
proper selection of isotopes belonging to the global group particularly if the problem involves liquid wastes,
the uncertainty of dose prediction under accident situations, the well-known difficulties in predicting the
development of nuclear industry and particularly the appearance of new sources of radiation, etc.
We note in conclusion that the USAEC, as a supplement to the basic standards, published a circular
in 1971 [18] in which the annual MPD from radioactive wastes of newly planned water-cooled reactors was
recommended to be approximately 1/100 of the MPD established for the sum of all sources, namely 5
mrem (instead of 500 mrem) for individuals in the population living at the boundary of the protection zone
(roughly 0.5 km) and 1 mrem (instead of 170 mrem) as the mean annual dose for the general population.
An extensive discussion of this concept of the USAEC is given in [6-8].
Analysis of actual gaseous, aerosol, and liquid wastes of a nuclear power station and also of actual
and predicted doses shows that the proposed distribution of maximum doses does not create any economic
or technical problems for nuclear power stations since the actual (calculated) doses are considerably lower
than those proposed.
Need for Evaluation of Population Dose
The population dose is a measure of the general irradiation of the whole body, or of a given organ,
for a group (population) as a whole. If the number of people receiving a radiation dose in the range from
D to D + dD is N(D)dD, then the population dose Dp is defined by [19]
D, = DN (D)dD, (1)
where the integration is carried out within the limits of the general distribution of dose for the entire
population. If one is talking of a portion of the population, the term "collective dose" is used.
The population dose can also be defined by a summation of the individual doses Di,i over all groups
of irradiated people Ni, i.e.,
(2)
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where j is the level of irradiation and the letter i indicates that the specified quantity (Di, Di, Gi) refers to
an individual. Sometimes one also uses the term "average individual dose"
= P,
(3)
where p = N. is the number of people in the population.
At the present time there are various mathematical models for the quantitative evaluation of indivi-
dual and population doses resulting from radioactive wastes of nuclear units. This paper briefly discusses
the model developed in [20-23].
Calculation of the individual dose Di from gaseous and aerosol discharges is conveniently performed
by means of the expression
D, = -97[(rem/sec )/(Ci/m3)] sec/ma] Q [Gil.
Here, Q is the discharge of the isotope; Ci is the "meteorological dilution factor" which is numerically
equal to the ratio between the atmospheric concentration of the isotope and the amount of isotopic discharge
per unit time; Tfi is a dosimetric conversion factor corresponding to the dose rate for unit atmospheric
concentration of the isotope. It should be noted that the determination of the dosimetric conversion factor
is a subject for serious study since it must take into account all paths for isotopic effects on humans (in-
halation, food chain, y -ray fields from radioactive clouds or soil, etc.). Its value may vary very widely
for a single given isotope. Numerical data for the factor 07 is given in [6,21, 24].
Unfortunately, there is no uniformity of opinion on the choice of a model for the determination of the
factor G. Thus in foreign practice, calculations of Gi are based on the Gaussian model of Pasquill and
Gifford [25, 26], which is recommended by IAEA [27]. In our country, other methods are used (for example,
see the review [28]). Strictly speaking, Eq. (4) for the individual dose Di is valid for the calculation of
doses from gaseous and aerosol discharges for any paths of action except those cases where the contami-
nated products travel into other regions. A similar formula for the population dose was produced in the
form [20, 21]
(4)
np= 2 r [persons/m2 I Gp[sec/m ]Q [Gi].
Here r) is the average population density for a given population; Gp is the so-called population dilution
factor, which is obtained by integration of the individual dilution factor Gi over the entire area. It can be
represented in the following form,
(5)
G p V- 2 -SI' [ _
exp
dt'
(6)
where F(t) is a dimensionless function which takes into account depletion of the plume because of radio-
active decay and deposition of isotopes on the soil during the time t; Hef is the effective height of the dis-
charge.
In the more complicated case, for example, where the products contaminated at the location of a
nuclear power station travel into other regions, the contribution to the population dose can be determined
from
Dp= DeNplj = D
(7)
where Dc is a normalization factor numerically equal to the integral dose per unit activity entering the
body, rem/Ci/person;* Ij is the intake of a given isotope with food into the bodies of a group of Nj people
(here j refers to the amount of the individual intake); Im = is the total intake of the isotope into the
bodies of all individuals, Ci.
In the simplest case (where one neglects radioactive decay, variation of isotopic content in process-
ing of foods, etc.), Im can be replaced by Am ? the total content of an isotope in all contaminated intake
products, Ci:
*The integral dose or dose commitment is given in general form (for any amount of isotope entering the
body) by the expression De = D(t)dt, rad, or De = H(t)dt, rem, where b(t) and H(t) are the absorbed-
dose rate and the dose-equivalent rate.
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17?
(8)
One of the purposes of the population dose is the determination of the public risk in using nuclear energy.
In this instance, a linear (and not a threshold)dose?effect dependence is used. Then when calculating the
population dose from contaminated products by Eq. (7), or with the approximation (8) included, there is
no need to know the distribution of individual doses, the number of individuals, or the locality in which they
live. It is only important to know what the total amount Im of an isotope is in contaminated source products
during the time of their consumption. In order to include the various metabolic paths of action, Eq. (7)
can be rewritten in the following form [22]
D p D iK,,K,Q, (9)
Here, K1 is the fraction of discharged isotopes deposited on fields or pastures; K2 is the fraction of the
isotopes from the discharge deposited on the soil which is transferred into the edible portion of plants; K3
is the ratio between the cumulative content of the isotope in the food intake of the population and its cumula-
tive content in the edible portion of cultivated plants or forage at the time of harvesting or at the time
cattle are out to pasture. The factor K3 takes into account decay and removal of an isotope during trans-
portation, processing and storage of the products as well as its "loss" through migration in the bodies of
animals.
These dimensionless coefficients are defined by the relations
K1 = Gpvgv;
(10)
K2 =11K4.+112,
(11)
where
K,=_C (Ci/kg) Yr kg
61
1
_1
(12)
L ci/m2 zt
[
m2
is the fraction of singly deposited activity in the soil which is transported into the edible portion of a given
type of plant grown during the time of complete removal of the isotope from the vegetative layer of the
soil; Vg is the rate of deposition, m/sec.
For dairy cattle out to pasture,
for farm animals,
for products of plant origin,
3T6 [[ dd aa yy ss yy rr 31 -
K3 ?
Tef Ways] ie.
0.693 ?k;
11 ?exp ( i?Tf. )1 Kr t.r, 1 ex1)(??.T);
f
1
Kf = 2 [i ? exp ( )1.
P
(13)
(14)
(15)
Here, 1, is the fraction of the area occupied by the corresponding agricultural land; v i and 772 are respec-
tively the fractions of all deposited contaminants transported into the edible portions of plants through the
roots and leaves; w is the agricultural productivity; C is the total content of an isotope in the edible por-
tion of a plant per kg weight for a one-time contamination of 1 m2 of soil surface by an activity of 1 Ci;
Fk is the average density of dairy cattle in the contaminated area; S is the area of pasture from which a
cow eats grass in a day; Tef is the time for half-removal of an isotope from the edible portionof grass;
Kr is the fraction of an isotope absorbed from forage by animals of the r-th type which is transferred into
products obtained from these animals (for cows, Kr = Kk); Er,/ is the fraction of all products yielded by
the r-th type of animal which is processed into primary food products; Tp and Tf are warehouse storage
times for plant products and forage; T1 is the time consumed in processing and transport of the primary
form of food products from cattle; TB is the time cattle are out to pasture; A is the decay constant for a
given isotope.
At the present time, the input parameters for this model are being refined and a computer program
is being written. Note that in contrast to Eqs. (1) and (2) where it is necessary to know individual exposure
doses, knowledge of population density or of the number of individuals in a population is not needed for
the calculation of the population dose from contaminated products when using Eqs. (7)-(15); one only needs
to know the amount of isotope present in contaminated food at the time of consumption.
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Of the other mathematical models for calculating population and individual doses from radioactive
wastes, one should single out the model developed, and already used in practice, by US scientists [10].
Based on this model, the HERMES computer program was written in BASIC; this program encompasses
all possible paths of action for radioactive materials in the environment and is intended to solve such
problems as the potential development of nuclear power in the US up to the year 2000, optimal selection of
sites for nuclear units, escape and propagation of radioactive materials and their resultant concentrations
in air, water, soil, and bottom sediments, concentrations in food products, and, finally, radiation doses
from radioactive materials entering the body with air, water, and food products and from external radiation
_ in air, water, or soil. Results obtained by the use of this and other programs have been presented [2,6,16,
17].
Population or collective doses are a required social criterion in the problem of radiation safety for
the population and in protection of the environment since, based on their evaluation, one can solve the
problem of the fundamental partial distribution of MPD within a population with respect to radiation sources
in order to assure consistency of established maximum doses from all types of nuclear energy used in the
activities of society; one can predict population exposure for further development of the nuclear industry
and on this basis determine risk factors for the public from the contributions to the population dose of
individual radiation sources. Since the risk concept is based on the assumption of a linear dose-effect
relation, the public risk factor Rp can be defined by
[damage/(rem-person)] N [persons/population] [rem] T, [rem] ---=-/T,Dp. (16)
Here, -Ai is the total individual risk factor including somatic and genetic effects (according to ICRP data,
10-4 for chronic irradiation). More detailed discussions of risk factors can be found in [2, 3, 6, 11-
14, 16, 17, 28-30].
The questions touched on in this review require extensive discussion and active participation by
specialists in various fields. They must be solved in planning for the development of the nuclear industry
of the future in order to ensure protection of all segments of the population against ionizing radiation and
protection of the environment against contamination by radioactive materials.
LITERATURE CITED
1. United Nations Scientific Committee on the Effects of Atomic Radiation, UN, New York (1972).
2. Estimates of Ionizing Radiation Doses in the United States, 1960-2000. US Environmental Protection
Agency, Washington (1972).
3. The Potential Radiological Implications of Nuclear Facilities on the Upper Mississippi River Basin
in the Year 2000, USAEC (1973).
4. Natural Radiation Exposure in the United States, US Environmental Protection Agency, Washington
(1972).
5. Report on Releases of Radioactivity in Effluents and Solid Waste from Nuclear Power Plants for
1972, USAEC, Washington (1973),
6. USAEC, Final Environmental Statement Concerning Proposed Rule Making Action: Numerical Guides
for Design Objectives and Limiting Conditions for Operation to Meet the Criterion:"As Low as
Practicable for Radioactive Material on Light-Water-Cooled Nuclear Power Reactor Effluents,"
Vol. 1-3, WASH-1258 (1973).
7. G. Whipple, Third Intern. Congr. of the Intern. Radiation Protection Association, Washington, 9-14
Sept., 1973, Rep. 156.
8. A. Hull, Nucl. News, 11, 53 (1972).
9. P. Pellerin, in: Proc. IAEA Symp. on Environmental Surveillance around Nuclear Installations,
Warsaw, 5-9 Nov., 1973, Rep. SM-180/76.
10. J. Soldat et al., in: Proc. IAEA Symp. on Environmental Behavior of Radionuclides Released in the
Nuclear Industry, Aix-en-Provence, France, 14-18 May, 1972, Rep. SM-172/82.
11. The Effect on Populations of Exposure to Low Levels of Ionizing Radiation, HEIR Rep., Washington,
D. C., November, 1972.
12. C. Comar, Third Intern. Congr. of the Intern. Radiation Protection Association, Washington, 9-14
Sept., 1973, Rep. 1.
13. J. Crow, ibid., Rep. 2.
14. A. Upton, ibid., Rep. 3.
15. A. Hull, ibid., Rep. 158.
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16. Environmental Radiation Dose Commitment: An Application to the Nuclear Power Industry, USA
EPA-520/4-73-002, Washington (1974).
17. Reactor Safety Study. An Assessment of Accident Risks in US Commercial Nuclear Power Plants,
USAEC, Washington (1974).
18. Licensing of Protection and Utilization Facilities, US-10-CFR-50, Federal Register, 36, No. 111
(1971).
19. Bo. Lindell, Proc. IAEA Symp. on Environmental Surveillance around Nuclear Installations, Warsaw,
5-9 Nov., 1973, Rep. SM-180/77.
20. N. G. Gusev et al., Third Intern. Congr. of the Intern. Radiation Protection Association, Washington,
9-14 Sept., 1973, Rep. 157.
21. N. G. Gusev and V. A. Belyaev, Proc. IAEA Symp. on Environmental Surveillance around Nuclear
Installations, Warsaw, 5-9, Nov., 1973, Rep. 82.
22. V. A. Belyaev, in: Experience in Operation of Nuclear Power Stations and Path for Future Develop-
ment of Nuclear Power [in Russian], Vol. II, Izd. FEI, Obninsk (1974), p. 355.
23. V. A. Belyaev, in: International Conference on Physical Aspects of Atmospheric Contamination [in
Russian], Vilnius, 18-20 June, 1974, p. 176.
24. P. Bryant, Proc. IAEA Symp. on Environmental Surveillance around Nuclear Installations, Warsaw,
5-9 Nov., 1973, Rep. 12.
25. F. Pasquill, Meteorolog. Mag., 90, 33 (1961).
26. F. Gifford, J. Appl. Meteorolog., 6, 644 (1967).
27. Application of Meteorology to Safety at Nuclear Plants, Safety Series, No. 29, IAEA, Vienna (1968).
28. N. E. Artemova, At. tnerg., 36, No. 1, 32 (1974).
29. Yu. I. Moskalev et al., Concept of Biological Risk for the Effect of Ionizing Radiation [in Russian],
Atomizdat, Moscow (1973).
30. Radiosensitivity and Spatial Distribution of Dose (ICRP Publication 14) [Russian translation], Atom-
izdat, Moscow (1974).
31. Recent Advances in Nuclear Medicine, New York-London (1974).
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CONTEMPORARY TRENDS IN EXPERIMENTAL
SHIELDING PHYSICS RESEARCH
V. P. Mashkovich and S. G. Tsypin
UDC 621.039-78
The contribution of experimental research to the solution of problems in the physics of shielding
against radiations has been decreasing in the last few years in comparison with theoretical and computa-
tional research. This change can be traced, for example, in [1,2]. Thus 60% of the papers in the 1969
Symposium were devoted to calculational research, while in 1974 the number was 85%.
Moreover, the limitations of theoretical methods require experimental confirmation of the computa-
tional methods and the set of constants assumed. At the present time a number of problems cannot be
solved by computational means because of limitations of the methods.
Contemporary experimental research in shielding physics is characterized by: 1) differentiation of
the information obtained; 2) more and more attention to complex geometries (multidimensional and hetero-
geneous shields); 3) shift of some of the best understood parts of shielding to engineering practice.
All such experimental research can be divided into two groups: research on verifying computational
methods and sets of interaction constants, which we call reference point research; mock-up experiments for
solving problems which at the present time cannot be solved by computational means because of limitations
in the computational methods or difficulties of the model representation. With the development of reference
point experiments the statement that "calculation gives the necessary information ? experiment the ref-
ence point" is becoming more and more valid.
The following are the most interesting reference point experiments on which experimentalists should
concentrate their attention.
1) Basic experiments (benchmark type experiments). They should be performed under "clean,"
standard, very elementary conditions. At the present time it is desirable to perform basic ex-
periments in multidimensional geometries.
2) Simulated experiments on actual nuclear-industrial installations such as reactors and accelera-
tors to estimate the quality of the computational techniques under actual conditions. These mea-
surements enable one to correct the methods and to introduce correction factors into the results
of the calculations.
3) Full-scale experiments on actual nuclear-industrial installations. These experiments test the
computational methods for solving the most complicated problems of making real shields. Full-
scale experiments become much more complicated with increasing dimensionality of the geometry.
This generally requires idealizing the problem, which in turn requires careful experimental testing
of the admissibility of the assumed idealization and a determination of the errors introduced by
such an idealization.
The main trends in radiation shielding research at the present time are listed below.
1. The Development of Theoretical Methods and Computer Programs for Calculating Distributions
of Ionizing Radiations. In recent years special attention has been paid to the development of the Monte-
Carlo method and the method of discrete ordinates. The complex of one-dimensional ROZ programs and
the multi-group RADUGA program for two-dimensional reactor shield calculations form a good basis for
solving many shielding physics problems. The MD and MDA methods are successful modifications of the
Translated from Atomnaya gnergiya, Vol. 38, No. 6, pp. 398-400, June, 1975. Original article sub-
mitted January 8, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Monte-Carlo method for calculating radiation fields. By using these methods radiation fields can be suc-
cessfully predicted at large distances from sources, even at earth?air and vacuum?air boundaries.
It is gratifying thatprograms have appeared which satisfactorily predict distributions of high-energy
particles and electrons. Computer programs have been developed for calculating radiation fields in in-
homogeneous media such as shields with multisectional channels and voids, and for nonstationary problems.
2. Accumulation of Experimental and Computational Information on the Shaping of Radiation Fields
in Shields. Specialized facilities have been built to study shields. A large amount of work has been done in
building various experimental arrangements at reactors and charged particle accelerators. Converters
for neutrons of various energies are interesting and seem promising for experimental research on reactor
problems.
Gamma ray distributions have been investigated. A number of studies have been made of the spatial,
angular, and energy distributions of gamma radiation for one-dimensional shield geometry. Interesting
work has been done on the time dependence of radiation fields from pulsed gamma sources, and on deep
penetration problems, mainly for elementary sources. Studies have been made of neutron and capture
gamma distributions. Extensive information has been accumulated on the shaping of distributions of neu-
trons of various energies, including intermediate energies, and on capture gamma radiation in various
media.
Gamma and neutron distributions have been studied in air and at earth?air and vacuum?air bound-
aries. These studies are distinguished by the systematic nature of the data and the performance of experi-
ments at large distances from sources of various energies, including low-energy gamma sources.
Research on shielding high-energy particle accelerators has progressed considerably. The dif-
ferential and integral characteristics of electrons beyond thick barriers have been studied intensively.
The study of albedos of gamma rays and neutrons from isotopic and reactor sources is largely com-
plete. The problems of determining the characteristics of quasialbedo radiation have been studied to a
lesser degree.
The penetration of radiations through shield inhomogeneities has been investigated: computational
methods based on the use of constants for the macroscopic interaction of radiation with matter are well
developed. Channels of basic shapes for radiations of various types and energies including intermediate
neutrons have been examined. Great efforts have been directed toward the study of the shielding charac-
teristics and radiation resistance of various concretes and structural materials which appear promising
for use in shields.
3. Studies of Nuclear Constants. Interesting work has recently been done on the preparation of
group constants and constants for calculations by the Monte-Carlo method. Many experimental investiga-
tions of the blocking of the resonance structure of the total group cross sections have been made. Interest-
ing studies have been made of the choice of nuclear constants for calculating secondary radiation, and the
effect of variations in the cross sections on neutron spectra. The problem of determining the nuclear con-
stants for the interaction of heavy charged particles with matter has been studied seriously.
4. Study of Shields of Actual Nuclear-Industrial Installations. The specialists have paid a great deal
of attention to reactor shields, to problems of the radiation safety of atomic power plants, the effectiveness
of the biological shielding, the study of radiation fields in atomic power plant rooms, the radiation shield
for refueling, and the prediction of the radiation shields required for maintenance and preventive inspec-
tions.
A number of problems in the physics of radiation shielding can now be considered essentially solved.
Various specialized test stands and facilities have been built and widely used in the Soviet Union. Thus a
large amount of important practical information has been obtained on an arrangement in the B-2 beam of
the BR-5 reactor [3], on a fission neutron converter [4] and an intermediate neutron converter [5] of the
BR-5 reactor, on test stands at the VVR-50 [6], the OR-M [6], and the RIZ [3].
We list the main problems for further theoretical and computational research in the physics of
shielding against ionizing radiations from nuclear-industrial installations.
I. The creation of complex efficient computer programs for calculating problems in the physics of radia-
tion shielding by using tested algorithms and programs for calculating radiation transport. Par-
ticular attention should be paid to the writing of programs for multidimensional geometries close
to shields around actual nuclear-industrial installations.
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2. The development of shield optimization programs which take account of primary and secondary
radiations. It is clear that these problems cannot be solved without programs which combine
various methods within the framework of a single program, in particular the Monte-Carlo and
discrete ordinates methods.
3. The development of new semiempirical methods and concepts for calculating biological shields
and predicting radiation fields in a shield and in the space surrounding it. These are convenient for
performing engineering calculations and making estimates.
4. Investigations of macroscopic shielding constants for the interaction of radiations with matter,
taking account of deep-penetration problems, and microscopic nuclear interaction constants.
We list the problems to be considered in completing these investigations.
Among the problems of shielding against ionizing radiations requiring further experimental research
are:
1. New experimental test stands and facilities using well-known radiation sources similar to those of
actual nuclear-industrial installations should be built for basic and simulated experiments.
2. Performing basic experiments to test the validity of computational methods and the sets of con-
stants used for the interaction of radiations with matter.
3. Conducting full-scale experiments on actual nuclear-industrial installations to improve the com-
putational methods and the design of biological shields. Special conditions must be provided for
such studies.
4. Performing basic experimental research on the penetration of radiations through heterogeneous
shields, the propagation of secondary and scattered radiations in media, the study of the energy
and dose compositions of radiations of different forms in shields, the problems of deep penetra-
tion, and the problems of shield optimization. The simulated and full-scale experiments should
include a study of the penetration of radiations through shield inhomogeneities.
5. The development and study of the properties of new, inexpensive, and promising heat- and radia-
tion-resistant shielding materials with good shielding, physical, and chemical characteristics.
The important problems of radiation shielding include a study of ways of increasing the effective-
ness and decreasing the cost of biological shields, the reliability of the shields around nuclear-industrial
installations, the solution of the problem of decreasing the radiation dose to atomic power plant personnel
during repair work, preventive inspections, etc.
The problems fisted in one degree or another are involved in the shielding of various nuclear-in-
dustrial installations ? sources of ionizing radiations ? and should be studied as they apply to nuclear
reactors of various classes and purposes, charged particle accelerators, irradiation facilities, devices
and apparatus with sources of ionizing radiation, etc.
It is satisfying to note that a large group of specialists in our country is working on the problems of
radiation safety. We look to this group for solutions of the problems posed.
LITERATURE CITED
1. Problems in Shielding against Penetrating Radiations from Reactor Installations. Collection. Vols.
1-7 [in Russian], SgV, Melekass (1969).
2. Abstracts of papers "Problems in the Physics of Shielding Atomic Power Plant Reactors" [in Rus-
sian], SEV, Moscow (1974).
3. Yu. A. Kazanskii et al., Physical Research in Reactor Shielding [in Russian], Atomizdat, Moscow
(1966).
4. V. P. Mashkovich et al., Atomnaya Energiya, 2, 125 (1967).
5. A. D. Lipunov etal., Atomnaya gnergiya, 6, 549 (1967).
6. V. G. Maleev et al., Paper presented at the first conference of specialists on problems of shielding
atomic power plants "Problems in the Physics of Shielding Atomic Power Plant Reactors" [in Rus-
sian], Moscow (1974).
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NUMERICAL SOLUTIONS OF THE KINETIC
EQUATION FOR REACTOR SHIELDING PROBLEMS
T. A. Germogenova UDC 621.039.51.12: 621.039.538
In recent years engineering calculations of shielding physics problems are being supplemented more
and more by transport theory computations. These furnish detailed accurate information on the spatial,
angular, and energy distributions of radiation fields in a reactor and shield. Radiation transport in a shield
is treated mathematically either by using the Monte Carlo method or by solving multigroup systems which
approximate the kinetic equation for radiation transport. Many numerical methods have been developed
for solving such systems. The present paper reviews these methods.
1. As a rule different degrees of accuracy and detail are required in describing radiation fields in
different parts of a shield and reactor. In a reactor the most important quantities are integral characteris-
tics such as ken., the breeding ratio, the spectral distribution of fluxes etc., while for a shield it is also
frequently necessary to know the angular distributions of the radiation fluxes.
By using the theorem on the equivalence of the solution of a boundary value problem for the multi-
group transport equations in the complete reactor-shield system and its solution for individual regions of
this system with corresponding boundary conditions [1], it is possible to reduce the original problem for a
large complex system to a somewhat simpler one. For individual regions of the shield such a boundary
value problem has the form
OF q,
ofczn
F n = nFn (In; (1)
OF,
(2)
Fnlin = [Fn lout] +q, FT in =lout] Pnv [FnI cut] ? Tv ?
Here Fn and FT are vector functions whose components describe the spatial and angular distributions of
fluxes in the corresponding groups; Fn and Ty are diagonal matrices with elements ?i(r) corresponding to
the total cross sections for the interaction of radiation with matter; 5'n En 7,a?d TY are tri-
angular matrices with elements corresponding to the integral scattering operators:
(EF)i = Eij(r, F (r. S2') do', OW.
The functions 7,i(r) and Fij (r, p5) are piecewise constant functions of r. The elements of the matrices
R in (2) are integral reflection coefficients (albedos), and the functions cpn and fp), describe the radiation
incident on the outer surface of the volume under consideration.
At the present time we are concerned mainly with numerical solutions of one- and two-dimensional
forward and adjoint problems. The algorithms and programs developed for solving such problems and
combinations of them by Monte Carlo methods, with perturbation theory for taking account of three-dimen-
sional effects, suffice for a broad circle of practical shielding physics problems.
2. Any numerical method for solving the multigroup system of equations (1) has two aspects: a
method for approximating the problem, and a method for solving the high-order linear algebraic system
arising in the approximation.
A successful approximation can be achieved only by understanding and taking correct account of the
qualitative behavior and the singularities of the solution related to the discontinuities of the coefficients
Translated from Atomnaya gnergiya, Vol. 38, No. 6, pp. 401-405, June, 1975. Original article sub-
mitted January 8, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Singularities of First Iterations in Problems with Concentrated Sources
Source
=
.2 point monodirectional,
VI 6 (t1 ? Slo) 6 (r ? ro)
8
...
.-.
P?int
distributed,
6(r ?r0)
line monodirectional,
6 (0 _ 0 a (s)8 (y)
line distributed,
6 (x) 6 (t)
plane mono-
directional,
6 (St ? (lo) 6 (z)
plane dis-
tributed,
6 (z)
r ?1'0 \
0 ileq6k1r?rol
i r ?1.0
Q)
e
2
e
z_
gez
?
nez 8 (S2 ? 00)
15(52--(20)xo(
ir?r0l
?()1
o
1/x2 -7 y2
142+ y2
ge2
?
_
nez
?
_
I r ? r0 12
Iir?r012?
i
? (r? r0, ft)2]-1. 2
In [ I r ?1'0 12-
- (r ? r0, 0)2]
in [(q)?(pa) 1/x2+y2]
?
1 ,
1/ 1 r ? 1.012 ? (r? ro. 96)2
2 In
(c ? Ton/x2+ Y2
VI r ? ro 12? (r ? rot no)2
in system (1) and the functions describing the radiation sources. These singularities of the solution cause
oscillations in finite-difference methods.
Discontinuities in the functions 97 and q are preserved only in the distribution of the unscattered
part of the radiation; the intensity of the scattered radiation is a smooth function. The singularities in the
intensity of the scattered radiation of the first few orders in problems with lumped sources [2] are given
in Table 1. Obviously the analytic elimination of the most essential singularities in such problems is most
effective.
Discontinuities in derivatives and in the solution itself arising from discontinuities in the coefficients
of the multigroup system (1) are more complicated. At boundaries separating different materials these
discontinuities are retained in the scattered radiation of all orders. Along straight lines tangent to the
boundaries the spatial and angular derivatives of the solution have singularities. If the curvature of the
surface is zero discontinuities in the solution itself arise along the corresponding tangents [3].
The analytical results obtained in the asymptotic study of a number of model problems play an im-
portant role in the development of computational methods in transport theory. Although such problems are
far from real, studying them on the one hand gives a qualitative idea of the solution, and on the other hand
enables one to construct tests to appraise the computational algorithms and check programs. This is very
complicated in real programs. Solutions of problems for infinite and semiinfinite media are widely used
for this purpose [4-6]. Recently certain successes have been achieved in constructing asymptotic formulas
in one- and two-dimensional one-group problems for bounded media.
In problems on the penetration of radiation through plane homogeneous and inhomogeneous layers of
finite thickness formulas have been found for the reflection and penetration of radiation and the conditions
inside the layer far from the boundaries. These formulas contain a number of one-dimensional functions
and parameters determined by the scattering indicatrix and the value of = Ts/i't [7-9]. These functions
and parameters are found from the numerical solution of one-dimensional integral equations. The accuracy
of the asymptotic formulas is adequate for a wide range of problems for layers several mean free paths
in thickness and increase rapidly with increasing layer thickness.
Some analytical results have been obtained recently in studies of two-dimensional one-group prob-
lems. Thus in the problem of a point source in a sufficiently thick slab the Wigner effect in the angular
distributions arising from multiple scattering was estimated. As a result of this effect a detector moved
along the surface of a slab records the maximum of the radiation intensity in a direction which does not
coincide with the direction of the source. There is a peculiar refraction of the radiation as a result of
multiple scattering. Theoretical estimates have been confirmed by a number of numerical calculations
(L. P. Bass et al.).
Lam and Leonard [10] have investigated certain properties of radiatton fields in multidimensional
models and have analyzed in detail the solution of the transport equation in the neighborhood of a boundary
surface of complex shape on the basis of the Milne problem for four-space.
3. In one-dimensional problems, particularly in problems with plane geometry, qualitative ideas of
local properties of the solution and its asymptotic behavior are widely used in an algebraic approximation
of the problem, both in finite-difference methods and in various semianalytic treatments. In the latter,
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auxiliary functions and parameters are ordinarily determined by using variational functionals of the problem
or various averages. The most used methods (discrete ordinates, spherical harmonics, Carlson, synthetic
etc.) are described in well-known monographs and summary articles [10-11]. However, the more compli-
cated the problem posed, i.e. the greater the demand for accuracy and detail in the information on the flux
distributions, the more complicated the geometrical and physical models, and correspondingly the simpler
the approximation methods that have to be used. Thus in determining the differential distributions of
neutrons and gamma rays in plane heterogeneous shields the method of discrete ordinates is the most
reliable, while in curvilinear one- and two-dimensional geometries the method of characteristics with
linear interpolation in which the singularities of the solution are taken into account in a natural way [12-14]
is preferred. The method of characteristics is stable for any ratio of stops, but because of linear inter-
polation it is only first order accurate.
The SN and DSN methods, based on the use of balance relations in the cells of the mesh, are second-
order accurate for smooth solutions and are generally simpler to use. As a rule they lead to instabilities
in the calculations, particularly often to oscillations in the angular distributions [15-17]. Various methods
have been proposed by a number of authors for eliminating the oscillations in quantities integral in the
angular variable. Among such methods we note the introduction of fictitious sources into the DSN equa-
tions approximating problem (1) and (2) to ensure that these equations are equivalent to the method of
spherical harmonics (DOPL method [18,191), and the use of variational principles to formulate various
schemes, in particular the method of finite elements [20].
It seems to us that in complex problems it is most expedient first to remove the singularities in the
solution, and to choose the form of approximation, in particular the shapes and sizes of the mesh cells, in
accord with the behavior of the solution, and then to use composite schemes which are first-order accurate
(the type used in the method of characteristics) along the "singular" straight lines with balance methods in
the regions where the solutions are smooth. Examples of such composite schemes are the BOX method
[21], the methods proposed in [22], and a combination of the "rhombic" scheme (second order) with the
"step" scheme (first order) [23].
While the theory of the method of characteristics is rather simple, estimates of the stability and
convergence of balance methods, and even more of combinations of different methods, are only in the
initial stage. As a rule authors make very rigid assumptions about the differential properties of the solu-
tions. These assumptions are not satisfied in real transport theory problems. However, we have ac-
cumulated considerable experience with numerical solutions of various boundary problems of the type (1),
(2).
4. As a result of approximation the original problems (1) and (2) are reduced to inhomogeneous
linear systems, generally of very high order p. In one-group one-dimensional problems p 103-104, and
in two-dimensional problems p 105-107. An iterative method is generally used to solve such systems.
In its primitive form this method, which corresponds to successively taking account of the fluxes of un-
scattered, singly scattered, doubly scattered etc. radiation, has been significantly improved in recent years
by the introduction of various methods for accelerating the convergence. Such methods are particularly
important for large regions where the simple iterative method converges very slowly. The most effective
methods alternate simple iteration with solutions of equations of lower dimensionality for average quanti-
ties appearing as correction factors (quasidiffusion and flux average methods [7]) or components (KR
methods [11]). The equations for these quantities are obtained by averaging over the angular variables of
problem (1) and (2), or by using appropriate variational functionals.
The proper choice of the parameters defining the mesh size and the duration of the iterative process
plays a fundamental role in the solution of practical problems. In shielding physics problems these para-
meters depend strongly on the class of problems, i.e. on the physical and geometrical models and on the
required accuracy in the differential distributions. As a rule the choice of parameters is based on intuitive
considerations. Recently, however, papers have appeared in which attempts were made to change from
intuition to quantitative rules. Thus V. A. Utkin examined a class of iron?water slab shields and studied
in detail the nature of the convergence of methods such as the method of discrete ordinates. Problems of
the accuracy of the 2PN approximations in one-velocity problems with various indicatrixes are discussed
in [24]
5. We have written two complexes of computer programs to solve the multigroup systems (1) and
(2): ROZ to calculate one-dimensional transport theory problems, and RADUGA to solve the two-dimen-
sional transport equations in axisymmetric systems. A large staff participated in the development of these
complexes.
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The methods of solution were chosen to yield high accuracy and detailed information on the spatial,
energy, and angular distributions of radiations. The algorithms used are based on the method of discrete
ordinates in plane geometry and the method of characteristics with interpolation in curvilinear geometries.
The finite-difference equations were solved by an iterative method with acceleration of convergence in
one-dimensional problems by the method of flux averages, and in two-dimensional problems by a quasi-
diffusion procedure.
Among the one-dimensional programs the ROZ-6 program has the broadest possibilities. It enables
one to treat various forward and adjoint problems: to calculate various functionals, derivatives of solutions
with respect to parameters, etc.
The apparatus of adjoint solutions can be used to lower the geometric dimensions of a problem to
dimensions determined by the properties of the medium and the character of the required functionals, in-
dependently of the form of the source. Thus a two-dimensional problem on determining the sensitivity of
a spherical detector is equivalent to a one-dimensional adjoint problem of a point isotropic source at the
center of the sphere.
This problem was solved by using a spherical variant of the 1OZ-1 program [25].
In contrast with the universal ROZ-6 program, which is suitable for solving a very broad class of
shielding physics problems, the ROZ-7 and ROZ-8 programs were designed to solve special problems.
The ROZ-7 program (M. V. Vyrskii) was written to calculate multilayer slab shields in the age-diffusion
approximation with a very large number of nodes in the energy variable. The ROZ-8 program (N. V.
Konovalov) was used to calculate asymptotic parameters and functions and the resulting distributions of
radiation in thick multilayer slab shields in the one-velocity approximation with very broad assumptions
about the scattering and absorption characteristics.
The complex of RADUGA programs was written as a modulator system for a BESM-6 computer to
generate programs for solving axisymmetric problems of the type (1) and (2) in heterogeneous cylindrical
regions for arbitrary irradiation conditions and internal source distributions. The variety of geometrical
models, source shapes, types of boundary conditions, and elementary types of interaction of radiation with
matter necessitate extremely complex and diverse algorithms for calculating radiation fields in such sys-
tems. The algorithms are combinations of independent elementary parts of basic elements. A specified
set of basic elements determines the content of the algorithm, and the memory_parameters fix its scale.
The important features ensuring high efficiency of specific programs are the hierarchy of equations for
taking account of various qualitative properties of the solution at various levels, and an algorithm for the
storage of parameters making possible a wide variation in mesh size.
The RADUGA systems uses a library of basic elements and a library of input parameters and mathe-
matical information for the BESM-6 computer [26]. The ROZ and RADUGA complexes were used in solving
many shielding-physics problems. The results of a number of calculations have been reported in the litera-
ture. An important feature in preparing for calculations is the specification of group constants determining
the coefficients in problem (1), (2). The well-known ARAMAKO [27] and OBRAZ [28] programs for cal-
culating constants are being added to the ROZ and RADUGA complexes.
LITERATURE CITED
1. T. A. Germogenova et al., Neutron Albedo [in Russian], Atomizdat, Moscow (1973).
2. T. A. Germogenova, Preprint No. 23 [in Russian], Institute of Applied Mathematics, AN SSSR (1971).
3. T. A. Germogenova, Dokl. Akad. Nauk SSSR, 187, 18 (1969).
4. M. Maslennikov, Atomic Energy Rev., 5, 59 (1967).
5. K. Case and P. Zweifel, Linear Transport Theory, Addison?Wesley, Reading (1967).
6. V. V. Sobolev, The Scattering of Light in Planetary Atmospheres [in Russian], Nauka, Moscow (1972).
7. T. A. Germogenova et al., The Transport of Fast Neutrons in Slab Shields [in Russian], Atomizdat,
Moscow (1971).
8. T. A. Germogenova and N. V. Konovalov, Zh. Vychisl. Mat. i Mat. Fiz., 14, 928 (1974).
9. N. V. Konovalov, Preprint No. 65 [in Russian], Institute of Applied Mathematics; AN SSSR (1974).
10. S. Lam and A. Leonard, Transport Theory and Statistical Physics, Vol. 3, No. 1 (1973).
11. G. I. Marchuk and V. I. Lebedev, Numerical Methods in the Theory of Neutron Transport [in Russian],
Atomizdat, Moscow (1972).
12. Handbook on Radiation Shielding for Engineers [in Russian], Vol. 1, Atomizdat, Moscow (1972), p.84.
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13. T. A. Germogenova and L. P. Bass, in: Problems in the Physics of Reactor Shielding [in Russian],
No. 3, Atomizdat, Moscow (1969), p. 69.
14. K. Takenchi and A. Jamaji, in: Proceedings of the Fourth International Conference on Reactor Shield-
ing, Vol. 2, Paris (1972), p. 339.
15. V. Rankin et al., JQSRT, 11, 949 (1971).
16. K. Lathrop, Nucl. Sci. and Engn., 45, No. 3 (1971).
17. W. Reed, Nucl. Sci. and Engng., 46, 309 (1971).
18. J. Jung et al., Nucl. Sci. and Engng., 49, 1 (1972).
19. J. Jung et al., Nucl. Sci and Engng., 53, 355 (1974).
20. W. Miller et al., Nucl. Sci. and Engng., 52, 12 (1973).
21. J. Arkuszewski et al., Nucl. Sci. and Engng., 49, 20 (1972).
22. V. Ya. Gol'din et al., Zh. Vychisl. Mat. i Mat. Fiz., 5, No. 5 (1965).
23. K. Lathrop, J. Comput. Phys., 4, 475 (1969).
24. Sh. S. Nikolaishvili and V. P. POlivanskii, in: Problems in the Physics of Reactor Shielding [in Rus-
sian], No. 5, Atomizdat, Moscow, p. 47; Yu. K. Shchekin, Izv. AN BSSR, Ser. Fiz. i inerget., No. 2
(1971).
25. V. A. Utkin, in: Problems in the Physics of Reactor Shielding [in Russian], No. 6, Atomizdat (1974),
p. 150.
26. L. P. Bass et al., Preprint No. 11 [in Russian], Institute of Applied Mathematics, AN SSSR (1973).
27. V. F. Khokhlov et al., in: Nuclear Constants [in Russian], No. 8, Part 3, TsNII Atominform (1972),
p.
3
28. V. F. Khokhlov et al., Nuclear Constants [in Russian], No. 8, Part 4, TsNII Atominform (1972),
p. 154.
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BOOK REVIEWS
Yu. A. Egorova (editor)
PROBLEMS OF THE PHYSICS OF REACTOR SHIELDING*
Reviewed by B. R. Bergel' son
It is more than 10 years since the collection "Problems of the Physics of Reactor Shielding" was
published. In it questions are reflected concerning the problems of shielding nuclear-technological installa-
tions from radioactive radiations. The data contained in the six issues of the collection are obviously of in-
terest to engineers and scientific workers working in the most diverse branches of science and technology.
In four sections of the sixth edition, more than 30 papers are assembled.
In the first section, devoted to the theory of radiation transfer and methods of calculating shielding,
the papers of a team fruitfully working under the direction of T. A. Germogenova are traditionally presented.
Among them, the most interesting is a paper in which the advantages are discussed of a method of sub-
groups for calculating the resonance structure of the neutron cross-sections. In the two papers by V. G.
Zolotukhin et al., the possibilities of the Monte Carlo method are shown for calculations of the radiation
field at large distances from the source and during the passage of 7-radiation through curved channels.
Two papers are devoted to practical methods of calculation and to the problem of shielding optimization.
A nonstandard approach to the problem is demonstrated in the paper by E. E. Petrov and B. L. Shemetko,
in which the authors used the device of small perturbation theory in order to determine the radiation
scattered by screens of small thickness.
In the second section, the results of the experimental investigation of different shields are recounted
and in the third section, a paper with a methodological leaning. Amongst these papers may be mentioned
the paper by A. L. Barinov et al., concerning the results of a detailed measurement of the absolute fluxes
and spectra of the fast neutrons in front of and behind the hull of the VVER-440 reactor and the paper by
V. I. Avaev and E. P. Efimov, devoted to the inadequately developed problem of determining radiation
energy releases in metal structures in those caseswhen the 7-emission spectrum is formed in the surround-
ing light medium. The paper by V. V. Bolyatko etal. is interesting, in which the passage of neutrons of
intermediate energy through shielding with inhomogeneities is investigated.
In the fourth section of the collection, there are three papers devoted to an investigation of concretes
as materials for the biological shield of reactors.
Usually, in experimental papers devoted to the measurement of the spectrum of radiation which has
passed through shielding screens, the conditions of the experiment are not discussed completely: the
geometry, source and detector characteristics. This complicates or even makes impossible the use of the
results of the experiment by a wide circle of readers for solving other problems and for verifying com-
putational programs.
These publications frequently are found to be useful mainly only for a small circle of workers. In
this sense, some experimental papers described in this collection are no exception.
At the recently constituted All-Union Conference on Shielding from Ionizing Radiations, many parti-
cipants spoke of the necessity for carrying out so-called test-experiments, according to the results of
which comparisons of the numerous computational programs might be undertaken. It can be hoped that,
in the near future, these experiments will be carried out and their results, with a detailed description of
the experimental conditions, will be published in subsequent issues of the collection.
*Atomizdat, Moscow, 1974.
Translated from Atomnaya gnergiya, Vol. 38, No. 6, p. 405, June, 1975.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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In conclusion, the editorial board of the collection, during preparations for the publication of new
issues may desire to attract a wider circle of authors, by informing them beforehand of the issues being
prepared.
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ARTICLES
PROBLEMS OF SECONDARY GAMMA RADIATION
IN REACTOR SHIELDS
A. A. Abagyan, T. A. Germogenova,
A. A. Dubinin, V. I. Zhuravlev,
V. A. Klimanov, E. I. Kostin,
V. P. Mashkovich, V. K. Sakharov,
and V. A. Utkin
UDC 621.039.534.7
A nuclear reactor shield is a complex system of materials of low atomic numbers to attenuate neu-
trons, and materials of high atomic numbers to attenuate gamma rays. Both heterogeneous and homo-
geneous mixtures of heavy and light materials occur in a real shield. To minimize the total shield weight
the heavy component of the shield must be placed close to the core. As a rule the shielding layers close
to the core consist of metal neutron shields, which leads to the production of intense secondary gamma
radiation.
The radiation environment outside a reactor shield is frequently determined completely by secondary
gamma radiation. Knowledge of the characteristics and rules of its propagation in a medium enable one to
0 250 500
x, g/cm2
Fig. 1 Fig. 2
Fig. 1. Relative doses of capture gamma radiation: ----) neutron
source with a fission spectrum; ?) neutron source with a fission
spectrum for E > 2.5 MeV and a 1/E spectrum for E < 2.5 MeV; 1)
water; 2) zirconium hydride; 3) concrete; 4) tungsten; 5) iron; 6)lead.
Fig. 2. Relative heat deposition of capture gamma radiation (notation
same as in Fig. 1): 1) water, 2) zirconium hydride; 3)iron; 4) lead.
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 406-409, June, 1975. Original article sub-
mitted January 8, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Shield Thickness for which D'Y
= Dn for a Neutron Source with a Fission
Spectrum
Material
ID, C111
50
LiH
67
H20
36
H20+1 wt. %
54
90
C+1 wt. % B
100
choose the optimum location of shielding layers close to
the core and in more distant regions. Therefore the
study of the characteristics of secondary gamma radia-
tion is very important in the reactor shielding problem.
This problem has been the subject of considerable
experimental and theoretical research. However, most
of the papers, the basic results of which are described
in [1,2], do not describe the fields of secondary gamma
radiation over the whole range of energies, and there-
fore the published data cannot always be used in calcula-
tions.
The purpose of the present article is to present a systematic investigation of certain general princi-
ples of the production, escape, and propagation of secondary gamma radiation in a shield on the basis of
experimental and computational data on the differential and integral characteristics of secondary gamma
radiation in a broad selection of shielding materials for various neutron spectra. The calculations were
peformed with the ROZ-5 program [3,4]. The neutron flux density in the q-th energy group cI)g(x, p) and
the gamma flux density in the i-th energy group Cy(x, p) are determined as functions of the coordinate x
and the angle 0 = cos-ip for plane one-dimensional geometry and azimuthal symmetry by the system of
equations
with the boundary conditions
Q ?1
2,'(x) 07, (X, 2 C dp,'(.13/71 (x, ft') g (x, u' -4- ;
(x)(rol, (x, u) = d0Dj(x, ft') q (x, )t' p.)
E sq- (x) dp.' (D7,(x, ?')
{
014, (x, 1.1) == 0)7,00i)
(Di,,(x, 0,,o.
r, (x, 0
(x,,)=0
for x=0 and >0;
for x --= Hand ? < O.
Here Eq and pi are the group averaged macroscopic cross sections for the interaction of neutrons and
gamma rays with matter; gP ?qand gj? i are the neutron and gamma ray scattering indicatrixes; 5q?
is the yield of gamma rays of group i in the interaction of neutrons of group q with matter. The ROZ-5
program solves the equations presented by the method of characteristics. The finite difference equations
are solved by an iterative technique using the method of nonlinear acceleration of convergence [5]. A com-
parison of the calculated and experimental results showed that the ROZ-5 program gives adequate ac-
curacy. The maximum divergences are 25% in the integral and about 40% in the differential characteristics
of the radiation field [6].
In the present paper we consider the relative characteristics of capture gamma rays beyond shield-
ing layers of various materials, defined as the ratio of the functionals resulting from capture gamma rays
to the functionals resulting from neutrons. For heavy shields those characteristics are practically in-
dependent of the angular distribution of neutrons at the inside of the shield for a broad class of azimuthally
symmetric angular distributions of the neutron sources, and therefore the basic information was obtained
for infinite plane monodirectional sources.
Abagyan et al. [5] investigated the effect on the fluxes of secondary gamma radiation in a tungsten
slab shield of taking account of the dependence of the capture gamma spectrum on the energy of the ab-
sorbed neutrons. They found that the relative characteristics of capture gamma rays differ by 30-40%
from the values calculated by using the spectrum of gamma rays accompanying thermal neutron capture
for all neutron groups. In addition the analysis of the original data showed that the total gamma energy
emitted in the radiative capture of neutrons with energies in the range 10-100 keV differed by just such
an amount from the energy of the gamma rays emitted in the radiative capture of thermal neutrons. It can
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X, g/cm2
Fig. 3 Fig. 4
Fig. 3. Doses of capture gamma radiation from the irradiation of a
slab by a unit current of neutrons having a fission spectrum. The
notation on the curves is the same as in Fig. 1.
Fig. 4. Relative doses of secondary gamma radiation: ----) capture
gamma radiation from a neutron source with a fission spectrum;
?) capture gamma radiation from a neutron source having a fission
spectrum for E > 2.5 MeV and a 1/E spectrum for E < 2.5 MeV;
--?-) gamma radiation accompanying the inelastic scattering of
neutrons from a source having a fission spectrum; 1) iron; 2) lead.
be assumed that the main inaccuracies in the calculation of the integral characteristics of capture gamma
radiation at the exit from a layer of heavy shielding material are due to the error in taking account of the
contribution to the capture gamma radiation of the various isotopes of a mixture of isotopes.
The rules for the production and escape of capture gamma radiation are of a completely different
character for light and heavy shield materials. Light shielding materials are typically characterized by a
strong dependence of the relative characteristics of the capture gamma rays on the neutron spectrum at
the inside of the shield. The relative characteristics in the first approximation are inversely proportional
to the fraction of fast neutrons in the source spectrum. All the relative characteristics of capture gamma
rays (relative dose, flux, heat deposition) increase exponentially with the increase in thickness of a layer
of light shielding material and for a certain thickness / become larger than unity. Naturally this thickness
depends on the form of the functional, the shielding material, and the neutron spectrum at the inside of the
shield. It is smaller the softer the neutron source spectrum.
Table 1 lists values of the thickness of the layer of light shielding material /13 for which the capture
gamma dose rate is equal to the neutron dose rate just outside a slab irradiated by neutrons having a
fission spectrum.
The fission spectrum is one of the hardest spectra encountered in reactor shielding calculations, and
light materials, which effectively attenuate the neutron flux, have little effect on the gamma radiation.
Therefore the values of 1D listed in the table determine approximately the maximum thickness of the outer-
most shielding layer of light material.
In heavy materials, in contrast with light materials, the neutron spectrum is not established until the
layer is thick, and the gamma radiation is strongly attenuated by the material. These features of heavy
materials cause all the relative characteristics of the capture gamma rays in media with a large atomic
weight either to decrease with the thickness of the shielding layer (for a soft initial neutron spectrum) or ?
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to increase with the thickness of the shielding layer (for a hard initial neutron spectrum) but much more
slowly in comparison with the corresponding characteristics for light media. A peculiarity of the relative
characteristics (Figs. 1 and 2) is the convergence of their values corresponding to different neutron source
spectra as the layer thickness is increased. This convergence is different for different materials and is
determined largely by the value of the radiative capture cross section.
Materials having both heavy and hydrogen nuclei in their composition (metal hydrides, concretes) are
similar to light shielding materials from the point of view of shaping the neutron spectrum, but unlike
light materials they have large gamma absorption cross sections. The transport of gamma radiation in
these materials is similar to that in heavy materials, and the gamma field at any point in the medium is
determined largely by the gamma sources in the immediate vicinity. It is typical of heavy hydrogenous
materials that the realtive characteristics of capture gamma radiation increase with the layer thickness
for all types of neutron spectra at the inside of the shield, but this increase is appreciably slower than in
light shielding materials.
An analysis of the relative (Figs. 1 and 2) and absolute (Fig. 3) values of the characteristics of
capture gamma radiation for various shielding materials leads to the conclusion that the best materials from
the point of view of minimum escape of capture gamma radiation are heavy hydrogeneous materials. Lead
is the best of the heavy nonhydrogeneous materials. The choice of any other material for a heavy shield
is determined by the neutron spectrum at the inside of the shielding layer and the required thickness of
this layer.
Studies were also made of the contribution to the various functionals of secondary gamma radiation
from the inelastic scattering of neutrons in iron and lead. As can be seen from Fig. 4 this radiation makes
an appreciable contribution to the characteristics only for hard initial neutron spectra and thin shielding
layers. However, in sufficiently thick layers of materials such as lead with a small radiative capture cross
section over the whole range of neutron energies, the contribution of inelastic scattering gammas can be
comparable with that of capture gammas.
The differential characteristics of capture gamma radiation are also significantly different for light
and heavy media. The energy spectrum of capture gamma radiation in light materials is complex. It is
continuously deformed as the thickness of the shielding layer is increased, and for thicknesses greater
than 40 g/cm2 it has the same shape as in an infinite medium. It is typical of heavy materials that the
gamma spectrum varies slowly with increasing shield thickness. The shape of the gamma spectrum in
such shields is similar to that resulting from the radiative capture of neutrons from a source having a
soft spectrum, since multiply scattered gammas make a small contribution. The angular distribution of
capture gamma rays at exit from a shielding layer of light material is strongly anisotropic and varies with
the layer thickness. In heavy materials the angular distribution is significantly less anisotropic and varies
slowly with the layer thickness.
LITERATURE CITED
1. Yu. A. Kazanskii et al., Physical Investigations of Reactor Shields [in Russian], Atomizdat, Moscow
(1966)
2. D. I. Broder, K. K. Popkov, and S. M. Rubanov, A Compact Reactor Shield [in Russian], Atornizdat,
Moscow (1967).
3. T. A. Germogenova, A. P. Suvorov and V. A. Utkin, in: Problems in the Physics of Reactor Shielding,
No. 2 [in Russian], Atomizdat, Moscow (1966), p. 22.
4. V. I. Zhuravlev et al., The Solution of the Transport Equation in Slab Problems (ROZ-5 Program),
Part 1 [in Russian], Preprint IPM SSSR (1972).
5. A. A. Abagyan et al., Fourth International Conference on Reactor Shielding, Paris, October 9-13,
1972, Paper No. 13-2, 18.
6. A. A. Abagyan et al., in: Abstracts of papers of the All-Union Scientific Conference on Shielding
against Ionizing Radiations from Nuclear-Industrial Installations [in Russian], MIFI, Moscow (1974),
p. 28.
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ABSTRACTS
EFFECT OF PROTON IRRADIATION ON THE
OPERATION OF A SCINTILLATION COUNTER
B. V. Gubinskii, E. M. Iovenko,
V. A. Kuz'min, V. G. Mikutskii,
and V. N. Nikolaev
UDC 539.1.074.3
The effects of proton irradiation (Ep = 18 MeV, flux = 6.1019 and 6.109 cm-2, density 2 -104 cm-2
.sec-1 and E = 360 MeV, 43 = 105, 8 -106, and 1.46 -107 cm-2, density 1.05 -105 cm-2 -sec-1) on an NaI(T1)
crystal were studied.
The changes taking place in the counting characteristics, the differential spectrum, and the position
of the photopeak corresponding to the y-radiation of 137Cs (recorded before and after irradiation of the
crystal) were estimated. The original counting characteristics were determined for an energy-discrimina-
tion threshold of U = 20, 40, and 60 keV.
Figures 1 and 2 show the counting characteristics measured before and a time bt after irradiation of
the crystals and the character of the changes taking place in these characteristics respectively.
10
12
? 10
8
?
2 I t
1200 1400 1600 1800
Uphotomult? V
N ? 103, pulses/sec
1200
1400
1600
1800
Uphotomult? V
Fig. 1 Fig. 2
Fig. 1. Counting characteristics of an FEU-70 + Nal(T1) scintillation counter
before and after irradiation of the crystals: IP) characteristics before irradia-
tion 0) At = 6 min, Ep = 360 MeV, 43 = 8.106 cm-2, Ug = 40 keV (No. 580); x)
At = 6 min, Ep = 360 MeV, 1 = 106 cm-2, Ug = 40 keV (No. 592); A) At = 4 min,
E = 100 MeV, 4) = 4.1 -10-7 cm-2 Ug = 20 keV (No. 624); 0) At = 8 min, Ep
= 18 MeV, 4) = 6 -109 cm-2, Ug = 40 keV (No. 712).
Fig. 2. Counting characteristics of an FEU-70 + Nal(T1) scintillation counter
obtained at various times At after the irradiation of crystal No. 605 with 300
MeV protons at a flux of 1.46 -107cm-2: 0) original; 0, ?, A, x) At = 8; 35; 80;
270 min respectively.
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 411-417, June, 1975.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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Analysis of the resultant data shows that after proton irradiation the most important change which
occurs in the counting characteristic is an upward displacement of the latter. This may be associated with
the development of induced activity (characterized by the emission of 7-quanta and fl-particles with a mean
energy of the order of 1 MeV and a mean half life of 30-40 min) in the crystal and the sheath around it. The
radioactive nuclei arising in the crystal may be identified, for example, on the basis of the probability of
star formation at the heavy and light nuclei under the influence of the protons. These nuclei include 1221,
1211, 128sb, 125sn, 123sn, 24Na, 18F, 29A1, 120s.
Thus for the irradiation fluxes studied the change in the slope of the plateau is very slight, and has
no serious effect on the operation of the scintillation counter. The counting error associated with irradia-
tion diminishes with time and is no greater than about 5% some 2-3h after the end of irradiation, depending
on the particular sample. The change fluctuates considerably for different crystal samples.
Original article submitted March 27, 1974
EXPERIMENTAL DETERMINATION OF THE
TEMPERATURE DEPENDENCE OF THE THERMAL
CONDUCTIVITY OF URANIUM DIOXIDE UNDER
CONDITIONS OF REACTOR IRRADIATION
B. V. Samsonov, Yu. G. Spiridonov, UDC 621.039.542.34(063)
N. A. Fomin, and V. A. Tsykanov
Experimental data relating to a determination of the thermal conductivity of uranium dioxide at 0-
2800?C based on the radial heat-flow method are presented. The measurements were carried out on fuel-
element samples containing compact uranium dioxide with a density of 10.4-10.7 g/cm3 and an oxygen coef-
ficient of 2.01?0.01 V in a stainless steel can 32.5 x 1 mm in diameter. The temperature of the surface
and center of the core were measured with VR5/VR20 thermocouples calibrated over the whole range of
working temperatures. In order to find X (T) at temperatures above 2300?C, i.e., after the central thermo-
couple had failed, experiments were carried out using a molten central zone of the fuel, with correspond-
ing analysis after removal from the reactor.
The power of the fuel element was determined calorimetrically, using a calibrated electric heater.
The depression of the neutron flux in the fuel elements was found from the fission density measured with
90%-enriched metallic uranium indicators. The distribution of the neutron flux with respect to the height
of the fuel element was determined from the activation of copper indicators.
We found that in the temperature range 0-2800?C the thermal conductivity of uranium dioxide was
described to an error no greater than 5% by the equation
55

(T)? 560+T +0.942.10-i2T3, w Acm ? ?C).
The resultant X (T) relationship is recommended for use in thermophysical calculations of fuel ele-
ments based on compact uranium dioxide fuel made by the technology employed for VVER-440 reactors.
Original article submitted April 21, 1974
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MECHANICAL STRENGTH OF URANIUM
FIELD-EMITTERS
A. L.
D. M.
A. F.
B. V.
Suvorov, G. M
Skorov, B. A.
Bobkov, V. A.
Sharov, and G
. Kukavadze,
Kali a,
Fedorchenko,
. N. Shishkin
UDC 535.82: 546.791
The mechanical properties of thin acicular tungsten and a-uranium samples were studied with the
aid of a field-emission ion microscope. The chief aim was to determine the limiting strength and the mode
of deformation of the uranium samples; the experiments with tungsten were treated as standards. The
samples were loaded directly in the field-emission microscope, using the strong electric field required
to form images of the sample surfaces. The technique of preparing the uranium field-emission samples
was described in [1]. Since one cause of sample deformation and rupture in the field-emission microscope
was the asymmetry of the sample, the sample profiles were carefully monitored, first in the optical micro-
scope, and after field-emission ion-microscope analysis in the electron microscope.
Rupture of the samples was indicated by a sharp change in the contrast of the field-emission ion
image (or the complete disappearance of the latter). Calculation of the stresses aK corresponding to
rupture was based on the equation a = F2/8r, where F is the electric field strength, proportional to the
sample potential. The resultant crK values for tungsten and a-uranium were respectively (1.31 ? 0.15) ?1019
and (1.13 0.20) .1010 Ni m-2
(sample orientiation along the [011] and [010] directions respectively). The
mean diameters of the samples were ?1000 A. The tungsten samples analyzed numbered 18 and the
uranium 10 (altogether 50 uranium samples were examined in various imaging gases; only eight were
ruptured by the field). The corresponding value of ok for tungsten obtained in [2] using an analogous
technique was (2.06 ? 0.18) ?1019 N/m2, which agrees with the results of the present investigation within the
limits of experimental error.
The values of the normal stresses ao in the samples on imaging in various imaging gases are pre-
sented in Table 1, together with the corresponding deformations e.
A comparison between the theoretical strengths UT of tungsten and a-uranium calculated from the
equation UT = riG, where ?I = 0.133 from [3], G is the shear modulus (for tungsten G = 14.85.109, for a-
uranium G = 7.35.109 N/m2) shows that these are respectively 1.98 .109 and 0.97 .109 N/m2. Thus the re-
sults here obtained lend weight to the assertion that the true theoretical strength is realized in such
crystals (whiskers); this situation is promising from the point of view of verifying theory and also for the
extensive practical use of the whiskers for example, as a base for modern composite materials.
TABLE 1. Calculated Values of Various Parameters
Imaging gas
F0 b/A
oo, N /m2
8, %
a-U
H2, Ar
2,2
2,1.108
0,63
1,9
Ne
3,5
5,3.108
1,6
4,8
He
4,4
8,4.108
2,5
7,5
Evaporation mode
5,7 (W)
4,35 (a-U)
1,41.108 (W)
8,2.108 (a-U)
4,2
7,4
LITERATURE CITED
1. A. L. Suvorov et al., At. t nerg., 36, No. 1, 14 (1974).
2. It. I. Garber, Zh. I. Dranova, and I. M. Mikhailovskii, Dokl. Akad. Nauk SSSR, 174, 1044 (1967).
3. J. Hirth, Relative Structure and Mechanical Properties of Metals, Vol. 1, London (1963), p. 218.
Original article submitted July 1, 1974
revision submitted January 28, 1975
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DOSE DISTRIBUTION IN A TISSUE-EQUIVALENT
MEDIUM FROM A PLANE THIN ISOTROPIC
ALPHA-PARTICLE SOURCE
D. P. Osanov, V. P. Panova, UDC 621.039.538.7
Yu. N. Podsevalov, and E. B. Ershov
A general method is presented for calculating the dose distribution in a tissue-equivalent medium
from a plane thin isotropic source of alpha particles of energy E0 s 9 MeV having a surface source strength
a.
The dose rate at point A (Fig. 1) due to all alpha particles reaching it with residual energy between
0 and E(x) is
E (x)
P (x)? k e dN ( ) dE dE,
dE
where N(x) is the flux density of alpha particles at depth x, and the conversion factor k depends on the
choice of units. It is obvious that dN(x) = (a/2)(pdp/r2) = (a/ 2)(dr/r). Then
E (x) E (x)
dE
P (x)?kLY- = k C
2 r (E) 2 .1 R,(E0)? R (E) '
0 0
(1)
(2)
where R(E0) and R(E) are respectively the total and residual alpha particle ranges.
Equation (2) can also be derived by starting from the definition of dose rate as the derivative of the
energy flux density with respect to the depth of the absorber P(x) dW/clx. The determination of the dose
function P(x) is reduced to the correct determination of R(E) for a tissue-equivalent material.
We have found that our results on the energy dependence of alpha particle ranges in a tissue-equi-
valent material and the data cited in the literature are best approximated by the expressions
By substituting (3) into (2) and integrating
P
p Ca [In
f R (E)=-- 6,3E, 0 < E < 3.5 MeV;
R (E)=-- 13.5E ?25.5, 3.5 < E [R 1.L;
R (Et') R (E c, ?22)
0.471n 22],
; 7 x < [R (E0)?
Here c = 28(rad/min).(cm2/pCi), a is in pCi/cm2, and x and r are in p.
The accuracy of Eq. (4) was tested experimentally for 239Pu alpha particles. The dose distribution
from a plane thin alpha particle source in direct contact with a tissue-equivalent absorber was determined
Fig. 1. Diagram for deriva-
tion of formula.
(rad/min)/(?Ci/cm2
80
70
50
50
40
30
20
10
0 5 10 15 20 25 3035 x, p
Fig. 2. Comparison of calculated (Eq.
(4)) and measured dose distributions for
239PU alpha particles: 0) semiconductor
detector; 41) scintillation detector.
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by measuring the spectrum of alpha particles (dN(x)/(dE))(E)penetratingvarious depths (x) of the absorber.
The measurements were made with a silicon semiconductor surface barrier detector and a CsI(T1) scintilla-
tion crystal 70p thick on a light pipe. The energy resolution for 5.14 MeV alpha particles was 2.2% for the
semiconductor and 6% for the scintillation spectrometer.
The total energy release rate W(x) behind an absorber of thickness x was determined by the measured
functions (dN(x)/(dE))(E)
E (x)
w (x) s= dN (x)
(E)E dE.
j dE
(5)
It is clear that P(x) = ?dW(x)/dx.
The calculated and experimental results are in good agreement (Fig. 2). Thus the absorbed dose
rate in biological tissues from plane thin sources of alpha particles of energy E0 5 9 MeV can be calculated
from Eq. (4) using the alpha particle ranges given by (3). The error in determining the dose rate does not
exceed 15%.
The dose rate in tissue-equivalent material from a thick tissue-equivalent alpha particle source can
be calculated from Eq. (4) by using the method described earlier.
LITERATURE CITED
1. D. P. Osanov et al., Meditsinskaya Radiologiya, 5, 44 (1971).
Original article submitted August 19, 1974
RECOVERY OF THE INTEGRATED SPECTRUM OF
NEUTRONS IN THE ENERGY RANGE 0.1-3 MeV
BY THE EXTRAPOLATION METHOD
R. D. Vasil'ev, E. I. Grigor'ev, UDC 621.039.57
G. B. Tarnovskii, and V. P. Yaryna
The proposed extrapolation method of recovering the integrated spectrum of neutrons in the range
0.1-3 MeV is based on the use of, first, experimental information on the spectrum of neutrons in the range
0.5-3 MeV obtained by means of a collection of threshold detectors and, second, a priori information on
the used spectrum in the range 0.1-3 MeV, which makes it possible to extrapolate the spectrum into the
region in which information is not available.
The integrated spectrum was recovered by an approximation by the method of least squares. An
optimal approximating function was obtained: g(E) = 0> E(E)/cps (where 0>E(E) is the energy dependence
of the integrated neutron flux density; 'vs is the integrated flux density of neutrons with energy greater than
the effective reaction threshold 32S (n,p)32P) in the form g(E) = alf(E) + a2, where af and a2 are parameters
which must be determined; f(E) is a function specified with allowance for the reactor type as follows: for
the fields of a water-moderated water-cooled reactor f(E) = exp (-0.8 E), for the fields of graphite and
heavy-water reactors and also for neutron fields with gNp > 11 and gNp < 6
f (E) =exp [ ? (1g E 2.2)2 ?0.15],
and for the remaining cases
0.04(g ?7,5)2-0.35
f exp (-0.8E) E
here, the neutron energy is expressed in megaelectron volts; gNp = q Np/vs corresponds to the reaction
237Np (n,f).
For measurements, one is recommended to use the neutron activation sets developed and supplied
by the All-Union Scientific Research Institute of Physicotechnical and Radiotechnical Measurements. These
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include five "detector?source" activation sets: 133Rh-241Am in a cadmium screen. 115In-51Cr, 1931Ig-133Ce,
58Ni-58Co, 32S-32P and one "detector?detector of fission fragments" fissile set: 237Np?mica.
We investigated the problem of determining the error of the spectral coefficient g(0,1) for the energy
0.1 MeV and formulas are given for its calculation.
The main advantage of the extrapolation method is that it ensures a correct result when a spectrum
is recovered on the basis of little information. This is confirmed by comparison of the results of measure-
ments obtained by this method and other methods for different types of static and pulse reactors. At the
present time, the extrapolation method has been standardized and is used to solve applied problems of
solid-state physics.
Original article submitted August 19, 1974
DETERMINATION OF TRACES OF NITROGEN IN
PURE METALS BY GAMMA ACTIVATION
A. F. Goreriko, ?A. S. Zadvornyi, UDC 539.172.3: 543.064: 621.039.32
A. P. Klyucharev, and N. A. Skakun
The most sensitive method available at the present time for determining the mean content of nitrogen
impurities in representative samples (5-10g) of various pure Metals is 7-activation analysis. After ir-
radiation of the samples the radioactive isotope 13N is separated, this being the product of the nuclear reac-
tion 14N(7, n)13N (Ti/ 2 = 10.1 min, p?); selective deposition and a measurement of the isotope activity
follows. In this operatirin the influence of activities induced in other impurities and the matrix by the y=
irradiation is eliminated.
Samples of Be, Y, V, and Nb were irradiated with T-quanta obtained by the retardation of 25 MeV
electrons (at a current of 18? A) in a tungsten converter 2 mm thibk. The metals were packed in aluminum
cans and transported to and from the irradiation site by pneumatic post. A standard with a known N con-
tent waa irradiated at the same time as the samples.
The 13N isotope was separated from the irradiated samples and standards in a furnace at T = 1200'C.
Using a helium flow, the 13N and other gases were passed to a zeolite trap cooled with liquid nitrogen. In
the path of the flow was a solid-particle filter followed by copper shavings heated to 500C in which the
nitrogen oxides were deoxidized. Absorption of halides took place over silver shavings heated to 350?C.
The activity deposited in the zeolite was recorded by means of a fast--slow coincidence scintillation
spectrometer with an efficiency of 1-2%, The absorption of 11C1502 took place in ascarite. The efficiency
of the absorption of 13N from the gas flow passing through the zeolite was almost 100%.
The following traces of nitrogen were found (wt.%): Be (10-3-10-5), Nb 10-3, Y 10-5 and V ? 10-3.
These characteristics of the method influencing the accuracy and reproducibility of the results are dis-
cussed.
Original article submitted September 24, 1974
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MICROSCOPIC DISTRIBUTION OF IONIZATION
EVENTS IN AN IRRADIATED MEDIUM AS A
CHARACTERISTIC OF THE QUALITY OF
IONIZING RADIATION
I. B. Keirim-Markus, A. K. Savinskii, UDC 539.12.08
and I. V. Filyushkin
The traditional way of characterizing the quality of the radiation by the average linear energy loss of
charged particles (L) is today recognized as inadequate [1]. In this connection, one seeks new parameters
and functions which more adequately describe the spatial distribution of energy transferred to a medium.
Of the functions of such kind one already knows the radial distribution of the energy transferred to the
medium in the tracks of charged particles [2], which in contrast to the linear energy loss gives an idea of
the two-dimensional spatial distribution of the transferred energy.
As a further characteristic one can take the spatial microdistribution of events of ionization (excita-
tion) in the irradiated medium, which enables one to take into account the volume distribution of the trans-
ferred energy in small regions within the track.
One seeks the average distribution (or mathematical expectation) of the initial distances between the
ionization (excitation) events when a charged particle passes through the medium. The required distribu-
tion AP ( p , E) is the conditional probability of finding an ionization eventin unit volume of a thin spherical
layer of radius p with center coinciding with an arbitrary ionization event. It can be represented in the
form
(' 1 2n
AP (p, E)? L (E) rD (r, E)D (p, E, r) dr ? (E) (E , E,5) (Ea) rD (r, E6)
j
0 E 0
? x7/5(p, E6, r) dr dEo,
(1)
where E and L(E) are the energy and linear energy loss of the charged particle; D(r,E) is the value of the
radial distribution of the transferred energy of the particle at distance r from the track axis; D(p, E,r)
is the mean value of the radial distribution of the transferred energy on a sphere of radius p with center
at distance r from the track axis (the same notation with E replaced by E6 applies to 6 electrons); f(E,
E(5) is the spectrum of the 6 electrons generated by the first particle in all generations.
Calculations of AP ( p , E) for particles with effective charge Z* from 1 to 8 and energies up to 100
MeV showed in particular that the function th( p) = 4irp2AP(p, E) depends solely on the ratio of the effective
charge of the particle to its velocity, Z*43. In Fig. 1 these functions are shown for a set of values of the
parameter.
9
8
7
6
5
4
3
2
530
Fig. 1. Microdistribution of dis-
tances between events in the tracks
of charged particles of arbitrary
species and energy in a tissue-
equivalent medium.
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It follows from geometrical arguments that th(p) 2L(E) as p (we ignore the variation of L along
the track). In this connection, the function th(p)/2L(E) for large p must become equal to unity. It can be
seen from the figure that indeed 1Np) = 1 for p 300 A, i.e., at such distances the proposed characteristic
of the quality of the radiation no longer gives additional information compared with the linear energy loss.
At shorter distances, down to interatomic distances, the required distribution is different for dif-
ferent particles and is determined by the parameter Z*/i3.
The distribution 0(p)/2L(E) at distances ?16 A has a maximum, whose value is the larger, the
smaller is Z*//3. This form of the function is due to the contribution of the concentration of ionization
events in the cloud of i5 electrons which surround the core of the charged particle's track.
This distribution together with the existing linear energy loss and radial distribution of the trans-
ferred energy can serve as an additional characteristic of the quality of the radiation when one considers
radiation events characterized by interaction lengths 300 A.
LITERATURE CITED
1. ICRU, Rep. No. 16, Washington (1970).
2. I. K. Kalugina et al., At. gnerg., 34, No. 4, 298 (1973).
Original article submitted January 24, 1974
ALLOWANCE FOR FLUCTUATIONS IN THE
IRRADIATION DOSE OF LUNGS BY HIGHLY
ACTIVE PARTICLES
0. M. Zaraev and B. N. Rakhmanov UDC 621.039.7
In real conditions one observes cases when several or just one highly active aerosol particle is re-
tained in the breathing organs. The existing methods enable one to calculate the dose averaged over a
large number of individuals. To choose a "risk criterion" of internal irradiation in such situations one
requires the distribution of doses within individuals.
To estimate the potential danger of radioactive aerosols one must take into account two independent
processes: 1) aerosol particles reaching the windpipe and being retained in different parts of the breathing
organs; 2) the removal of aerosol particles from the breathing organs.
In the development of a method of probabilistic estimation of doses of internal irradiation it was as-
sumed, first, that the "history" of each particle Is independent of the "history" of the other particles and,
second, the material is removed dynamically, i.e., the rate of removal is proportional to the amount of
retained material. If n particles are retained in the breathing organs, the probability of their being re-
moved in time tn is
10-1
104
rc-4
1D-7
10-8
mr" 10.6 10 102 10 102
a, rel.units
Fig. 1. Maximal irradiation dose of a
lung for which the probability of being
exceeded is 0.05% for different da,?:
1) 0.4; 2) 0.8; 3) 1.0; 4) 2.0; 5) 4.0; 6)
6.0; 7) 8.0; 8) 10.0.
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? (Art)n i -Ant
(n?I)! n
where A is the constant for the removal of the radioisotope from the breathing organs. With a probability
of 99.95% one can assert that the removal time of one particle exceeds by not more than 7.6 times the
average removal time of the same amount of radioactive material uniformly distributed among many
particles. The mathematical model developed applies to any organ from which the removal is described
by an exponential law.
As the risk criterion when a relatively small number of radioactive particles get into the breathing
organs one must evidently take the so-called local absorbed dose, i.e., the radiation energy absorbed in
1 g of the irradiated tissue. The radiation danger cannot be estimated by the formal comparison of this
dose with the maximally allowed dose since the latter is essentially the tissue average, i.e., it refers to
unit mass of the complete organ.
In this connection, it is desirable to determine the tissue-averaged absorbed doses from radioactive
particles calculated on the basis of the one-component variant of the exponential model of their removal
with effective constant Aeff and with allowance for the statistical nature of the processes of arrival and
removal of the aerosol particles.
The processes of deposition and removal of the particles are independent. The probability that the
mean-tissue dose absorbed in part j of the breathing system after the inhaling of an aerosol during time
T with mean number N of particles that arrive is the quantity D, equal to
V (D)-= Ecoj (n) 147? (D),
where (0j (n) ? ("C'PJ)ThexP(-7'Pv) characterizes the process of inhaling of the particles and their deposition
it!
n--1
in part j of the breathing system; w ?Poqi (Dn-1)!
,i(D)= exp(?XeffD/Piqi) characterizes the process of removal
of the particles; D is the maximal irradiation dose of the lung; Pi is the probability of deposition of a
particle in part j of the breathing system; Pi is the power of the mean-tissue dose from a source with
activity 11iCi; qi is the activity of one particle.
The average dose adsorbed in part j of the breathing system is
i
.c DV PTVPjqt
(D)dD?
'eff ?
0
Here, D does not depend on the number of retained particles but is entirely determined by the total amount
of the radioisotope retained in part j.
Figure 1 shows universal curves which enable one to calculate the maximal irradiation dose of the
breathing organs of an individual as a function of the number of radioisotopes that arrive averaged for the
complete contingent of workers. For convenience, Q and Dmax are given in relative units a and b, which
are related to the corresponding absolute values through the parameters of the aerosol particles by
VI3
Dmax = b rem.
VT' Xeff
The linear sections of these dependences correspond to the arrival amounts at which the fluctuation
of the doses has no practical importance.
Original article submitted January 31, 1975
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LETTERS TO THE EDITOR
CALCULATION OF HETEROGENEOUS NUCLEAR
REACTORS BY THE METHOD OF
INSERTED ELEMENTS
I. S. Slesarev and A. M. Sirotkin UDC 539.125.52:621.039.51.12
With the appearance of computers, finite-difference schemes are widely used in reactor calculations.
However, difficulties in their application to calculations of nuclear reactor models which are complex in
composition, have led to the development of variational-difference methods which are suitable for the cal-
culation of more realistic models [1]. A general approach is given below to the construction of a sufficiently
versatile scheme of reactor calculation, which is suitable both from the point of view both of knowledge of
the reactor composition and of the improvement of the local approximation and increase of the asymptotic
convergence of the algorithm. By using the proposed method, the possibility emerges for the effective cal-
culation of a reactor with an almost arbitrary disposition and geometry of its zones.
In the majority of cases, the nuclear reactor model can be represented in the form of a system con-
sisting of arbitrarily disposed zones of quite simple geometrical shape. We designate as a reactor element
the phase volume of space variables bounded by some external surface. In particular, the boundaries of
the element can be the boundary of the zones. A zone is the simplest element. Thus, the reactor consists
of elements inserted one in the other (see Fig. 1). We shall assume the outside element to be dominant
in relation to the element completely inserted in it. The insertion of element n in m is equivalent to the
subordination of the first element to the element m. Elements which do not have a common volume are
assumed to be independent. Suppose that the neutron field 4, in the reactor is described by a diffusion
equation with zero boundary conditions at the outer surface of the reactor. In order to construct a scheme
for calculation, we shall use the variational formulation of the problem [1], which consists in the require-
ments of extremal properties of the functional, obtained by taking account of the starting equation. In dif-
fusion problems, the solution belongs to a class of continuous functions with a continuous derivative Dr(d4,r
/dn) at the inside boundaries, where D(r) is the step-continuous coefficient of diffusion.
It is obvious that the solution of the problem of quasicritical distribution of neutrons in a reactor
can be represented in the form of a sum of sufficiently continuous functions, defined inside each of the
elements and vanishing at their boundaries. We represent the approximate solution of the problem in the
form of a set of polynomials. We shall assume that to the outside element n = 0, an arbitrary polynomial
Po is assigned, which satisfies the zero boundary conditions at the boundary of this element and coincides
with the boundary of the reactor. In each element n = 1, 2,... we define an additional polynomial Pn, not
identically equal to zero only inside this element and vanishing at its boundary. The solution of the start-
ing equation inside the element n will be found in the form ftn = Po +...+Pn so that in the composition of
chn in addition to Pn are included polynomials of those elements which are subordinate to element n. This
construction, first of all, leaves the solution continuous for any degree of approximation and takes account
of the possible discontinuities of the derivatives; secondly, it permits local inhomogeneities in the solution
to be described effectively, and which originate because of the change of properties in a heterogeneous
reactor; thirdly, it preserves the generality of the structure of the scheme in all practically important
cases.
In constructing the polynomials Pn with the properties mentioned (and, consequently, also of the co-
ordinate functions [1]) the following approach is recommended. Functions of the type Wn = con(x, y,...)xa
.343 are chosen as ordinate functions, where cen is a positive continuous function within the element n,
having bounded and continuous partial derivatives and satisfying the conditions
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 419-420, June, 1975. Original article sub-
mitted April 22, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
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0 b5 10 20 r, cm
Fig. 1. Quasicritical neutron distribution
in a reactor consisting of two elements.
1) Principal element (active zone, a = 50
cm); 2) subordinate element (rod, b = 5
cm); 1.x. is the precise solution of the
problem.
grad ca? 0; co (x, y, ...)=0 for x, y, ? ? ? E
where r n is the boundary of the element n. There exist
[2] simple general rules of construction of the function
w for elements of different geometrical shape, which per-
mits a reactor of complex construction to be calculated.
A proof of the completeness of the chosen type of coordi-
nate functions can be found in [2].
The asymptotic convergence of variational methods
of the type being discussed depends to a strong degree on
the continuity of the solution. Traditional direct methods
under these conditions have a slow convergence. The
special method of constructing the coordinate functions in
the method of inserted elements permits the class of
functions to be expanded only by selecting the coefficients
being varied. Hence, a higher asymptotic rate of con-
vergence results, which is characteristic of this me-
thod.
Let us consider the structure of the matrix operators originating during the calculation of the reactor.
A system of equations can be obtained for the unknown coefficients A with the coordinate functions W in the
Kn
polynomials Pn = "F, AWi by using the extremal properties of the functional and the chosen coordinate
functions (Kn is the number of unknown parameters Aj in the element n). It will have the form
I1A= ,
Ken.
The independence of a part of the elements leads to discharging of the matrix with zeros and, as a con-
sequence, to its better conditionality. The singularities of the matrix structure permit the problem of its
transformation for solving the problem to be simplified.
When approximating the solution with power series, the quantities representing integrals of the co-
ordinate functions with the operators of the equation and forming the matrices R and B, can be calculated
a priori and included in the composition of some library, if the geometry of the elements and their neutron-
physical properties are known. The possibility of creating a library gives appreciable advantages in solv-
ing the problem on a computer: it dispenses with the necessity of carrying out a large volume of calcula-
tions during integration of the coordinate functions.
The inherent form of the setting-up of the reactor composition is characteristic for the method of
inserted elements. The setting-up procedure can be formalized by analogy with the block structure used
in machine languages of the ALGOL type.
The proposed method, based on the special structure of the coordinate functions used, permit the
accuracy of the calculation of the neutron distribution in any part of the reactor to be locally increased (in
accordance with an accurate geometric form of the elements) without the necessity of increasing the ac-
curacy (and, this means, also the difficulties of the calculation) in the entire reactor, which is characteris-
tic with combined methods.
In order to illustrate the possibilities of the method, we shall consider the simplest problem of
calculating a one-dimensional reactor with a cylindrical active zone, at the center of which is positioned
an absorbing rod (see Fig. 1). The characteristics of the zones in one-group approximation are: diffusion
coefficients Da .z = 2 cm; Drod = 0.5 cm; absorption cross-section Za.z = 0.005 cm-I; Erod = 0.03 cm-1;
secondary neutron generation cross-sectionvrf,a.z= 0.01 cm-1. The accurate value for the neutron multi-
plication factor (with rod) is keff = 0.95, and the efficiency of the rod is Akeff = 8.65%. These same char-
acteristics were calculated by means of the algorithms of the traditional Ritz method (TRM) and the method
of inserted elements (MIE). In the TRM-method, the neutron distribution was found in the form do TRm
= (a2?z2) (A0
+ Air +...). In this case, the problems are solved in the two simplest approximations with
one (c1 1TRM ) and two (( TRM 2 ) unknown coefficients Ao and Al. The error in estimating Lskeff varied from
33% for 4,1 to 30% for 0.75 MeV and P = 9.9.105
R/sec, permitted transient changes to be detected, equal to +26?C for chromel?alumel and ?16?C for
tungsten?rhenium (VR-5/20) thermocouples. The measurements were carried out at the setting point of
aluminum [5].
In all the experiments to determine the transient changes of thermo-e.m.f., a calibration of the
thermocouple was carried out immediately at the instant of irradiation at the temperature of intensive an-
nealing of the radiation defects formed and with low radiation (-1017-1018 n/cm2). The amount of radiation
defects in the crystal structure of the thermoelectrodes formed in this case, conditioned by the action of
the neutron irradiation, is very insignificant (< 0.01% at.) and cannot be the source of the transient changes
in the thermo-e.m.f.
One source of transient thermo-e.m.f. changes may be induced currents in the thermocouple loops.
These currents are due to free charges originating at the electrodes and in the measurement lines, in con-
sequence of electrons knocked out of the thermoelectrodes and the thermocouple sheath by 'y-quanta. With
an unfortunate choice of the measurement circuit, the induced current will distort the useful signal of the
thermocouple. The induced current is independent of the time of irradiation but is proportional to the y -
radiation intensity.
TABLE 1. Thermoelectric Characteristics of Thermocouples r
,oth = 1.44 -1014 n/(cm2
?sec); ?fas 1.75 .1013 n/(cm2.sec), for En 7-1-- 1.15 MeV]
t
Integrated neutron flux density, n
/cm
Eav, my
Tay, 't
Tmean square, *C
Cycle
thermal
fast
5,2.1017
6,3.1016
17,350
1086
0,35
Setting
1,4.1018
1,26.1017
17,385
1089
0,38
0
1,56.1018
1,89.1017
17,275
1082
2,25
Melting
2,08.1018
2,52.1017
17,348
1086
0,20
Setting
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 420-422, June, 1975. Original article sub-
mitted May 13, 1974; revision submitted December 13, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
536
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0
1,5
1,0
0,5
130
120
0- 0 0,5 ,0 r, sec 1180 5
Fig. 1 Fig. 2
Fig. 1. Induced current in KTMS-2 x 0.2 (chromel?alumel) cable. The dashed
curve is the intensity profile (Q).
2
0
t x
0
?
?
0
10
sec
Fig. 2. Calibration of thermocouples at the setting point of the alloy 44.5%
Pb + 55.5% Bi: ?) VR-5/20: x) Chromel?alumel; 0) chromel?Copel.
The induced current for a thermocouple cable of KTMS-2 x 0.2 (chromel?alumel) was measured in
the IRO reactor [6] at a ,'-radiation dose intensity of P = 3 -106 R /sec and (p 1015n/(cm2 -sec) (fast and
thermal neutrons). Its magnitude was ?0.1 pA (Fig. 1). Depending on the choice of the measurement
circuit, the induced thermo-em.f. due to this current, will distort the useful thermocouple signal. For
example, for a thermocouple made from KTMS-2 x 0.2 (chromel?alumel) cable, with an insulated working
junction and using a measuring device with a grounded input, the induced thermo-e,m.f. of chromel?alumel,
chromel?Copel and VR-5/20 thermocouples were also measured at a temperature of 125?C (the setting
point of the eutectic alloy 44.5% Pb + 55.5% Bi), 5 2.1014 n/(cm2.sec) (fast and slow neutrons) and P = 5
?105 R/ sec.
The results of the measurement of the thermo-e.m.f. of the thermocouples are shown in Fig. 2. It
can be seen from the figure that a temperature, constant in time, corresponding to the alloy setting cycle,
was observed for some time during operation of the reactor, but the thermo-e.m.f. of the thermocouple
increased somewhat with the appearance of radiation (up to 30pV for VR-5/20 and up to 400 pV for chromel
?Copel thermocouples). The increase of the thermo-e.m.f. of the thermocouples investigated in the
presence of radiation can be explained by local heating of the working junctions of the thermocouples, due
to the absorption of y-radiation. The calculation showed that this heating may amount to 3 to 5?C with a
spatial energy release in Kh18N1OT steel equal to ?108 W/m3.
Calibration of the VR-5/20 thermocouples was carried out at the melting (setting) point of copper.
The construction of the thermocouples investigated was: diameter of thermoelectrodes 0.2 mm; insulation
? alundum; sheath ? molybdenum and tantalum, with diameter 0.8 mm; the working junction was made con-
current with the sheath. The experimental results are shown in Table 1 [at the melting (setting) point of
copper, 1083C].
It can be seen from the table, that the readings of all thermocouples, within the limits of error of the
temperature measurement (1%), corresponded to the handbook value of the melting (setting) point of copper.
Thus, in the experiments carried out by the authors, the contribution of transient changes in the
thermoelectric characteristics of thermocouples did not exceed magnitudes which lie within the limits of
the standard variance of calibration variations, established by GOST.
LITERATURE CITED
1. R. Carrol and P. Reagon, ORNL-p-1066 (1965).
2. W. Strum and R. Jonnes, Rev. Sci. Instrum., 25, 392.
3. G. Dau,R.Bourassa, and S. Kuton, Nucl. Appl., 5, No. 5 (1968).
537
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4. G. Bianchi and S. Moretti, Energ. Nucl., 11, No. 8 (1964).
5. N. V. Markina, B. V. Samsonov, and V. A. Tsykanov, Fizika Metallov i Metallovedenie, 32, No. 4
(1971).
6. I. V. Kurchathy et al., Third Geneva Conference, Report No. 322a [in Russian] (1970).
538
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OXIDATION OF SOLID SOLUTIONS OF URANIUM
AND NIOBIUM MONOCARBIDES
V. G. Vlasov, V. A. Alabushev, UDC 546.261(791+ 882):546.21
and A. R. Beketov
Data hitherto published [1] provide a reasonable account of the behavior of uranium carbide contain-
ing refractory carbides in air, but offer no conclusions regarding the actual mechanism of the oxidation pro-
cess.
In this paper we shall present the results of an investigation into the oxidation of UC?NbC solid solu-
tions at 300-1100'C for oxygen pressures from 3.6 to 20.2 mm Hg. The characteristics of the original sam-
ples are given in Table 1.
TABLE 1. Physicochemical Properties of
the Original Samples
Values of the coefficients in
the formula UxNhyCz
11
0,69
0,31
0,56
0,44
0,33
0,67
0,08
0,92
0,01
0,99
Weight gain, mg/g
Pycnometric
density, g
/cm3
Lattice
parameters,
A
0,97
1,00
0,99
1,00
1,00
11,42
10,41
9,40
8,19
7,81
4,805
4,592
4,505
4,477
20 40 60 80 100 120
Time, min
Fig. 1
The preparation of the samples, the determination
of the proportions of their components, and the experi-
mental methods involved were described in [2-8]. The
impurity content of the present set lay within the limits
of analytical accuracy. The single-phase character of
the samples was monitored by x-ray diffraction and
metallographic analysis.
It was initially established that, for niobium carbide
contents of less than 30 mol. %, the alloys ignited spon-
taneously, so that it was impossible to study the oxida-
tionkinetics of uranium carbide with low NbC contents.
140
120
wo
bo
00
E 8o
bo 69
20
20 40 60 80 MO MO
Time, min
Fig. 2
Fig. 1. Oxidation isotherms (400?C) of carbide solid solutions of the following compo-
sitions: U0.56Nb0.44C1.00; A) U0.08Nb0.92C1.00; x) U0.01Nb0.99C1.00.
Fig. 2. Oxidation isotherms (900?C) of carbide solid solutions of the following compo-
sitions: 0) U0.69Nb0.31C0.97; 0) U0.56Nb0.44C1.00; x) U0.33Nb0.67C0?99; A) U0.08Nb0.92C1.00; A)
tr0.01Nb0.99C1.00.
Translated from Atomnaya gnergiya, Vol. 38, No. 6, pp. 422-425, June, 1975. Original article sub-
mitted June 17, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
539
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
Weight gain, mg /g
20 40 60 80 100 120
Time, mm
Fig. 3
Fig. 3. Oxidation isotherms of samples with the
P02 = 7.2 mm Hg: 0) 300; 41) 400; A) 500; A) 600;
x) 1100?C.
Fig. 4. Effect of a change in oxygen pressure on the oxidation of samples of com-
position U0.33Nb0.07C0.99 at 600?C for various degrees of oxidation, mg/g: 0) 5; x)
10; A) 20; *) 30.
ig.v
48
46
44
0,2
0
?42
?44
46
0,8
1,0
Fig. 4
composition U0.33Nb0.87C0.88 for
0) 700; 40) 800; II) 900; +) 1000;
1,2 19 Paz
The principal results of our investigations into the oxidation kinetics of UC?NbC solid solution at
400-900'C are presented in Figs. 1 and 2. It follows from the results presented that the influence of the
alloying additive depends not only on its concentration but also on the temperature. Whereas at 900?C a
change in the NbC concentration from 31 to 67 mol.% has hardly any effect on the corrosion resistance of
the alloy, at 400?C this only applies to NbC contents of no greater than 44 mol.%. The corrosion resistance
of the samples increases considerably for high NbC concentrations and relatively intensive levels of oxida-
tion (at 900'C, for example, in the case of more than 20 mg/g oxidation).
Figure 3 illustrates the influence of temperature on the oxidation of samples of composition U0,33-
Nb0.07C0.97 at 300-1100?C for an oxygen pressure of 7.2 mm Hg. For samples of other compositions the
kinetic relationships are analogous. We may distinguish two temperature ranges: 300-800?C, in which the
temperature coefficient is positive, and 800-1100?C, in which it is either negative or zero. This latter is
characteristic of the oxidation of solid solutions containing more than 50 wt.% NbC.
The values of the apparent activation energy determined for all compositions of the solid solutions
studied and for various oxygen pressures fluctuate from 12 to 16 kcal/mole.
The influence of oxygen pressure on the oxidation rate was studied for samples of composition
U0.33Nb0.67 C0.99 (Fig. 4). At 600?C an increase in the oxygen pressure accelerated the reaction in accordance
with the equation
V = kP02,
where V is the velocity of the reaction, k is a certain constant, P02 is the gas pressure, n is the power
index. We see from Fig. 4 that the power index changes during the reaction. For degrees of oxidation
equal to 5, 10, and 20 mg/g, n = 1; for 30 mg/g, n = 1.3. At 900?C for an oxygen pressure of under 7.2 mm
Hg, n = 1; for higher pressures n = 0.22.
The oxide phases were identified by metallogra.phic and x-ray analysis. Figures 5 and 6 illustrate
diffraction recordings of the oxide layers formed on samples of compositions U0.08Nb0.92C1oo; U0.33Nb0.67-
C0.99. Solution of the diffraction patterns shows that the introduction of oxygen into the lattice of the mixed
carbide leads to phase separation of the solid solution, with the formation of uranium and niobium oxy-
carbides. Poorly-crystallized niobium pentoxide appears after the formation of large quantities of UO2 and
U308. On the background of the diffuse N13205 peaks we find peaks of an unknown phase; identification of
this phase based on the data presented in [9] showed that it might belong to the niobium suboxides, in
particular NbOx. A crystalline Nb205 phase is formed in the initial stages of the process at temperatures
of over 600?C. At 800?C and over the first oxide layer contains the phases Nb02,UO2, Nb205 but not U308.
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N
U., 0
0 ?C)
.1
,,,, .4,..j4 - 0 2 _s.
'' - 2
? c
It
c14
et; cr
j?-,
ILA)
40
310
20
10 8
a
0
* N
cs,
50 40 JO 20
Fig. 5 Fig. 6
Fig. 5. Diffraction recordings of the oxide layers formed on samples of Composition
U0.33N0.67C0.99: a) original sample; b) powder flaking off at 300?C; c), d),e) substrate under
the oxide layer at 400, 500, and 600?C; f) top sintered oxide layer at 800?C.
Fig. 6. Diffraction recordings of the oxide layers on samples of composition U0.88Nb0.92-
C1.00: a) original sample; b), c) oxide film with a violet tint at 400 and 500?C; d) oxide
film of green color at 500'C.
Increasing the amount of NbC in the alloy opposes the rupture of the samples. In the fracture sur-
face of samples oxidized at temperatures above 800?C several layers may be distinguished. At the top
there is usually a sintered oxide layer of violet color, adjacent to a black, compact film, under which lie
layers exhibiting interference colors.
DISCUSSION OF RESULTS
Oxidation of UC?NbC solid solutions starts with the adsorption of oxygen and the formation of ura-
nium and niobium oxycarbides on the surface. The introduction of oxygen atoms into the lattice of the
solid solution is accompanied by the release of an equivalent amount of free carbon. Subsequent attach-
ment of oxygen leads to the preferential oxidation of the uranium oxycarbide, with the formation of UO2 and
U308. The niobium oxycarbide is stabler with respect to oxygen, and oxidizes at later stages in the pro-
cess. The great corrosion resistance of niobium oxycarbide is evidently associated with the formation of
niobium suboxides of variable composition on its surface. On the basis of metallographic and x-ray
analyses, it is reasonable to assume that the Nb2O5 phase is formed directly from the suboxides, by-pass-
ing other stable lower oxides. During the oxidation of the mixed uranium and niobium carbides in the tem-
perature and oxygen-pressure ranges under consideration, a scale consisting of individual phases (uranium
and niobium oxides) is formed; this appears especially for low NbC contents and relatively low tempera-
tures. In this case self-ignition of the samples occurs as a result of the low protective properties of the
scale, all the more so in view of the fact that, at the boundaries of the adjacent oxide phases, the sample
is almost unprotected from the direct action of the oxygen. At high temperatures the niobium suboxides
are unstable, and the difference between the rates of formation of Nb2O5 and the uranium oxides is negli-
gible. As a result of this, a layer of oxide of uniform thickness is formed, and the conditions for the self-
ignition of the samples are no longer operative.
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At 600?C and over, the carbon in the scale interacts with the oxygen. The change in the index n of the
equation as the oxidation process develops, and also the results of chemical analysis show that intensive
combustion of the carbon takes place as the degree of oxidation increases, since a thick layer of scale de-
velops, preventing the access of oxygen to the phase interface, so that the combustion of the carbon be-
comes the preferred reaction.
At 800?C and over, the scale sinters, the degree of sintering increasing with temperature. The
sintered oxide film impedes the access of oxygen to the surface of the oxidized sample and the release of
the gaseous reaction products CO and CO2 from the latter. Carbon monoxide and amorphous carbon in the
oxide layers promote reduction reactions at elevated temperatures. This may well explain the appearance
of lower niobium oxides and the absence of the uranium mixed oxide from the scale, as well as the reduc-
tion in the total rate of oxidation with rising temperature. The phase U308 only appears at the final stages
of the process.
Since the value of the apparent activation energy depends little on the composition of the solid solu-
tion, the degree of oxidation, and the oxygen pressure, it is reasonable to assume that the rate of oxidation
is in all cases determined by the supply of the oxidizing gas through the porous scale, i.e., the formation of
the oxide takes place at the boundary of the carbide as a result of the preferential diffusion of oxygen
through the scale.
LITERATURE CITED
1. Physicochemistry of Alloys and Refractory Compounds Containing Thorium and Uranium [in Russian],
Nauka, Moscow (1968).
2. V. A. Alabushev, Candidate's Dissertation [in Russian], Ural. Poli. Inst., Sverdlovsk (1974).
3. V. A. Vlasov et al., At. gnerg., 36, No. 3, 207 (1974).
4. B. V. Linchevskii, Technique of Metallurgical Experiments [in Russian], Metallurgiya, Moscow
(1967).
5. H. Mailer, High-Purity Gases [Russian translation], Mir, Moscow (1968).
6. V. S. Saltykova et al., Methods of Complete Chemical Analysis for Complex Rare-Metal Minerals
[in Russian], Nauka, Moscow (1972).
7. P. Ya. Yakovlev, Determination of Carbon in Metals [in Russian], Metallurgiya, Moscow (1972).
8. V. K. Markov et al., Uranium, Methods of Its Determination [in Russian], Atomizdat, Moscow (1964).
9. I. I. Kornilov et al., Interaction of Refractory Metals of the Transition Groups with Oxygen [in Rus-
sian], Nauka, Moscow (1967).
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
SPECTRAL CHARACTERISTICS OF THE BACKGROUND
NOISE IN THE PRIMARY LOOP OF AN ATOMIC
GENERATING PLANT
K. A. Adamenkov, V.1. Gorbachev,
Yu. V. Zakharov, V. P. Kruglov,
S. A. Paraev, Yu. A. Reznikov,
and R. F. Khasyanov
UDC 621.039.564.2
An important prequisite to the application of the acoustic emission method [1-3] for the nondestruc-
tive testing of equipment is the determination of the frequency range in which the acoustic emission signals
are reliably recorded when background noise is present in the testpiece and its auxiliary equipment. We
have studied the background noise in the VVER-440 III section of the Novovoronezh atomic electric power
Ill
my:
Ill
8
9
10
11
f, mHz
Fig. 1 Fig. 2
Fig. 1. Schematic of piezoelectric transducer. 1) Testpiece; 2)
connector; 3) cover; 4) casing; 5) conductor; 6) adjusting nut; 7)
spring; 8) Teflon bushing; 9) current collector; 10) damper; 11)
Teflon mandrel; 12) piezoelectric element.
Fig. 2. Spectrum of primary-loop background noise. 1) Wideband
piezoelectric transducer on MCP cover plate; 2) wideband trans-
ducer on duct valve lock-band; 3) 0.2 MHz resonance transducer
on MCP cover plate; 4) 2.0 MHz resonance transducer on MCP
cover plate.
Translated from Atomnaya inergiya, Vol. 38, No. 6, pp. 425-426, June, 1975. Original article sub-
mitted January 14, 1975.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
543
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
generating plant. The investigations were carried out in the frequency range from 0.2 to 2.5 MHz with the
reactor operating at full capacity.
We recorded the background noise with piezoelectric transducers mounted by means of permanent
magnets on the cover plate of the main circulation pump (MCP) and on the lock-band of the primary-loop
duct valve. The construction of the transducer is illustrated in Fig. 1. The transducers had two types of
piezoelectric elements: commercial TsTS-19 lead zirconate ?titanate ceramic with resonance frequencies
of 0.2 and 2.0 MHz, and specially designed wideband elements of the same ceramic with a pass band from
0.6 to 2.5 MHz at the half-power points. The wideband elements enabled us to record the acoustic noise
of the primary loop with a flat response over a wide frequency interval, and with the resonance elements
we were able to estimate the noise levels at separate frequencies. The acoustic noise signals picked upby
the piezoelectric transducers were sent to a wideband preamplifier situated in the immediate vicinity of
the transducer. The amplifier signals were sent along an rf cable to the input of the main amplifier and
then to the input of a V6-1 selective voltmeter and S4-8 spectral analyzer.
The spectral characteristics of the background noise are shown in Fig. 2, from which we see that
the operation of the primary-loop equipment of the atomic generating plant is attended by strong noise in
the frequency range below 500 or 600 kHz. From 500 kHz to 2.5 MHz the noise amplitude is low. It is
evident from a comparison of curves 1 and 2 that the noise spectrum recorded on the duct valve does not
contain the strong noise signals recorded on the MCP at frequencies above 200 kHz. Damping of the high-
frequency components of the spectrum apparently causes the noise of the operating MCP to be filtered in
transmission through the metal of the conduit, and mainly the low-frequency components of the MC 13 noise
spectrum prevail outside the reactor casing.
A comparison of curves 3 and 4 shows that the use of high-frequency resonance piezoelectric trans-
ducers to record acoustic emission signals significantly lowers the level of the detected background noise
signals, thereby permitting more reliable extraction of the useful signals.
It is evident, therefore, that frequencies above 500 kHz are relatively devoid of background noise
signals created by the operating MCP and coolant conduits.
LITERATURE CITED
1. R. S. Sharpe (editor), Research Techniques in Nondestructive Testing, Academic Press, New York
?London (1970).
2. R. Zipfai and D. Harris, Materials Research and Standards, 11, No. 3, 8 (1971).
3. Yu. I. Bolotin et al., Defektoskopiya, No. 6, 5 (1971).
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
PORES IN HELIUM-SATURATED NICKEL UNDER
IRRADIATION BY NICKEL IONS
S. Ya. Lebedev, S. D. Panin, UDC 621.039.51
and S. I. Rudnev
It is of interest to clarify the effect of helium on the process of formation of pores in the crystal
lattice of a metal irradiated by accelerated ions. In [1-3] the effect of helium on the magnitude of the flow-
ing of structural steels under irradiation by carbon ions and protons was investigated, as well as its effect
on nickel and copper under bombardment of nickel and copper ions.
The purpose of the experiments performed consisted in clarifying the effect of helium on the processed pore
formation in nickel under irradiation by nickel ions over a wide range of concentrations. The procedure for ir-
radiating and investigating samples are analogous to those expounded in [4, 5]. Strips of annealed nickel 0.2 mm
thick were subjected to preliminary irradiation by helium ions having an energy of 70 keV on an I LU-100 ac-
celerator. Saturation with helium was carried out without heating, and the target was mounted at an angle
of 15' with respect to the ion beam. The helium concentration in the sample ranged from 10-4 to 10 at.%.
Thermokinetic analysis performed according to the described procedure [6] demonstrated good agreement
between the actual helium content in the sample and the calculated value. After irradiation by helium
disks having a diameter of 3 mm were cut out from the nickel strips; these disks were then thinned electro-
lytically on the side opposite the irradiated side for study by the method of transmission electron micro-
scopy. Irradiation with Ni + ions having an energy of 46 keV was carried out at a temperature of 520?C
until an integral dose of 1017 ions/cm2 was attained. The irradiation time was 1.5h.
120
100
80
80
40
20
0
7
to-3 10-2 10-1 to tol
Helium concentration, atomic %
Fig. 1 Fig. 2
Fig. 1. Microstructure of irradiated nickel for a helium concentration in the sam-
ple (atomic %): a) 10-3; b) 0.1; c) 1; d) 10.
Fig. 2. Effect of helium concentration on the variation of the average pore size dv,
the pore density Nv and the volume of the sample AV/V.
Translated from Atomnaya Energiya, Vol. 38, No. 6, pp. 426-427, June, 1975. Original article sub-
mitted July 10, 1974.
? 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
545
Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
Certain typical microstructures of the irradiated samples are illustrated in Fig. 1. The distribution
of the pores on the inspected area of the samples was uniform. It is evident that, to the extent that the
helium concentration increased, the pore density likewise increases, while the size of the pores decreases.
The size of the pores having a facing ranged from 20 to 280 A.
Figure 2 displays the dependences which characterize the effect of helium concentration on the aver-
age pore size, the pore density, and the variation of the volume of the investigated sample as a result of the
development of porosity. Beginning with the helium concentration of 0.1 at. %, the density of the pores in-
creased abruptly. At a low concentration (from 10-4 to 10-2 at. %) the role played by the helium atoms in
the process of pore formation in nickel was negligible. Thus, the increase in helium concentration by a
factor of 100 leads to an increase in pore density by only a factor of 1.5. The effect of helium at concen-
trations above 0.1 at.% is more perceptible. An increase in helium concentration by a factor of 100
changes the pore density by a factor of 5.3. The change in volume (.V/V) is independent of the concen-
tration of implanted helium within the limits of the measurement error.
Consequently the helium atoms merely stimulate the process of cavity nucleation. An increase in
the number of helium atoms does not alter the magnitude of the swelling of the irradiated metal.
LITERATURE CITED
1. R. Nelson, D. Mazey, and J. Hudson, in: Proc. Reading Conf. on Voids Formed by Irradiation of
Reactor Materials, BNES, Harwell (1971), p. 191.
2. D. Keefer and A. Pard, J. Nucl. Mater., 45, 55 (1972/1973).
3. J. Delaplace, J. Nucl. Mater., 47, 278 (1973); L. Glowinski, et al., ibid., p. 295.
4. V. N. Bykov et al., Fiz. Tverd. Tela, 15, No. 3, 910 (1973).
5. S. Ya. Lebedev and S. D. Panin, Pribory i Tekh. Eksperim., No. 3, 179 (1973).
6. V. S. Karasev et al., At. Energ., 34, No. 4, 251 (1973).
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
SCINTILLATING PLASTICS WITH IMPROVED
RADIATION RESISTANCE
V. M. Gorbachev, V. V. Kuzyanov,
Z. I. Peshkova, E. A. Rostovtseva,
and N. A. Uvarov
UDC 539.1.074.3: 539.1.04
The commercial scintillating plastic based on polystyrene containing 2% PPP* and0.02-0.06% POPOP,
which is widely used for low-intensity neutron and 7-radiation, decreases in light output significantly under
the effects of constant-intensity radiation [1] and pulsed radiation [2]. This paper discusses the results of
a search for polystyrene-based scintillating plastics possessing more stable light output when subject to
the action of hard x-rays. The prescription for the luminescent additives introduced into the polystyrene
was selected on the basis of optimal matching between the spectral regions of luminescence and the maxi-
mum spectral sensitivity of the photodetectors. All samples had high transparency and allowed mechanical
working. Samples containing 5-15% N by weight turned out to be unstable when stored; evaporation of the
naphthalene produced surface cracking after 1-2 months. This effect was not present for lower naphthalene
content (0.5-2%). Sample composition and relative light yield "'rel is shownin Table 1 (d is thickness in
cm).
The scintillators were irradiated by bremsstrahlung from a 15-MeV linear electron accelerator [3]
at a dose rate of 2.5.103 rad/sec. The samples were in the form of rectangular prisms with a base 25 x 25
mm in size and thicknesses ranging from 1 to 50 mm. Light output from irradiated samples was recorded
by means of a photocell which was separated from the scintillator and which was shielded against scattered
radiation. The photocell current was registered on a recorder.
Particular samples showing high stability of light output when irradiated by a flux of constant in-
tensity were studied for the effects of pulsed x-radiation. For this purpose, a pulsed light source which
simulated the luminescence of the scintillaor [4) was turned on [4-6] approximately 100 psec before the
pulse from a high-power x-ray generator [5]. The light passing through the scintillator was recorded by
a photocell and displayed on an oscilloscope. Assuming that irradiation of plastic scintillators leads
simultaneously to degredation (quenching) of luminescence and to loss of transparency by the material,
*PPP is paraterphenyl; POPOP, 2,2'-p-phenylene-bis-(5-phenyloxazole); PPO, 2,5-diphenyloxazole; N,
naphthalene; St, stilbene; T, tolan; An, anthracene.
Fig. 1. Oscilloscope traces of the change in scintillator transparency for pulsed irradia-
tion. Sweep time is 130 psec; vertical sensitivity is 1 V/cm.
Translated from Atomnaya E.nergiya, Vol. 38, No. 6, pp. 427-429, June, 1975. Original article sub-
mitted July 10, 1974.
0 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming,
recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.
547
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Declassified and Approved For Release 2013/09/25: CIA-RDP10-02196R000400050004-2
TABLE 1. Characteristics of Radiation Ef- the combined effect of these processes can be repre-
fects on Certain Organic Scintillators with a sented as the product of the two functions fi = J/Jo = 1
Polystyrene Base /(1 + 13D), which describes the reduction in intensity of
luminescence [6] and f2 = S/So = (i_e-aDh)/(aDh),which
describes the loss of light output because of reduction
in sample transparency [2], where D is the absorbed
dose; h is the scintillator height in cm; Jo, So and J, S
are respectively the luminescence intensity and sample
transparency before and after irradiation.
Additives, ?10
d ,11,trel
gis,
rad-1
as,
rad-1
as, rad-1
? cm-1
2 PPP
5
1
8,1-10-7 1.10-8
3,2.10-7
+0,06 POPOP
5
0,56
2,6.10-7 6,840-8
7,2.10-8
2 PPO
2 PPO
5
0,85
2,4.10-7 1,14.10-7
7,4.10-8
+0,06 POPOP
2 PPP
5
0,4
7.10-8 1.10-8
3,7.10-8
+0,2 St
ION
5
0,7
6-10-8 4,5.10-8
5,6.10-9
+0,2 POPOP
0,5N
5
0,53
2,4.10-81,57.10-8
3.10-9
+0,2 POPOP
5
0,36
1,25.10-8 1,9.10-8
2.10-9
+0,02 POPOP
St
2
1,85.10-7
T
2
1,74.10-7
N
2
1,63.10-7
2 T +0,2 An
2
0,037
1,87.10-7
2 N +2 St
2
0,11
1.10-7
2N +0,2 An
2
0,135
9.10-8
2 PPP
2
0,78
5.10-7
2 PPP+ 2 T
2
0,17
9.10-8
+0,2 An
15N
2
0,15