SOVIET ATOMIC ENERGY VOL. 48, NO. 5

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000800030004-0
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 77
• Document Creation Date: December 23, 2016
• Document Release Date: February 1, 2013
• Sequence Number: 4
• Publication Date: May 1, 1980
• Content Type: REPORT

Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
Russian Original Vol. 48, No. 5, May, 1980
November, 1980
SATEAZ 48(5) 281-352 (1980)
SOVIET
E NERGY
ATOMHAH 3HEPTMA
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
,CONSULTANTS BUREAU, NEW YORK
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is a translation of Atomnaya Energiyam, 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.
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
Secretary: A. I. Artemov
V. V. Matveev
1. D. Morokhov
A. A-. Naumov
A. S. N i kiforov
A. S. Shtan'
B. A. Sidorenko
M. F. Troyanov
E. I. Vorob'ev
I. N. Golovin
V. I. ll'ichev
V. E. lvanov
V. F. Kalinin
P. L. Kirillov
Yu. I. Koryakin
A. K. Krasin
E. V. Kulov
B: N. Laskorin
.Copyright ? 1980, Plen4m Publishing Corporation. Soviet Atomic Energy partici-
pates in the program of Copyright Clearance Center, Inc. The *appearance of a
code line at-the bottom of the, first page of an article in this journal indicates the
copyright owner's consent that copies of the article may be made for personal or
internal use. However, this consent is given on the condition that the copier pay the
stated per-copy fee through the Copyright Clearance Cen'tar, Inc: for all copying not
explicitly permitted by Sections 107 or 108 of the U.S. Copyright Law. It does not
extend to other kinds of copying, such as copying for general distribution, for
advertising or promotional purposes, for creating new collective works, or for resale,
nor to the reprinting of figures, tables, and text excerpts.
Consultants Bureau journals appear about six months after the publication of the
original Russian issue. For bibliographic accuracy, the English issue published by
Consultants Bureau carries the same number and date as the original Russian from
which it was translated. For example, a Russian,issue published in December will
appear in a Consultants Bureau English translation about the following June, but the
translation issue will carry the December date. When ordering any volurf a or particu-
lar issue of a Consultants Bureau journal, please specify the date and, where appli-
cable, the volume and issue cumbers of the original Russian. The material you will
receive will be a translation of that Russian volume or,issue.
Subscription (2 volumes per year)
Vols. 46 & 47: $147.50 per volume (6 Issues) - Single Issue: $50
Vols. 48 & 49: $167.50 per volume (6 Issues) Single Article: $7.50
Prices somewhat higher outside the United States.
Soviet Atomic Energy is abstracted or in-
dexed in Chemical Abstracts, Chemical
Titles, Pollution Abstracts, Science Re-
search Abstracts, Parts A and `B, Safety
Science' Abstracts ,Journal, .Current Con-
tents, Energy Research 'Abstracts, and
Engineering Index,
CONSULTANTS BUREAU, NEW?YORK AND LONDON
lJ
227 West 17th Street
New York, New York 10011
Published monthly. Second-class postage paid at Jamaica, New York 11431.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
November, 1980
Volume 48, Number 5 May, 1980
CONTENTS
Engl./Russ.
ARTICLES
The Lithium Zone in the Blanket of a Fusion Reactor - V. G. Vasil'ev, Z. V. Ershova,
and E. V. Dmitrievskaya ....................................... 281 283
Temperatures in the Graphite Stacks in the Reactors at the Bilibinsk Nuclear Power
Station - O. V. Komissarov, N. I. Logosha, M. E. Minashin, G. E. Soldatov,
N. V. Filippova, and V. N. Sharapov ................................ 286 287
Safety in Servicing Operations at the BOR-60 Nuclear Power Station - V. D. Kizin,
V. I. Polyakov, Yu. V. Chechetkin, and L. M. Levin ..................... 290 291
Semiempirical Method of Calculating Isotopic Composition of Uranium
and Plutonium in Irradiated Fuel from a Water-Cooled-Water-Moderated
Reactor - B. A. Bibichev, A. V. Lovtsyus, V. P. Maiorov, M. A. Razuvaeva,
A. V. Stepanov, and P. I. Fedotov ................................. 294 294
Effects of Transducer Location on the Azimuthal and Radial Stabilization
in a Reactor - B. Z Torlin ..................................... 297 297
Effects of Neutron-Distribution Pattern on the Stability of a Power Reactor
- I. Ya. Emel'yanov, L. N. Podlazov, A. N. Aleksakov, and V. M. Panin ........ 302 301
Thermohydraulic Calculation of Multirod Heat-Liberating Piles Cooled
by Single-Phase Heat Carrier - G. S. Mingaleeva and Yu. V. Mironov ......... 306 303
Nonstationary Slowing Down of Neutrons from a Plane Pulsed Source in a System
of Two Media with a Plane Interface - Yu. A. Medvedev, and E. V. Metelkin .... 311 308
Retardation in Medium of Variable Density -A. A. Kostritsa ................... 317 313
Irradiation Levels of Professionally Exposed Groups and Radiation-Monitoring
Optimization - V. I. Ivanov, I. P. Korenkov, and O. N. Salimov .............. 320 315
Nonlinear Dependence of Intensity Effects on Number of Particles in Ring Current
- S. G. Arutyunyan and G. A. Nagorskii ............................. 323 318
Isotope Analysis of Nanogram Uranium Samples - R. N. Gall', A. M. Korochkin,
V. A. Lednev, B. N. Sokolov, and V. N. Vyachin ........................ 327 321
LETTERS TO THE EDITOR
Field Ion Microscopy of Radiation Defects in Tungsten Irradiated with 50-keV W+
Ions. I. Method and Results - A. F. Bobkov, V. T. Zabolotnyi, L. I. Ivanov,
G. M. Kukavadze, N. A. Makhlin , and A. L. Suvorov ..................... 331 325
Field Ion Microscopy of Radiation Defects in Tungsten Irradiated with 50-keV W+
Ions. II. Discussion of Experimental Results - V. T. Zabolotnyi, L. I. Ivanov,
N. A. Makhlin, and A. L. Suvorov ................................. 333 326
Effects of Gas Dissblved in Water on Critical Heat Loadings - V. V. Fisenko,
Yu. D. Katkov, A. P. Lastochkin, and V. I. Maksimov .................... 335 327
Effect of Fluorescence on y-Ray Buildup Factors in Lead - I. N. Butueva
and I. N. Trofimov ........................................... 336 328
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
CONTENTS
(continued)
Engl./Russ.
Spatial and Energy Distributions of the Thermal Neutrons in a Cell of a Reactor
at Bilibinsk Nuclear Power Station - G. G. Panfilov, A. A. Vaimugin,
A. V. Gusev, A. P. Korneeva, A. G. Kostromin, V. I. Kulikov, S. S. Lomakin,
V. F. Lyubchenko, and V. N. Sharapov ................................. 338 329
Viability of Resistance Thermometers Under Reactor Conditions - M. N. Korotenko,
V. A. Salamakha, S. 0. Slesarevskii, and V. P. Maksimenko ........ . ....... 340 331
Recovery of the Fast-Neutron Spectrum in a Model for a Liquid-Salt Blanket
in a Fusion Reactor - V. M. Novikov, A. A. Shkurpelov, V. A. Zagryadskii,
D. Yu. Chuvilin, and Yu. V. Shmonin .................................. 342 332
Optimum Neutron Spectrum for Activating Fuel Pins in Delayed-Neutron
Monitoring - B. P. Maksyutenko ..................................... 344 334
Effects of y Rays onthe Inherent Resolution of a Thallium-Activated Sodium Iodide
Crystal - E. L. Vinograd, N. Yu. Gurevich, and Yu. A. Tsirlin ................. 346 335
Calculation of Photon-Radiation Mass Attenuation Coefficient - V. I. Gudima
and G. V. Pekina ................................................ 348 337
A Monte Carlo Algorithm for Local Evaluation of Perturbations in y-Ray Transport
Problems - V. G. Zolotukhin, A. I. Ksenofontov, and A. P. Gnutikov ............. 349 337
The Russian press date (podpisano k pechati) of this issue was 4/24/1980.
Publication therefore did not occur prior to this date, but must be assumed
to have. taken place reasonably soon thereafter.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
ARTICLES
V. G. V a s i l ' e v , Z . V . E r s h o v a, UDC 621.039.6: 621.039.573
and E. V. Dmitrievskaya
A controlled deuterium-tritium thermonuclear reaction in a fusion reactor involves producing tritium
in the reactor itself, which is then used to supply the plasma. It has been suggested that tritium can be pro-
duced by using either metallic lithium or various lithium compounds in the reactor blanket. Schemes were
first proposed [1, 2] for the blanket zone in pure reactors, where the fusion neutrons are absorbed in the
breeding zone of the blanket, which contains lithium materials in the molten or solid states [3-5]. In the first
case, the lithium material is used also as the heat carrier. In the second case, the heat carrier is some other
working body, e.g., helium. Therefore, the lithium zone in a pure reactor acts as a tritium accumulator and is
a source of thermal energy. Table 1 gives the lithium materials that have been suggested for the breeding
zone. A fusion reactor differs from a fission one in that the heat-transport loop is involved in the production
and isolation of the tritium required for fusion. The performance of a pure reactor is examined in terms of
three parameters : improvement in the efficiency of the reactor (station) as a whole, attainment of the maxi-
mum tritium breeding factor, and optimization of the working conditions in the first wall.
High efficiency involves raising the heat-carrier temperature, and this complicates various aspects
related to the accumulation of tritium. Elevated temperatures increase the diffusion and dissolution of tritium
in the material. Also, there are serious problems of corrosion failure in constructional materials in contact
with molten lithium or salts.
The tritium breeding factor may be increased by incorporating elements into the lithium or the construc-
tional material that undergo (n, 2n) and (n, 3n) reactions: beryllium, molybdenum, tungsten, etc.
The following major problems arise in the lithium breeding zone for a pure reactor:
1) 'choice of the lithium isotope composition (natural or enriched in 6Li) and determination of the required
macroscopic cross section;
2) provision of high temperature in the coolant, which is required for high efficiency in the station;
3) radiation safety problems arising from leakage of tritium from the loops by diffusion;
4) the interaction of the molten coolant with the constructional materials and the choice of the most sta-
ble ones for long-term operation;
5) choice of a lithium material for the blanket zone resistant to radiation damage and also thermally-
stable; and
6) determination of the economic features of various schemes for the accumulation and extraction of tri-
tr ium.
Hybrid reactors have also been proposed, in which the blanket contains fissile material, such as depleted
or natural uranium [22, 23]. This can raise the energy yield to 100 MeV per fusion neutron, which gives a sub-
stantial advantage over a pure reactor. A hybrid reactor not only produces electrical energy but also pro-
duces plutonium, while still producing tritium for the plasma. The advantages of a hybrid reactor are accom-
panied by some obvious disadvantages, such as increase in the radiation hazard and the need to process fissile
materials.
The lithium zone is designed to breed tritium in the blanket, and the optimum dimensions and composition
of the latter are determined by neutron-physics calculations. Figure 1 shows a scheme for a blanket with
uranium and lithium zones [24, 25].
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 283-287, May, 1980. Original article submitted
January 30, 1978; revision submitted March 20, 1979.
0038-531X/$0/4805-0281$07.50 ?1980 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
Li
Li2C2
Lr14SiO4
LiAIO2
Li2O
Li
Li2C2
Li4SiO4
LiA102
Li2O
Fig. 1. Forms of blanket with various mate-
rials.
Fusion system or
Coolant tempera-
ture, ?C
Temp. of
lithium
Ref.
reactor
Lithium zone
Function
material,
C
inlet
outlet
T-20 blanket module
Coolant and tritium
300/480
470/550
[6, 7]
UWMAK I
} Liquid lithium
production
283
630
483
980
[8]
[9]
UWMAK III
260
550
[10]
Blanket module for the
50% Pb-Li; 44% Pb
Tritium production
- 450?
[11]
LINUS fusion reactor
and 6% Cd
T-20 blanket module
Molten 50% LiF-
Coolant and tritium
500
650
up to 700
[6]
Blanketfor tokamakhybri
50% BeF2
Molten 47,5% LiF-
production
Tritium production,
up to 700
[12-13]
reactor
52% BeF2, balance
coolant helium
Symbiotic system of
PuF3 or UF4
Molten LiF-BeF2
Coolant and tritium pro-
ti
d
up to 700
[14-15]
fusion-fission reactors
on
uc
T-20 blanket module
Solid inorganic lithium
Tritium production,
300
570
up to 700
[6]
compound
coolant helium
450
650
up to 900
[16]
UWMAK II
LiA102
GTRT
Solid inorganic lithium
[17]
compound
,~
300
500
up to 600
[18-19]
JAERI-M7300
L20
,>
275
585
upto700
[20]
Doublet DPR blanket
Li7Pb2 or Li4BiO4
module
Mirror blanket module
Li2Be203+Be
Tritium production,
coolant helium with
5950
[21]
lithium
The lithium zone in a hybrid reactor operates under a variety of. functionally conflicting conditions [17].
Most of the energy is produced in the uranium zone in a hybrid reactor, while the heat produced in the lithium
zone is not more than 5-6% of the.total produced in the blanket, so the lithium zone is mainly a tritium gen-
erator, where the tritium accumulates for subsequent extraction and return to the plasma.
The dimensions of the lithium zone have not been finally established; they may vary during calculation
and development, but they should lie in the range 50-150 mm. Figure 1 indicates that the lithium zone con-
sists of two sections, the first of which lies beyond the uranium zone, while the second has the lowest thermal
and neutron loadings. It is found [23-26] that the ratio of the tritium formation rates in these sections is 5 : 1.
. On existing proposals, a fusion reactor is designed for long-term operation (not less than 20 years), but
the provision of long-term thermal stability and radiation resistance has not been finally resolved for the con-
structional materials in the various zones of the blanket and in the lithium material itself.
In all models, the lithium breeding involves fairly prompt extraction of the tritium and return to the
reactor, which should be self-sufficient in tritium. Economy requires that the cost of the tritium stock should
be minimized during the startup .period. For a reactor with a thermal power of about 7 GW, the daily consump-
tion of tritium in the plasma would be about 100 g, and the same amount of tritium must be produced in the
lithium zone. The problem is to reduce the hold-up of tritium in the blanket, i.e., to begin the extraction of
tritium at very low concentrations. This not only reduces the, demand for tritium in the start-up period but
also provides the maximum radiation safety for this element, since continuous extraction of tritium at low con-
centrations will keep the total amount in the blanket reasonably small (not more than 1 kg).
Experimental data are available on the isolation of tritium from irradiated inorganic compounds such as
lithium fluoride, sulfate, carbonate, oxide, aluminate, chromate, and nitrate when the levels of tritium are less
than 10-4 mass %; heat treatment under vacuum can extract 90-99% of the tritium in the range 500-800?C [21,
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
,uu 1 6U
Radius, mm
Fig. 3
Fig. 2. Release of tritium from irradiated lithium sulfate for an initial tritium
concentration of 1'108 Bq/g at 15-550?C (0) and 1' 107 Bq/gat 550?C (0).
Fig. 3. Energy production and temperature difference in a sphere of diameter
10 mm with A = 1 W/m ' ?C, q = 8 W/cm3.
27, 28]. Figure 2 shows the extraction of tritium from irradiated lithium sulfate during heat treatment under
vacuum. Preliminary estimates indicate that the tritium diffusion coefficient is 10-10 cm2/sec at 550?C.
At present one envisages the following modes of operation for the lithium zone in a hybrid reactor, which
provide for fairly independent production of the temperatures needed for the accumulation and extraction of
tritium (Table 2).
1. Low-temperature (100-200?C) irradiation of the lithium material for instance in the form of spheres
with hard coating or in some other form. In that case, the lithium material may be cooled to the required tem-
perature for example with helium. Figure 3 shows the energy production and the temperature difference over
the radius of the sphere for a thermal output of 8 W/cm3 on the assumption that the thermal conductivity of the
lithium material is a- 1 WAn' ?C (A 1.7 W/m ? ?C for lithium aluminate and oxide) at room temperature [16, 18].
A gap of 0.5 mm between the shell and the contents of the sphere may result in an additional temperature dif-
ference of about 200?C if the gap is filled with argon or about 20?C if the gap is filled with helium. This pro-
vides for minimal loss of tritium from the breeding zone during irradiation and minimum contamination of the
helium coolant with tritium.
2. Operation of the lithium zone with helium as coolant at about 500?C; in that case the tritium is
released from the lithium material by diffusion and is continuously carried out of the zone by the helium. This
requires continuous treatment of the helium to extract the tritium. The operation of the lithium components
may be complicated by the fact that the helium formed in 6LI (n, cv) T cannot be extracted from the lithium com-
ponent without breaking the sealing in the sheath. The accumulation of helium within the lithium components
causes a gradual increase in pressure, and within a year of operation the helium in a sphere of diameter 10 mm
with a free volume of 0.05 cm3 will give rise to a pressure of 9.8 ' 106 Pa. In addition to the gas released from
the lithium elements, one has to consider the temperature at the wall of the lithium zone. A preliminary cal-
culation on the leakage of tritium through the hot outer wall of this zone shows that this can be minimized. Then
the main difficulties in the isolation of tritium from the helium, where the partial pressure of tritium is to be
kept not more than 13.3 Pa, are transferred to the processing section. The tritium can be extracted from the
zone continuously or periodically, as in the production of tritium by continuous irradiation in fission reactors
[29-311.
The energy production in the parts of the lithium zone of about 3 ' 10 W/m3 is distributed as 5 1 between
them [26]. Figure 4 shows the expected distribution of the temperatures in zone I for two-sided cooling and for
zone II with one-sided cooling. However, it is clear that one can produce conditions required for tritium ex-
traction throughout the lithium zone. Compounds of lithium such as the aluminate, silicate, and oxide having
X 1-2 W/m' ?C can result in temperature differences of several hundred degrees in the first 5-10 mm of the
layer. The lithium material in the central part of the zone will be at the melting point.
Table 2 gives characteristics for the lithium zone in a hybrid reactor; further research is required on
the operation of the lithium zone, particularly the complications arising in continuous isolation of the tritium.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
10 0 1 2 3 4
Zone thickness, cm
Fig. 4. Distribution of temperature differences in lithium material
in the zones of a blanket, for A= 1 W/m ? ?C and q = 3 ? 106 W/m3; tm
LiAIO2 = 1600?C, tm Li4SiO4 = 1250?C: a) zone I, thickness 10 cm;
b) zone I, thickness 5 cm; c) zone II, thickness 10 cm.
TABLE 2. Characteristics of the Lithium Zone in a Hybrid Reactor
Advan-
tages
Lithium zone cooled to 200?C
by helium (wall temp. 200?C,
spherical elements)
Safe operational zone with
minimum trition loss from
elements
Scope for rapid change of
elements under emergency
situations
Tritium extraction outside
the reactor
Disadvan-I Tritium hold-up in reactor
tages
Periodic or continuous dis-
placement of elements for
trition extraction
Increased consumption of
initial material and for-
mation of radioactive
wastes
Lithium zone cooled to 600?C
by helium (wall temp. 500-
600?C, spherical elements)
Continuous isolation of tri-
tium with a minimum level
in the blanket
Prolonged operation of ele-
ments without replacement
Scope for rapid change of
elements under emergency
situations
Maintenance of a small tern
perature difference between
the spherical elements for
tritium isolation
Considerable dilution of the
tritium with helium
Contamination of the cool-
ant and need to cool the
walls to reduce diffusion
leakage
Lithium zone at a high temp.,
wall temp. 200?C, temp. of
lithium material between
600?C and the melting point
Continuous isolation of tri-
tium with a minimum level
in the blanket
Elimination of radiation
damage by melting of the tri-
tium material in the zone
Production of tritium in con-
centrated form
Severe working conditions in
the lithium zone with pressure
differences
Change in the composition of
the lithium material by mass
transport
A hybrid reactor allows one to control the temperature of the lithium zone and to isolate the tritium
under safe conditions of operation. Here it is necessary to consider the construction of the lithium components
for the blanket in order to provide reliable operation in the lithium zone. This requires lithium material of
high thermal stability and good radiation resistance on exposure to integral fluxes of 1021_1022 neutrons/cm2,
as well as constructional materials for the sheaths compatible with the lithium materials, and Improved de-
sign of the blanket as a whole and of the lithium zone in particular.
LITERATURE CITED
1. D. J. Rose and M. Clark jun., Plasmas and Controlled Fusion [Russian translation], Gosatomizdat, Mos-
cow (1963).
2, W. Homeyer, "Thermal and chemical aspects of the thermonuclear blanket problem," MIT TR-435 (1965).
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
3. G. Kulcinski and R. Conn, in: Fusion Reactor Design Problems, Proceedings. of an IAEA Workshop Held
at Culham, UK, Jan. 29 to Feb. 15, 1975, p. 51; F. Tenney, ibid., p. 17; K. Sako et al., ibid, p. 27.
4. J. Darvas, in: Proceedings of the International Conference, Gatlinburg, 1-3 Oct. 1975. Conf. 750985,
v. III.
5. Z. V. Ershova et al., in: Proceedings of the All-Union Conference on Engineering Problems of Con-
trolled Fusion [in Russian], Vol. IV, NIIEFA, Leningrad (1975), p. 14.
6. V. A. Glukhikh, N. A. Monoszon, and G. F. Churakov, ibid., Vol. 1 (1977), p. 42.
7. G. N. Zhemchuzhnikov, A. M. Benevolenskii, and A. N. Topil'skii, in: Proceedings of the Second Soviet-
American Seminar [in Russian], Atomizdat, Moscow (1978), p. 164.
8. B. Badger et al., "UWMAK I, A Wisconsin toroidal fusion reactor-design," Nucl. Eng. Dept. Report
UWFDM-68, University of Wisconsin at Madison (1974), Vol. 1 (1975), Vol. 2.
9. B. Badger et al., "UWMAK III, A conceptual noncircular tokamak power reactor design," Nucl. Eng. Dept.
Report UWFDM-150, University of Wisconsin at Madison.(1976).
10. S. Majumbar and B. Misra, Trans. Am. Nucl. Soc., 27, 73 (1977).
11. A. Robson, ibid, p. 45.
12. W. Price et al., "The Princeton beam-driven tokamak fusion-fission hybrid study," PPPL-TM-299.
Feb. (1977).
13. F. Tennly, in: Proceedings of the US-USSR Symposium on Fusion-Fission Reactors. Conf. 760733.
Livermore, 13-16 July (1976), p. 71.
14. V. L. Blinkin and V. M. Novikov, IAE Preprint 28-19, Moscow (1977). Proceedings of the Second Soviet-
American Fusion-Fission Seminar [in Russian], Atomizdat, Moscow (1978).
15. V. Blinkin and V. Novikov, Nucl. Fusion, 18, 893 (1978).
16. B. Badger et al., "UWMAK III, A conceptual noncircular tokamak power reactor design," Nucl. Eng.
Dept. Report UWFDM-112, University of Wisconsin at Madison (1975).
17. E. P. Velikhov et al., [6], Vol..1, p. 5.
18. K. Sako et al., First Preliminary Design of an Experimental Fusion Reactor, JAERI-M 7300 (1977).
19. H. Kubo, K. Tanaka, and H. Amano, J. Inorg. Nucl. Chem., 40, 363 (1978).
20. D. Kearney et al., Mechanical and Thermal Design of a Gas-Cooled Fusion Blanket Module GA-A14671,
September (1977).
21. T. Galloway, in: Proceedings of the Conference of the Second Topical Meeting on the Technology of Con-
trolled Nuclear Fusion, Richmond, 21-23 Sept. (1976). 760935. v. III, p. 1351.
22. I. N. Golovin, At. Energ., 39, No. 6, 379 (1975).
23. G. E. Shatalov, Izv. Akad. Nauk SSSR, Ser. Energ. Transport, No. 6, 85'(1975).
24. S. V. Marin et al., "Some parameters of the blanket around a fission reactor containing fissile material,"
Paper at the USSR-USA Joint Seminar, Leningrad, December 9 (1974).
25. V. Kotov and G. Shatalov, [13], p. 129.
26. V. Gur'ev et al., [13], p. 119.
27. I. Owen, [41, p. 433.
28. Z. V. Ershova and V. G. Vasil'ev, in: Proceedings of the All-Union Conference on Engineering Pro-
blems of Controlled Fusion [in Russian], Vol. IV, NIIEFA, Leningrad (1975), p. 3.
29. Czechoslovak Patent No. 103871, cl. 12.01. Publ. 13.06.1962.
30. U.S.A. Patent No. 3079317, cl. 204.154.2. Publ. 26.02.63.
31. V. G. Vasil'ev, Z. V. Ershova, and E. V. Dmitrievskaya, At. Energ., 44, No. 5, 440 (1978).
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
TEMPERATURES IN THE GRAPHITE STACKS IN THE REACTORS
AT THE BILIBINSK NUCLEAR POWER STATION
O.
V.
Komissarov, N. I. Logosha,
M.
E.
Minashin, G. E. Soldatov,
N.
V.
Filippova, and V. N. Sharapov
The reactions at the Bilibinsk combined heat and power station each have a pile of graphite blocks, in
which there are vertical technological channels TC and control and protection channels CPC [1]. The pile is
contained in a sealed volume filled with nitrogen to prevent rapid burnup of the graphite at high temperatures.
The heat deposited in the graphite by neutron moderation and y-ray absorption is output in the main to the TC
and CPC, although some part passes through the reflectors to the foundations and to the biological shielding
tank filled with water.
The thermal power of each of the four reactors in the station is 62 MW, of which 12 MW is utilized in
electrical form and 29 MW represents the heat load. Figure 1 shows a cross section of one-quarter of a
reactor. Five three-zone thermocouples are installed at various distances from the center of the core to mon-
itor the temperature of the graphite. Each measures the temperature at three points along .the height of the
graphite stack. Temperature measurements are also made on the metal jacket surrounding the graphite and
on the foundations and uppercover of the reactor.
Temperature Distribution in a Technological-Channel Cell. Figure 2a shows the cross section of a cell
in a technological channel; the channel consists of six tubular fuel rods within the core, which are enclosed in
graphite sleeves around the central tube. The outside diameter of the fuel rods is 20 mm, while the central
tube in the channel is of diameter 25 mm, and the graphite sleeves have diameters of 88 mm. There is the gas
gap 61 between the central tube and graphite sleeve, while between a fuel rod and a sleeve there is the gap 62,
together with the gap 63 between the channel sleeve and the graphite blocks in the stack. The coolant moves in
the channel by natural circulation.
The heat released in the graphite in a TC cell in the main is transmitted to the fuel rods, whose surface
temperature is about 310?C. The maximum temperature in the graphite is dependent on the channel power.
Figure 3 shows an example of the calculated temperature distribution along the radius for a cell of output
250 kW. The calculations were performed by simulation with conducting paper. This method has been de-
scribed [2] in application to temperature distribution determination for reactor cells. Figure 3 shows that
the temperature of the graphite is determined mainly by the thermal resistance of the gas gaps.
These gaps should provide ready extraction of the channels from the reactor and free movement of the
fuel rods in the graphite sleeves. They must be chosen in accordance with the thermal and radiation-induced
changes in the sizes of the graphite and in the fuel rods throughout the time spent by the latter in the reactor,
but on the other hand they should be small enough to prevent an unacceptable temperature rise in the graphite.
In a reactor with natural circulation, the distribution of the heat flux from the graphite to the fuel rods
and to the central tube is dependent on the relation between 61 and 62. To prevent the natural circulation from
being interrupted when the emergency protection gear operates, when the heat flux from the graphite becomes
comparable with the residual heat production in the uranium, it is necessary to minimize the amount of heat
transmitted to the central tube [3]. Figure 4 shows the proportion of heat transmitted from the graphite to the
central tube as a function of 61 for various gaps between the fuel rods and the graphite sleeves.
Most of the heat from the graphite must pass to the fuel rods, so the gap between these and the graphite
sleeves should not be large. When the fuel rods are a close fit to the graphite sleeves, the part of the fuel-rod
surface facing the central tube is screened and plays little part in removing heat from the graphite, which
causes the temperature to rise. In the TC at this station, the minimum size of the graphite wall between fuel
rods is about 8 mm. Then the heat flux from the graphite via the surfaces facing the central tube is half that
through the surface facing the graphite block.
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 287-291, May, 1980. Original article submitted
February 5, 1979; revision submitted July 16, 1979.
286
0038-531X/80/4805-0286$07.50 ?1980 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
0-1 ?-2 o-3
O
15
o
o
0
Q1
01
0
0
0
01
01
01
01
0
0
0
0
0
0
1
0
1
0
0
0
0
01
01
01
01
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
O
0
0
0
0
0
0
0
0
0
O
^
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Fig. 1. Cross section of a reactor: 1) TC;
2) CPC; 3) thermocouples for measuring
graphite temperature; 4) reactor jacket; 5)
biological shield.
Fig. 2. Cross sections of a TC cell (a) and a CPC cell (b): 1) fuel rod; 2) absorbing rod; 3) channel
tube; 4) graphite sleeves; 5) graphite block.
Fig. 3. Temperature distribution over the radius of a TC cell: 1) channel tube; 2) fuel rod; 3) gra-
phite sleeve; 4) graphite block.
. Figure 5 shows the theoretical relationship between the maximum temperature of the graphite block and
62 derived on the basis of the uneven distribution of the heat flux at the outer surface of the fuel rods. This
relationship has been used on the basis of possible rod swelling during operation to choose o2 in the cold state.
If we choose for the cold state o2 = 0.25 mm, o3 = 0.35 mm, while the heat production in the graphite in
a cell is 8.7% of the power and the coefficient representing the nonuniformity over the height of the reactor is
1.35, we get the maximum graphite temperature in relation to TC power as shown by curve 1 of Fig. 6. This
relationship was derived for fuel rods coaxially placed in the holes in the graphite sleeves and the same for the
sleeves in the holes in the graphite blocks. Under real conditions, these elements are always in contact. Cal-
culations by electrical simulation show that the maximum temperature of the pile may be reduced by con-
siderably more than 10? on account of the contact. There is a temperature reduction of about 10?C on account
of heat leakage over the height of the graphite stack.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
u,%
t,?C
700
300 L
0
0 02 0,4 06
Fig. 4
t,?c
800
750
.700
650
0,1
0,2 03 0,4 0,5
Fig. 5
L I
0,6 62,mm
Fig. 4. Proportion of heat transferred from graphite to central
TC tube, power 340 kW, b2 = 0.7 mm (1) and 0.2 mm (2).
Fig. 5. Theoretical dependence of maximum graphite temperature
on 62 (TC power 340 kW;61=1 mm; 63=0.35 mm).
100 200 300
Fig. 6
I I
Ntc. kW
40 60 80 N,,
Fig. 7
Fig. 6. Theoretical dependence of maximum graphite temperature on TC
power (dimensions in TC cell: 61 = 1 mm, 62 = 0.25 mm, 63 = 0.35 mm, in
CPC cell: 61 = 3 mm, 62 = 0.20 mm, 63 = 0.35 mm) : 1) homogeneous TC
lattice; 2) TC cell with angular disposition relative to CPC cell; 3). TC cell
adjacent to CPC cell; 4) CPC cell.
Fig. 7. Water temperature at the exit from a CPC channel in relation to
reactor power for tin = 104?C : solid line from calculation with allowance for
contact between fuel rod and CPC channel tubes; points from experiment.
Effects of CPC on Graphite Temperature. In a homogeneous TC lattice, the heat production in the gra-
phite constitutes 8.7% of the channel power, but in the presence of CPC the graphite in the latter produces
5.0% of the heat, while the graphite in the TC cells in line with the CPC cells and at angles to them will pro-
duce, respectively, 7 and 8.4%. The CPC cells in the pile reduce the maximum graphite temperature by about
70?C (Fig. 6).
Figure 7 shows theoretical and experimental data on water heating in the CPC in relation to reactor
power. The temperature rise is almost independent of whether the absorbing rods have been withdrawn from
the core or not, and about 70% is due to heat produced in the CPC cells (including heat from the absorbing
rods), while about 30% is accounted for by heat coming from adjacent TC cells. The set of CPC extracts about
2% of the thermal power of the reactor into the deaerator.
Graphite Temperature in the Core. The graphite temperature was measured at three points along the
height of the pile: at the center of the core and at the interfaces with the upper and lower reflectors, where
the temperature does not greatly exceed the fuel-rod temperature and is about 350?C for the top and bottom at
the nominal reactor power.
The graphite temperature is maximal at the center of the core; the value increases with the reactor
power and does not exceed 510?C at the nominal power. The temperature variations in the graphite over the
radius of the core are not more than 20?C although the TC power at the center is 1.5 times that at the peri-
phery. This is because the CPC channels lie predominantly at the center of the core, and calculations (Fig. 6)
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
crSg 0 6
~ f ? n ^ ^
__ o i O ? ^ ^
0
Fig. 8. Maximum graphite temperature in relation to reactor power: 0, 0, 0) from
experiment (first, second, and third reactors); solid line) calculation without allowance
for contact between fuel rods and channel tubes in CPC; broken line) calculation on the
basis of contact, by use of reduced concentric gaps (S2 = 0.12 mm in TC, 62 = 0.1 mm in
CPC).
Fig. 9. Calculated distributions of heat pro-
duction and temperature over the radius of
the lateral reflector at the minimal power: 1)
TC cell; 2) reflector layers; 3) reactor jacket;
4) biological shield; p temperature measure-
ments at 93% of the nominal power.
show that this tends to equalize the graphite temperatures in the central and peripheral TC cells. Figure 8
shows how the temperature of the graphite in the center of the core varies with the reactor power.
Graphite Temperature in the Lateral Reflector. Calculation indicates that the total heat production in
the laterial reflector is about 400 kW; measurements of the water flow rate and temperature rise for the
foundations and biological shield indicate heat removal of about 500 kW, i.e., 100 kW more. The difference is
due to the additional influx of heat from the lower end reflector and the core. Figure 9* shows the distribution
of the heat production and the temperature pattern in the lateral reflector. The temperature distribution has
been derived on the basis of the axial heat leak.
Conclusions. The graphite stack temperature in the Bilibinsk reactors is maximum in the core and is
measured as 510?C at the nominal power. The calculated temperature for average gas gaps is about 50?C
*The heat production in the peripheral layers of the reflector and in the reactor jacket was calculated by L. B.
Kuznetsova and A. P. Suvorov.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
higher. The measured temperatures of the graphite at the center and edge of the core are virtually identical,
in spite of differences in the TC power. This occurs because the central thermocouples lie near the CPC cells,
whose channels are cooled by water at only about 120?C. When the graphite pile temperature is calculated, it
is necessary to correct for the reduction in thermal resistance of the gas gaps arising from contact between
the components of the pile.
LITERATURE CITED
1. A. A. Vaimugin et al., At. Energ., "39, No. 1, 3 (1975).
2. O. V. Komissarov et al., in: Calculation of Physical Fields by Simulation Methods [in Russian], Mashi-
nostroenie, Moscow (1968), p. 200.
3. V. M. Abramov et al., in: Proc. IAEA Symposium on Small and Medium Power Reactors, 1970. IAEA,
Vienna (1971), p. 363 (IAEAMSM-140/16).
SAFETY IN SERVICING OPERATIONS AT THE BOR-60
NUCLEAR POWER STATION
V. D . K i z i n, V . I . P o l y a k o v, UDC 621.039.58:621.039.526.004.6
Yu. V. Chechetkin, and L. M. Levin
The high levels of radioactivity and chemical activity in the sodium coolant in a fast reactor often lead to
pessimistic evaluation of the radiation environment in a nuclear power station during servicing operations.
Complicated multitone shielded equipments have been built for removal systems, along with complicated de-
contamination systems, and means of cleaning the gas in the first loop. Some experience has been accumulated
with servicing operations on working fast reactors, particularly the BOR-60, especially for equipment in con-
tact with the coolant and contaminated by fission products and corrosion deposits.
Servicing the First Loop. During the planned prophylactic servicing on the BOR-60, various operations
were performed on modifying and replacing the transducers for the monitoring and measuring instruments, and
checks were made on the states of certain parts of the hot zones, which were serviced, and further checks were
made on the cabling systems, the fire alarms, the transducers in the monitoring systems, etc., with replace-
ment of various items subject to wear (pumps, valve gear, nonreturn valves), etc.
The units in the first and second loops (heat exchangers, pumps, and valve gear) were designed in such
a way that parts showing wear could be replaced without entering the first-loop space or cutting the main pipe-
lines. In each case the equipment consisted of a body welded to the pipelines and a removable part containing
the components and items needing servicing.
The most complicated servicing operation is to extract the removable parts of the heat exchangers and
pumps, which is followed by transport and decontamination. When these removable parts are being demounted,
there may be high-intensity radiation fields at the working site, and the films of coolant on the surfaces may
ignite, with the production of large amounts of oxide within the loop, which hinders installation of the removable
parts after servicing. Further, such operations often give rise to aerosols, which may enter the working loca-
tion.
The following servicing operations involving the removal and replacement of parts from the first loop
were performed during the .working cycle of the BOR-60:
1) removal of filters installed in the bodies of the valve gear during the start-up period, with replace-
ment by standard removable parts of this gear;
2) replacement of removable parts of the nonreturn valves;
3) replacement of parts in slides after prolonged operation;
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 291-294, May, 1980. Original article submitted
April 23, 1979.
290 0038-531X180/4805-0290$07.50 ?1980 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
TABLE 1. Staff Irradiation in Servicing Operations on the BOR-60
Dose rate
SR/sec
Total dose,
ber
Operations in the heat-exchanger sections
of the first loop, including examination
and modification (checks on smoke detec-
tors, examination of thermocouples, re-
placement of electric lamps, replacement
of vibrational transducers, etc.)
Servicing in the heat-exchange sections
for the first loop (connection of electrical
flowmeters, replacement of electrical
heaters. on parts of pipelines, servicing of
thermal insulation, servicing of base of
oxide trap, etc.)
Replacement of removable parts (pump
level gauge, pump, etc.)
Reloading of fuel-rod and experimental
assemblies
200-300
200-1000
1-25
4) removal and replacement of pump components; and
5) replacement of reloading tubes and experimental devices in the core.
0.5-3.0
0.2-0.7
1-3
No major servicing and replacement operations were performed in the heat-exchanger segments of the
first loop, and only one small leak of sodium (about 1-2 kg) was detected as coming from a butt weld under the
thermal insulation. The removable parts of the equipment were extracted in a working hood (without biological
shielding) flushed by argon, either with a low level for the sodium (without drainage of the bodies) or with the
coolant completely removed from the loop. When the removable part of the pump was being extracted, argon
was injected into the body, while nitrogen was injected under the working hood. The use of a sealed hood made
of a plastic film facilitated the transport and other operations during the reloading,. and this also prevented the
ignition of the sodium and formation of oxides in the body, as well as the production of aerosols in the working
site.
Radiation Environment during Servicing. The BOR-60 has now operated about seven years with the
coolant contaminated by fission products. The number of fuel pins with ruptured sheaths is 0.1-1% of the load.
The level of radioactivity in the gas phase in the reactor with this number of defective pins is governed by
133Xe and has risen to 1200 Ci.* However, the gas system is sealed, so this level of radioactivity has not
resulted in any difficulties. The gas release from the reactor to the environment is governed by 41Ar (in the
shield cooling) and is not more than 25 Ci/day. The protective gas was purified on activated charcoal before
the reactor was opened for reloading.
The fission-product activity in the sodium at certain periods has greatly exceeded the radioactivity
arising from the main long-lived activation isotopes 22Na (0.7 mCi/kg) and 11omAg (0.2 mCi/kg). This has
resulted in increased radiation fields outside the heat exchangers in the first loop, which have risen to 300-
500 pR/sec. Up to 8% contribution to the dose rate comes from the y rays of 137Cs and 134Cs, and the specific
activity of 137Cs has varied from 2 to 20 mCi/kg at different times.
See [1] for the isotope compositions of the surface contaminants on various parts of the loop and more
detailed information on the radioactivity in the coolant. The 140Ba_140La and 95Nb activities, which govern the
contamination of the surfaces in the loop, are dependent on the run time since the defects were formed in the
fuel-pin sheaths in the core; at certain times, the y rays from these nuclides contributed up to 65% of the dose
rate from the pipelines. Drainage of the coolant from the loop then did not reduce the dose rate in the heat-
exchanger sections below 100-150 pRy ec. ~ The activity due to 60Co and 54Mn, which are nuclides of corrosion
origin, increased on the surfaces during the years of operation of the reactor, but they never contributed more
than 10% of the dose rate from the pipelines.
*1 Ci = 3.700 ? 1010 Bq; 1R - 2.58 - 10-4 Cu/kg; 1 ber = 0.01 J/kg.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
When the nuclear power station is operated normally, there is no leak of radioactive gases and aerosols
into the working locations, nor are there any sources of surface contamination of the equipment and buildings.
Some such contamination occurred during reactor reloading, particularly during removal of the loading tube
and effector mechanism for the CPC, which involved modification and servicing of-the loading machine. The
contamination levels of the surfaces were not more than the equivalent of 4000 9 particles per minute per cm2,
which were due to 95Nb, 137Cs, and 141Ce. When equipment was removed from the reactor into the central bay,
there were brief episodes of radioactive aerosols, whose concentrations were not more than 1.10-10 Ci/liter
(mainly 137Cs).
A coefficient was formulated to characterize the escape of radionuclides from the contaminated surfaces
into the atmosphere as aerosols (the ratio of the activity in the air to that at the surface) by reference to mea-
surements, which gave 3 ? 10-2 M-1 for 137Cs and 134Cs or (1-5) - 10-4 m-' for 141Ce, 95Nb, "Co, and 54Mn; the
high cesium activity in the coolant and the high volatility of the element make it obligatory to use respirators
in servicing operations. The surface contamination in the central bay was purely local in character and was
readily flushed away.
Personal Exposure during Servicing. We examined the exposure records arising from planned prophy-
lactic servicing after prolonged operation with fill pins that had begun to leak; we found that examination and
minor servicing of monitoring and measuring equipments in parts of the first loop involved certain does levels
to a comparatively large number of staff (Table 1).
During operations in the heat-exchanger sections for the first loop, the y-ray doses to the hands were
30-40% higher than those to the body as a whole; the exposure due to 9 rays was not more than 3% of the total
dose. The mean radiation dose per person was 0.3-0.5 her per year. Not more than 2-3% of the staff received
doses of 1.5-5 ber.
We now consider the radiation environment and staff irradiation during one of the major servicing oper-
ations, namely replacement of the replacable parts of pumps in the first loop, which are extracted by a special
technique using an isolating cover without biological shielding. The cover was supplied with nitrogen to pre-
vent combustion of the sodium on the pump surfaces.
The exposure dose rate from y rays from the extracted part was 200-300 ?R/ec at a distance of 3-5 m.
The radioactive aerosol concentration in the building at that time was not more than 10-13 Ci/liter. The total
working time from start of lifting for the removable part to immersion in the decontamination tank was about
1 h. The total dose to the staff concerned with preparatory operations and removing the part of the pump was
0.7 her. The use of an isolating plastic-film cover in place of a special shielded container enabled us to remove
the part of the pump rapidly and did not lead to contamination of the building or any considerable staff irradi-
ation. The removable part of the pump was placed in a decontamination tank. The exposure dose rate from the
pump after removing the remaining sodium and decontamination was reduced to 0.4-5 pR/sec.
Estimates show that replacement of the cables, valve gear, electrical heaters, etc. in the heat-exchanger
segments give rise to a collective staff dose of 100-500 her at the level of contamination of the coolant and sur-
faces corresponding to prolonged operation with pins with leaking sheaths. Consequently, such operations must
be performed after drainage or purification of the coolant, and sometimes after the loop has been decontami-
nated.
Consequences of Sodium Ignition during Servicing The radioactivity of aerosols during reloading and
servicing operations seldom exceeded 1.10-11 Ci/liter, which represents no hazard if individual protection is
used. However, there may be unacceptable effects from the chemical action of sodium oxide on the skin and
eye. Also, sodium oxide rapidly becomes caustic soda and sodium carbonate in contact with air, and these
materials can corrode construction materials. The most hazardous consequences arise from combustion of
the residual film of sodium on the surfaces of removable parts during extraction when there are coolant leaks.
The resultant dense clouds of sodium oxide greatly reduce visibility and may hinder the escape of staff from
the hazard zone. A concentration of 50 mg/rn3 of sodium combustion products can be tolerated by th e respira-
tory system for only 2.5 min. A rise in concentration from 50 to 100 mg/m3 irritates the eyes and lungs and
interferes with vision.
When the removable part of the pump was being extracted from the BOR-60 with an isolating hood, there
was some combustion of the sodium film on account of lack of match between the nitrogen supply to the hood
and the lifting of the component. However, the smoke lasted only a short time and the sodium aerosol concen-
tration in the working site was low (the radioactivity of the aerosol was about 10-13 Ci/liter, while the sodium
concentration was below 1 mg/m) .
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
TAL ~E 2. Nuclide Concentrations in the
Air of the Central Bay on Burning of Sodium
Film on the Surfaces of Intermediate Heat
Exchanger
Activity
on sur-
Activity
in air
faces, Ci
,
Ci
t=t mini
t=cumin
22N a
3.10-2
4,5.10-3
1,7.10-7
5,3.10-8
6.10-9
110,nAg
1
210-3
1,8.10-4
7.10-8
2,2.10-?
3.10-10
137CS
,
1,1
0,66
2,5.10-;,
7,8 10-0
9.10-,
134CS
0,1
6.10-2
2,310-c
7,1.10-
8.10-8
As a limiting case one can consider the combustion of the residual sodium film on the very extensive sur-
face of the heat exchanger. We assumed that the surfaces of the removable parts bore a sodium film about
0.2 mm thick. This corresponds to about 50 kg of sodium for the BOR-60 heat exchanger. We do not propose
to consider all the-possible emergencies and envisage the case where the inert-gas supply to the isolating
cover is interrupted for some reason. The sodium film on the surfaces of the heat exchanger burns up very
rapidly (in about 18 sec). The maximum sodium concentration in the air may rise to 290 mg/rn 3. Calculations
were performed on the sodium aerosol concentration and the radioactivity due to the main nuclides in the air
of the central bay of the BOR-60 for this situation on the assumption of instantaneous mixing with the ventilation
disconnected, using the maximum observed values for,the nuclide activities in the coolant (Table 2). The co-
efficients representing transition of the nuclides into the aerosol in the combustion of sodium were taken from
[2]. The nuclide activities and the sodium concentration in the air of the central bay would greatly exceed the
permissible values. It would be impossible to enter this space, and the building would have to be evacuated
temporarily. If the ventilation was not working, about 80% of the combustion products would settle on the floor,
18% on the walls, and 2% on the ceiling. All the surfaces would be contaminated and. require decontamination.
Experience with the BOR-60 thus indicates the following positive factors occurring in sodium-cooled sys-
1) retention of a large proportion of the radionuclides escaping from the fuel pins;
2) low activity in nuclides of corrosion origin in the coolant and in deposits;
3) reliable operation of the main units and equipments;
4) prolonged perfect sealing in the first loop at high sodium temperatures;
5) the possibility of cutting pipelines containing frozen sodium;
6) low surface contamination of buildings and low aerosol activities; and
7) low radioactive gas releases from the nuclear power station, with consequently no effect on environ-
mental radioactivity.
However, there still are some problems to be envisaged in the design and operation of sodium-cooled
reactors, which arise mainly during servicing operations:
1) the high level of radioactivity in the coolant on prolonged operation with leaking fuel rods, which
requires efficient means of purifying the coolant;
2) ignition of the residual sodium film on the surfaces of removable units at elevated temperatures,
where protective hoods with inert atmospheres must be used;
3) production of oxides in the loop on opening, which tend to be deposited at the points of installation of
removable parts. It is necessary to maintain an inert atmosphere at such a point throughout servicing;
4) the possibility of sodium leakage, which requires reliable systems for detecting and suppressing com-
bustion in buildings containing the loops; and
5) the possibility that aerosols containing sodium combustion products will enter the buildings if the
sodium burns. It is then necessary to protect the organs of respiration and the eyes from chemical effects of
the sodium.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
LITERATURE CITED
1. V. D. Kizin et al., At. Energ., 44, No. 6, 492 (1978).
2. Yu. V. Chechetkin, I. G. Kobzar', and G. I. Poznyak, At. Energ., 35, No. 6, 401 (1973).
SEMIEMPIRICAL METHOD OF CALCULATING ISOTOPIC
COMPOSITION OF URANIUM AND PLUTONIUM IN IRRADIATED
FUEL FROM A WATER-COOLED - WATER-MODERATED REACTOR
B.
A.
Bibichev,
A. V. Lovtsyus,
V.
P.
Maiorov,
M. A. Razuraeva,
A.
V.
Stepanov,
and P. I. F'edotov
The method of fission-product y spectrometry is widely used to measure the burnup of power-reactor
fuel. However, such measurements do not contain direct information on the concentration of heavy nuclides in
the fuel. Broader prospects for the method of fission-product y spectrometry may be secured by combining y-
spectrometric measurements with theoretical calculations [1].
The concentration of fission products in irradiated fuel depends on the initial isotopic composition of the
fuel, on the conditions of irradiation (the duration of each irradiation cycle and the mean relative thermal .
power of the given fuel element in each irradiation cycle), and also on the neutron-flux parameters and their
variation in the course of irradiation of the given fuel element. This allows the neutron-flux parameters in the
course of fuel irradiation to be determined and the concentration of heavy nuclides to be calculated from the
known initial fuel composition and the measured concentration of certain fission products, for known irradiation
conditions.
The change in isotopic composition of the fuel in the course of irradiation is described by the following
system of equations
dNi (t)l dt = (l)thai-1Ni-i (t) - ((t.h6 i Xi) Ni (t); (1)
dNj (t)/dt = q>th v Yji&iN1 (t) + q)th6i-lNj-i (t) - (Dth6j +?) Nj (t), (2)
where Ni(t) is the concentration of the i-th heavy nuclide; Nj(t), concentration of the j-th fission product; `I)th,
thermal-neutron flux density; oi, effective cross section of the i-th nuclide; Y.i, yield of the j-th fission pro-
duct in the fission of the i-th heavy nuclide; of-1i effective cross section of the (n, y) reaction at the (i - 1)-th
nuclide; 64, effective absorption cross section for the i-th nuclide; Xi, decay constants of the i-th nuclide.
In solving Eqs. (1) and (2), the neutron spectrum is divided into two groups : thermal and superthermal.
In addition, in calculating the contribution of 238U to the formation of fission products, the fission neutron spec-
trum is also considered. The effective cross section for all nuclides except 238U is determined from the for-
mula
6 - 6th+-CGI, (3)
where 6th is the thermal cross section; I, resonance integral; a, hardness of the neutron spectrum.
For 238U, the product 623BU'r is taken as 0238U, where az38U is the 238U fission cross section averaged
over the fission neutron spectrum; r is the ratio of the fission-neutron flux density to 4)th. In the calculations,
use is made of the dependence of the variation of'Dth and a on the concentration of fissile nuclides from [2].
On passing from the n-th irradiation cycle, with relative thermal power Rn, to the (n+1)-th cycle, 4th is
multiplied by Rn+l/Rn.
There are three free parameters in Eqs. (1) and (2) : 4th(O) and a (0), which are the values of 4,th and a
at the beginning of irradiation, and also r. In [1] it was noted that r has a weak influence on the fission-pro-
duct concentration, and therefore in the present calculations the value of r is taken from theoretical calcula-
tions for a water-cooled-water-moderated reactor [3]. Having measured concentrations of 137Cs and 134Cs, a
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 294-297, May, 1980. Original article submitted
October 30, 1978; revision submitted October 14, 1979.
0038-531) 0/4805-0294$07.50 ? 1980 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
TABLE 1. Uranium-Isotope Concentrations in Fuel-Element Samples, 1018 atom/g U
Fuel-element
position over
Calculated
23511
23611
Sample No.
No
fuel-element
height, mm
burnup, kg/ton
U
expt.
calc.
expt.
calc.
1
98
125
6,2
58,5
60,1 (+
2,7) *
2,87
3,09(+7,7)
2
76
2125
10,7
49,1
49,9(+
1,6)
5,02
4,86(-3,2)
3
4
375
12,8
44,9
45,3(+
0,9)
5,30
5,59(+5,5)
4
4
1125
14,6
41,6
41,8 (+
0,5)
5,89
6,14 (+4,2)
5
107
50
15,0
40,0
41,0 (+
2,5)
6,22
6,25 (+0,5)
6
87
375
28,5
20,8
21,3 (
+2,4)
9,38
9,04 (-3,6)
7
76
375
28,9
21,1
21,4(+
1,4)
9,29
9,04(-2,7)
8
68
1625
33,7
15,8
16,0 (
+1,3)
9,65
9,58 (-0,7)
*The figure in brackets is the discrepancy between the calculated and experimental results
%
specified irradiation program, and the initial isotopic concentration of the fuel, the values 4)th(0) and 6x(0) are
found by fitting the calculated values N137 and N134 (N137)2 to measured values. The values of N137 and N134/(N137)2
may expediently be used for finding the parameters 4'th(0) and a(0), since each value strongly depends on only
one of the parameters: N137 on 4'th(0) and N134Y (N137)2 on a(0). For example, for a fuel burnup of around 20
kg/ton on U
8]nN137 =1.0;
6 In l th (0)
8In [N134! (N137)2] = 0,05;
S In 0th (0)
6 In N137 = 0.18;
6 In a (0)
6 In [N134! (N137)21 = 0.60.
6lna(0)
Numerical integration is used to solve Eqs. (1) and (2), with an irradiation time step of 1 day. The values
of 41th(0) and a(0) are found by the gradient method. The following nuclides are included in the system of equa-
tions: 235U, 236U, 238U, 239pu, 240pu, 24ipu, 242pu, 137Cs, 133Cs, 134Cs, 144Ce, 106Ru. Note that the accuracy obtained
in calculating the burnup and isotopic composition of the fuel within the framework of the given method depends
significantly on the choice of nuclear data: 0th, I, and Y. In the present calculations, values of oth and I for
heavy nuclides calculated using the ROR program [3] are taken as the basis. However, these values change as
burnup proceeds, and so averaged values of 0th and I for burnup from 0 to 35 kg/tononU are used. The value
of Y is taken from [4].
The error in calculating the concentration of uranium and plutonium isotopes was verified experimentally
on fuel-element samples by destructive methods. To this end, eight samples were cut from fuel elements of
two cassettes of the VVER-365 reactor, with an initial 235U enrichment of 3% and with various irradiation his-
tories. Samples 1-4 were cut from DR-3 No. 80 cassette, with a mean burnup of 12.7 kg/ton on U, and the
remainder from cassette RP-3 No. 223 with a mean burnup of 30.2 kg/tononU. The numbers of the fuel elements
and the positions over the height of the fuel element at which the samples were cut are shown in Table 1 (the
total fuel-element height is 2500 mm). The samples were dissolved, and the concentrations of 137Cs and 13`1Cs
and also the concentrations of uranium and plutonium isotopes were measured in aliquots of the solutions. The
137Cs and 134Cs solutions were measured by a y-spectrometric method. The uranium concentration was deter-
mined by potentiometric titration using the Davis and Gray method, and the plutonium concentration by the
method of isotopic dilution with a-spectrometric termination and using 238Pu as isotopic label. The isotopic
composition of uranium and plutonium was determined using a mass-spectrometric method (Tables 1 and 2).
The error in measuring the 137Cs and 131Cs concentrations in the samples was, on average, 1.5%; for 235U,
0.8%; for 236U, 1.3%0; for 239Pu, 0.8%; for 240Pu, 1.2%; for 241Pu, 1.5%; and for 242Pu, 1.8%.
Note that the measured concentrations of uranium and plutonium isotopes in sample 8 were used in cor-
recting and 0c for 235U and 239Pu? Ic for 240Pu and 133CS; and also for correcting r. The values of these
g th th
quantities were chosen in accordance with the condition of best agreement between the calculated and experi-
mental values for sample 8. For the remaining samples these quantities were chosen in the same way as for
sample 8. The important point in the correction of 0th and I is the choice of IF33, since the rather stronger
resonances of the reactions (n, y) on 133Cs and 238U partially overlap, which leads to IC133 blocking. Table 3
shows the values of 0th and I for uranium, plutonium, and cesium nuclides used in the calculations.
The greatest discrepancies between the calculated and measured concentrations for 235U and 236U (see
Table 1) are 2.7% and 7.7%, respectively. The difference in calculated and measured concentrations for plu-
tonium isotopes is larger (see Table 2) than for uranium isotopes. The greatest discrepancy for 239Pu, observed
in end samples, may be explained in that the thermal-power distribution over the irradiation period may differ
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
TABLE 2. Plutonium-Isotope Concentrations in Samples
Sam-
233Pu, 1018 atom/gu
24Upu, 1018 atom/g'u
241Pu, 1017 atom/g U
292Pu, 1018 atom/g U
Pu, 1018 atom/ g U
ple
expt.
calc.
expt.
I calc.
expt.
I calc.
expt.
I calc.
expt.
calc.
No.
1
6,76
7,28 (+7,7) *
0,75
0,73 (-2,7)
2,08
1,25 (-40)
1,16
0,60 (-48)
7,73
8,14 (+5,3)
2
10,3
10,4 (+1,0)
1,76
1,72 (-2,3)
7,53
4,83 (-36)
6,94
4,29 (-38)
12,9
12,6 (-2,3)
3
10,8
11,0(+1,9)
2,20
2,20(0)
9,98
7,00(-30)
12,2
7,77(-36)
14,1
14,0(-0,7)
4
11,3
11,2 (-0,9)
2,54
2,59 (+2,0)
11,9
8,85 (-26)
17,4
11,6 (-33)
15,2
14,8 (-2,6)
5
9,26
10,9 (+18)
2,27
2,65 (+17)
8,74
8,74 (0)
14,1
12,1 (-14)
12,5
14,5 (+16)
6
13,1
13,4 (+2,3)
5,02
5,19 (+3,4)
27,6
29,0 (+5,1)
96,2
94,0 (-2,3)
21,8
22,4 (+2,8)
8
13,1
13,2 (+0,8)
5,64
5,77 (+2,3)
31,8
34,7 (+9,1)
140
146 (-4,3)
23,3
23,9 (+2,6)
*The figure in brackets is the discrepancy between the calculated and experimental results,
TABLE 3. Thermal Cross Sections and
Effective Resonance Integrals Used in Cal-
culations
clide
I uth
1 It
I ?th
I I~ I
lclNU_ ide
J.Qth
I It
I ?th
Ic
235U
307
292
58,0
119
241Pu
744
459
267
331
236U
-
-
3,73
350
242Pu
-
-
9,91
1210
238U
0,349
0,349
1,45
23,5
193Cs
-
-
16,6
300
238Pu
672
286
374
180
134CS
-
-
80,2
-
240pu
-
-
173
3400
13709
-
-
0,063
-
for end and central sections of the fuel element. In addition, '238 may also differ somewhat for end and central
sections of the fuel element. The considerable discrepancy between the calculated and experimental data for
the 241Pu and 242Pu concentrations in samples with small fuel burnup is related to the strong dependence of 1240
on the fuel burnup. Since the value of 1240 was chosen for sample 8 with large fuel burnup, it is not optimal for
samples with small burnup.
To estimate the contribution of the error in measuring N137 and N134 to the total error in determining the
concentrations of uranium and plutonium isotopes, the change in isotopic composition of uranium and plutonium
in samples 4 and 8 when N137 and N134 change by 1.5% was calculated. The change in the concentrations of
uranium and plutonium isotopes in sample 4 was as follows: 235U by 1.1%; 236U by 1.0%; 239Pu by 1.2% ; 240pu
by 2%; 241Pu by 0.003%; 242Pu by 2.4%. In sample 8, the corresponding figures were as follows: 235U by 4.3%;
231U by 0.7%; 231 Pu by 3.5% ; 240Pu by 1.5%; 241Pu by 1.7%; and 242Pu by 2.5%. It is evident from Tables 1 and 2
that, except for, the 235U concentration, the discrepancy between the calculated and measured concentrations of
uranium and plutonium isotopes in all the samples, taken as an average over the sample, considerably exceeds
the error due to N137 and N134?
Note, in conclusion, that experimental and calculated data for a considerably larger number of samples
are necessary for reliable estimation of the error of the method. In addition, it is also necessary to verify the
correction of the most important effective cross sections used in the calculations over the whole set of experi-
mental data on the isotopic composition of the fuel in the fuel-element samples. After correcting the effective
cross sections, the method may be used for nondestructive measurements of the content of uranium and plu-
tonium isotopes in the fuel elements and cassettes of water-cooled - water-moderated reactors. The 137Cs and
134Cs concentrations in intact fuel elements and cassettes may be measured y-spectrometrically.
1. O. Eder and M. Lammer, in: Proceedings of IAEA Symposium on Nuclear Data in Science and Tech-
nology, Vol. 1, Vienna (1974), p. 233.
2. T. S. Zaritskaya, A. K. Kruglov, and A. P. Rudik, At. Energ., 41, No. 5, 321 (1976).
3. V. D. Sidorenko and E. D. Belyaeva, Preprint IAE-1171 (1966).
4. M. Meek and B. Rider, Compilation of Fission Product Yields, Vallecitos Nuclear Center, NEDO-12154-1
(1974).
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
A form factor ? analogous to the Randall form factor. [1] has been introduced for a reactor with N fast-
acting astatic regulators* [2, 3] as an eigenvalue for the system
A (p Boq) I ~0? N] Fjsj + ?cp = 0; (la)
j=1 .
KjVidV=0, j=1,2, ...,AT, (lb)
V
where B0 and 4)0 are the unperturbed material parameter and the neutron-flux distribution, while Fj describes
the spatial localization of the reactivity sj introduced by control rod j and Kj is the weighting function in the
formation of the transducer signals for control of this rod. The spatial stability of a reactor for slow pro-
cesses is the greater the higher the minimum value Amin [1-6]. Various control systems influence ?min' and
a study has been made [3] of the effects of various arrangements of the transducers and control rods for a
height problem. The same method has been applied [7] to the effects of a central automatic regulator on the
spatial stability for the cylindrical case. Such a regulator cannot correct the azimuthal distortion in the neu-
tron distribution, and this requires eccentrically placed control rods. The BASIRA program has been used with
a BESM-6 in detailed analysis of the stability of such a system with a complicated distribution of the param-
eters; however, the situation can be analyzed qualitatively without resort to a computer. We consider a homo-
geneous cylindrical reactor of unit radius with zero boundary conditions (Bo = 2.405).
If the thin control rods are placed at points with coordinates (Rj, 9j), j = 1, 2, ..., N, then the solution to
(1a) will [8] be the sum
N
cP (r, '0) = u ajfj (r, 0), (2)
j=s
" (B) cos n (0 -15j).
fj (r, 0) = No (Brj) - J? (B Rj) J?. (Br) N
Jn (B)
Here Jn and Nn are Bessel and Neumann functions, respectively, of order n, B2 = B,+?, and rj is the di8tance
from control rod j to the point with coordinates (r, 0).
The relation between the aj and the eigenvalues B can be derived from (1b); it has been shown [2, 3] that
conditions (1b) become cp (rj, ej) = 0; j = 1, 2, ..., N (rj and 0j are the polar coordinates of transducer,j) if
each regulator is designed to maintain a given neutron flux at the position of its transducer.
We consider six control rods symmetrically disposed in azimuth at a radius p and six transducers at
radius rg on the same radii as the control rods. We put fi = fl (rg, 0), f2 = f1 (rg, ir/3), f3 = fl (rg, 27r/3), and
f4 = fi (rg, 7r), and instead of (1b) we have Aa = 0, where a is a vector with components aj and matrix A takes
the form
It is assumed that the regulators have fast-process stability.
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 297-300, May, 1980. Original article submitted
July 2, 1979.
0038-531X/`8O/4805-0297$07.50 ? 1980 Plenum Publishing Corporation 297
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
1 1
0,3 r4
Fig. 1. B as a function of the distance
between control rod and transducer for the
first roots of: 1) (3a) ; 2) (3b) ; 3) (5) ; 4) (6a) ;
5) (6b) ; 6) (7).
b, b2 b3 b4 b3 b2I
b2 b, b2 b3 b4 bs
b3 b2 b4 b2 b3 b4
b4 b;, by b4 b2 1i3
b3 b4 b3 b2-b, b2
~b2 b3 b4 b3 b2 b4
where bl = fl.
Matrix A belongs to the circulant class [9].. We use a property of such matrices to convert
form and get the following four transcendental equations, for B:
b, + 2 (b2 + b3) + b4 = 0;
b,+b2-b3-b4=0;
b, -b2-b3-I-.b40;
b,-2(b2-b3)-b4=0.
.We substitute the corresponding expressions for the bl and get after elementary steps
No (Bri) + 2No (Br2) + 2No (Br3) + No (Br4) - 6
Z Ugh 1 = 0;
(3a)
No (Br4) -f- No (Brz) - No (Br3) - No (Br4) - 6
Li
UI1 +Bnl = 0;
(3 b)
No (Br4) - No (Brz) - No (Br3). -I- No (Br4) - 6
U12+cnj= 0;
No (Br4) - 2No (Brz) + 2No (Br3) - No (Br4) - 6
I
Up+snI=
where Uk = Jh (Bp) Jk (Brg) 7k j , ri is the distance from the first control rod to transducer i, and rl = erg-pl.
Apart from the sum of (2), the solution to (1) for this example is provided by functions of the form Jan
(Br) sin 3n9 for those values of B for which
Jan (B) 0, n = 1, 2, ... (3e)
Therefore, the minimum eigenvalue Bmin = Bo+?min should be selected from the complete set of roots
of these equations.
The simplest of the equations is (3e). The least of the set of values defined by this is B = 6.380. This is
not dependent on p or on rg, so such a system in principle cannot provide stability in the reactor if the latter
is unstable on more than two azimuthal modes in the absence of the regulators. Although the other equations
are complicated in form, they can be analyzed quite simply, and the least roots can be estimated even without
a computer. Equation (3a) is related to the scope for radial stabilization (including the fundamental), while
(3b), (3c), and (3d) are related mainly to the scope for eliminating dipole, quadrupole, and higher-order azi-
muthal perturbations in the neutron distribution. These considerations alone indicate that one should seek the
minimum eigenvalue primarily alongst the roots of (3a). The same conclusion is reached by considering the
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
I I ' S
0,6 0,7. 0,8
Fig. 2. Dependence of B on control rod
placing: 1 and 2) first roots of (3a) and (3b)
respectively; 3 and 4) first root of (4) for
l = 0 and l = 1; 5) first root of (5).
limiting case r1-0. Then N0(Br1)---oo. The structure of the expressions for Uk shows that the roots of all
equations are then zeros of Bessel functions. Therefore, the minimum roots of (3a)-(3d) will be correspondingly
2.405, 3.832, 5.136, and 6.380. The same technique can be applied to the performance of eccentrically disposed
control rods [8] for r1 small to demonstrate readily that these values of B increase with r1. It is difficult to
demonstrate analytically that there is monotone growth of these throughout the entire range in r1, but this is
confirmed by numerical calculations, and it is demonstrated also below analytically for large r1. Therefore,
one should not seek the Bmin among the roots of (3d), and this equation can be eliminated from the subsequent
analysis. If only the first azimuthal mode is unstable, we can also eliminate (3c) from consideration. Very
often, the minimum eigenvalue is found from the equation related to radial stabilization, i.e., (3a) in this exam-
ple.
An important feature of the sums appearing in (3) is the rapid convergence; as a rule, it is sufficient to
take the term in the sum with the least subscript in order to determine the least of the roots. These are cor-
respondingly UO, U1, and U2 for (3a), (3b), and (3c). Figure 1 shows the r1 dependence of the least roots of (3a)
and (3b) for p=2/3 . The solution was obtained graphically. Incorporation of the second term in the sum results
in a correction to the root not exceeding 3%. Figure 1 shows that the stability of the system is limited by the
least root of (3a), i.e., the fundamental mode is actually stable. Further, the stability is increased within rather
narrow limits as the transducer recedes from the control rod to the edge of the core. However, such displace-
ment of the transducer has a much greater effect on the azimuthal stability (curve 2). Figure 2 shows the
effects of control-rod position on the least roots of (3a) and (3b) for rg = 0.9. It is clear that the stability. can
be varied widely via the separation between the control rod and the transducer. Stability on the fundamental is
the limiting factor throughout the range.
Curves 3 and 4 of Fig. 2 are described by B = 2.405/p and B = 3.832/p; Fig. 2 shows that the divergence
between curves 1 and 3 decreases as the distance between the transducer and the control rod is increased, and
the same applies to curve 2 and 4. This is explained as follows. The addition theorem [10] for Neumann func-
tions enables us to transform (3) into
Y, V11+6,,i=0,
n=-~
Jk (Brg) ~N~: (BP) - Jk (Bp) Nk (v)
Jk (B)
for p > rg.
If the terms of (4) are arranged in order of increasing subscript, then the sums will converge the more
rapidly the greater the difference between p and rg. If this difference is sufficiently large, we can restrict our-
selves to the following equations in estimating the least roots:
V1 0, 1 = 0, 1, 2..
These equations have previously been published [7], where it was pointed out that the p dependence of the least
1=0,1,2,3, (4)
Jk(Bp)[Nh(Brg)-Jk(Br'g) Nh I
k (B)
for p < rg
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
.. ___ ~.. ~., ,, DulJW11 111 r ig. z curves ;i and 4) for l = 0 and l = 1 for rg sufficiently large.
Figure 2 shows that curves 1 and 3 almost coincide for rg = 0.9 and p'>1, the functions F1 and Fli are expanded in series in inverse powers
F'1, II = y'-L, II u j 1' (12)
II (N) Y_Zn
n=0
where a1 = 3, all = 4. After replacing the variable of integration x by z/, it becomes obvious that only terms
to the fourth power appear in the sum. Note that it is possible for F`n)(N) to depend on In y. At large y, only
the first nonvanishing term of the expansion in Eq. (12) exists.
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
*
The expression obtained for the radial component in the case N?y-3 is of the form
F1' (N) = - 3N + 2CN - 8 + 2N 8N
In y4 + 4N + 2(1+u4) _ 4N ( dz In z dz
n n n. n n n (1-M) U (1-E-b2)3 n dzz
0
( z 1 8N 1 dz exp [k (z)] [1-Nz (1+z)2]-1 8N dz r 1 3
lexp[k(z)]-1J n (1+z).3 {exp [k(z)]-1)1 + n exp (z)1-1 L3-{-4z (9+4z)21'
0
where C is an Euler constant; M = exp (2N/3); also
i n2+ 3n 1/3 1/3
u=n) 9n2
-(V*+ 3n
1-*I
N2 N N2 N ;
is the real root of the equation a3+3u-67r/N = 0; k(z) = ~z(1-z2`3); and p(z) = (2NC3)(1+4z/3) (1.
In the limiting case y 3?N?1, the first nonvanishing term in Eq. (12) takes the form
* F1' (N--0) =1/2a.
In the other limiting case N>>1, the first term of the asymptotic expansion in Eq. (12) takes the form
F1'(N-oo)=4n (In 2Vz-}-C).
Note that the formula for the radial force obtained in the approximation of the field of a charge moving in a
straight line contains an additional factor -y 2 in comparison with Eq. (15). For N-'1, all the terms in Eq.
(13) are comparable in size.
The ratio of the radial component Fl of the beam self-action to the external force maintaining circular
motion of a single particle over a path of radius R may be of the order of unity in certain cases (e.g., in
adhesators, where y-10, N- 1013, R -1 cm [5]). However, for large electron and proton accumulators and
accelerators, the important factor is not this ratio, which is less than unity for such machines, but the fre-
quency shift of the betatron oscillations arising due to beam self-action. The corresponding analysis, while of
considerable interest, is beset by great computational difficulties.
For the tangential component in the case N>> y-3, the first term of the expansion in Eq. (12) takes the
form
* * 00
~' * 8 2(1+uz--+ 2u4) N= 12N dz f 1 6
FII, (N) = 3 + u2 (1+u2)3 Ln2 +
n exp {p (z2)}-7 l_ _9_+ -4z2 (9+4iz)"
o
3-4zz 18N dz d 1 1
(3 [ 4z2)2 ] + z dz ((9 4z2) (exp (p (z2))
-1) l
* 0
In the limiting case y 3 E') and a, (E) = r aE (E --> E) dE'
u
are the microscopic differential and total cross sections for Compton scattering, Eb = min (E0, E'/1-2E') for
Translated from Atomnaya Energiya, Vol. 48, No. 5, pp. 337-339, May, 1980. Original article submitted
July 23, 1979; revision submitted January 2, 1980.
0038-531$0/4805-0349 $07.50 ?1980 Plenum Publishing Corporation
Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
 Declassified and Approved For Release 2013/02/01: CIA-RDP10-02196R000800030004-0
- 81 1
0 0,2 0,4 0,6
Fig. 1
0,1 0,2 0,3 0,4 E, MeV
Fig. 2
Fig. 1. Perturbations of the intensity due to scattering in water for a point
isotropic source with E0 = 0.5 MeV in relation to distance l between the source
S and the surface of an absorbing disk of radius 5.5 cm (J is the intensity of
the scattered radiation without the absorbing disk).
Fig. 2. Energy distribution for the scattered radiation intensity: solid line
ordinary calculation by Monte Carlo method (lo = 2); broken line calculation
by perturbation theory (lo = 2 and 1 = 0.1).
E'