SOVIET ATOMIC ENERGY - VOL. 39, NO. 1

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• Release Decision: RIFPUB
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• Document Page Count: 102
• Document Creation Date: January 4, 2017
• Document Release Date: September 24, 2013
• Sequence Number: 1
• Publication Date: January 1, 1976
• Content Type: REPORT

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Russian Original Vol. 39, No. 1, July, 1975
January, 197
SATEAZ 39(1) 571-666 (1975)
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HEPITIR
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
rc"
q4.) CONSULTANTS BUREAU, NEW YORK
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:pup:
ATOM IC
'ENERGY'
't?
,
Soviet Atomic Energy is' abstrated, or in- ?
- dexed in Applied? Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physias Abstracts and Electrical and Elec-
tronks ? Abstracts, Current Contents, and
Nuclear Science Abstracts: 7'1
'
Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
,
Energiya,-a publication of the Acadeiny of Sqences of the USSR!
, ?
An agreement with the Copyright Agericy of the USSR (VAAP)
Makes available, beth advance 'copies of Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publicatkm of thepriginal ariad
publicatiqn of the transletion and helps to improve the quality
Of the latter. The transletion began with the first issue of the
? Russian journal. '
/Editorial Board of Atomnaya 'Energiya:
? Editor: M. D. Millionshchikov
Deputy Director ,
I. V. Kurthatov Institute of Atomic Energy
Academy of Sciences of the USSR.
Moscow, USSR
,Associate Editor: N. A. Vlasov
A. A. Bochvar
N. A. Dollezhal'
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 ?
Copyrigbt C) 1976 Planum Publishing Corporation, 227 West 17th Street, New liork,
N.Y. 10911,? All rights reserved. No article contained kerein may ,be reproduced,
stored in a retrieval system; or transmitted, in any form'br by any means, electronic?
mechanical, photocopying, microfilming, recording or otherwise, without Written
permission of the publisher.
? '
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
January, 1976
Volume 39, Number 1
July, 1975
ARTICLES
Investigation of the Physical Characteristics of the Reactor during Startup of the First
Unit of the Bilibinsk Nuclear Power Station ? A. A. Vaimugin,
CONTENTS
Engl./Russ.
V. V. Bondarenko, V. K. Goryunov, A. V. Gusev, B. G. Dubovskii, P. G. Dushin,
A. N. Efeshin, L. D. Kirillovykh, I. M. Kisil', V. I. Kozlov, 0. V. Komissarov,
E. V. Koryagin, A. G. Kostromin, N. I. Lagosha, M. A. Lyutov, M. E. Minashin,
K. N. Mokhnatkin,A.P. Paniko, Yu. F. Taskaev, V. N. Sharapov,
and A. I. Shtyfurko
571
3
BOOK REVIEWS
V. G. Zolotukhin, L. R. Kimell, A. I. Ksenofontov,et al. The Radiation Field from a
Point Unidirectional Source of Gamma Quanta ? Reviewed by B. R. Bergelyson
577
8
ARTICLES
Some Problems of the Economics of a Research Nuclear Reactor ? V. I. Zelenov,
S. G. Karpechko, and A. D. Nikiforov
579
9
BOOK REVIEWS
A. A. Vorob'ev, B. A.Kononov, and V. V. Evstigneev. Betatron Electron Beams
? Reviewed by P. S. Mikhalev
583
11
ARTICLES
Synthesis of a Digital System for Control of Neutron Flux Distribution
? E. V. Filipchuk, P. T. Potapenko, V. G. Dunaev, N. A. Kuznetov,
and V. V. Fedulov
585
12
Absolute Measurement of the Radiative Capture Cross Section of 238U for 30 keV
Neutrons ? Yu. G. Panitkin and L. E. Sherman
591
17
Heat-Transfer Crisis in a Steam-Generating Tube on Heating with a Liquid?Metal Heat
Carrier (Coolant) ? A. V. Nekrasov, S. A. Logvinov, and I. N.Te"="6""""mg
595
20 ---
X-Ray Diffraction Study of the Effect of the Temperature of Deformation in the Alpha
Phase on the Quench Texture of Uranium Rods Containing Various Proportions of
Iron and Silicon ? V. F. Zelenskii, V. V. Kunchenko, V. S. Krasnorutskii,
N. M. Roenko, V. P. Ashikhmin, A. V. Azarenko, and A. I. Stukalov
599
24
A Loop Converter Channel for Testing Highly-Enriched Fuel Elements in a Research
Reactor ? V. G. Bobkov, V. B. Klimentov, G. A. Kopchinskii, M. V. MePnikov,
and V. A. Nechiporuk
603
28
Tests on Experimental Fuel Elements Containing Carbide Fuel,Irradiated in the LallS.1.)
Reactor up to a Burn-Ups of 3 and 7% ? E. F. A. A. Maershin,
608
33-
V. N. Syuzev, Yu. K. Bibilashvili, I. S. Golovnin, and T. S. Mentshikova
Recollections of Professor Boris Vasil'evich Kurchatov, Doctor of Chemical Science,
on His Seventieth Birthday ? S. A. Baranov, A. R. Striganov, and P. M. Chulkov
612
39
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CONTENTS
REVIEWS
Problems in Shipment of Spent Fuel, from Nuclear Power Stations ? Yu.I. Arkhipovskii,
(continued)
Engl./Russ.
615 42
620 48
621 49
V. A. Burlakov, A. N. Kondratiev, E. D. Lyubimov, and A. P. Markovin
ABSTRACTS
Total Stability of a Nuclear Reactor with Connected Cores ? N. A. Babkin
Frequency Criterion for the Stability of a Circulating-Fuel Reactor ? V. D. Goryachenko
and V. V. Mikishev
Estimation of the Effect of Physico-Geometric Factors on the Distribution of Delayed
Fission Neutrons in a Borehole ? Yu. B. Davydov
622
49
Spatial Distribution of Fission Neutrons in a Breeding Medium, Crossed by a Drill Hole
? Yu. B. Davydov
623
50
Variable Mechanical Stresses, Induced in the Fuel Element Claddings of the IBR-30
Reactor by Power Pulses ? V. S. Dmitriev, L. S. Winskaya, G. N. Pogodaev,
V. V. Podnebesnov, A. D. Rogov, V. T. Rudenko, and 0. A. Shatskaya
624
51
Correction of the Group Constants by the Results of Experiments on the BFS Critical
Assemblies ? A. A. Van'kov and A. I. Voropaev
625
51
The Influence of Beam Noise on the Critical Current of Linear Electron Accelerators
? I. N. Mondrus
625
52
Model of Grouping of Low Energy Transfers in Calculating Electron Fields by the Monte
Carlo Method ? A. V. Plyasheshnikov and A. M. Kol,chuzhkin
626
53
LETTERS TO THE EDITOR
Use of a252Cf FissionChamber in Certain Physical Measurements ? V. F. Efimenko,
V. K. Mozhaev, and V. A. Dalin
628
54
Eio.?11/sza2.1s,........anibuti of Neutrons Emerging from 13, R-10 Reactor Channels ? L. A. Trykov,
631
56
V. P. Semenov, and A. N. Nikolaev
Track Detectors with an Extended Range of Measurements ? L. P. Roginets,
0. I. Yaroshevich, A. P. Malykhin, and I. V. Zhuk
636
60
?-Detectors of the Radiation Typed Based on "Pure" Germanium ? V. K. Eremin,
E. P. Dudnik, D. I. Levinzon, N. B. Strokan, N. I. Tisnek and O.P. Chikalova
638
62
Comparative Characteristics of Nal(T1) and CsI(T1) Detectors ? 0. P. Sobornov
and 0. P. Shcheglov
640
63
Calculation of tremsstrahlung Spectra at Various Angles in the 1-30 MeV Range
? V. E. Zhuchko and Yu. M. Tsipenyuk
643
66
Monocrystalline Films of GaAs as Spectral Detectors of X-Rays and Soft y-Radiation
? V. M. Zaletin, I. I. Protasov, 0. A. Matveev, P. I. Skorokhodov,
and A. Kb. Khusainov
646
68
Density, Surface Tension, and Viscosity of Uranium Trichloride?Sodium Chloride Melts
? V. N. Desyatnik, S. F. Katyshev, S. P. Raspopin, and Yu. F. Chervinskii
649
70
INFORMATION
On the So-Called Cosmion ? N. A. Vlasov
652
73
INFORMATION: CONFERENCES AND MEETINGS
Thirty-Seventh Session of the Academic Council of the Joint Institute of Nuclear Research
(JINR) ? V. A. Biryukov
654
74
The European Conference on the Effect of Radiation on Materials for Fuel Element
Cladding and Cores ? Yu. N. Sokurskii
659
77
Seminar on the Use of Thermal Nuclear Reactors in Ferrous Metallurgy
? E. F. Ratnikov
660
77
INFORMATION: NEW INSTRUMENTS AND APPARATUS
Self-Contained Radioisotope Power Units for Navigation Equipment Systems
? Yu. B. Flekel', B. S. Sukov, and A. I. Ragozinskii
661
78
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CONTENTS
(continued)
Engl./Russ.
TOR-3 Reflecting Gamma Thickness Gage ? P. G. Lakhmanov, Yu. A. Skoblo,
and V. B. Timofeev 663 79
BOOK REVIEWS
S. M. Gorodinskii and D. S. Goltdshtein. Decontamination of Polymer Materials
? Reviewed by E. E. Finkel' 664 80
The Russian press date (podpisano k pechati) of this issue was 6/26/1975.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
INVESTIGATION OF THE PHYSICAL CHARACTERISTICS
OF THE REACTOR DURING STARTUP OF THE FIRST UNIT
OF THE BILIBINSK NUCLEAR POWER STATION
A. A. Vaimugin, V. V. Bondarenko,
V. K. Goryunov, A. V. Gusev,
B. G. Dubovskii, P. G. Dushin,
A. N. Efeshin, L. D. Kirillovykh,
M. Kistlt, V. I. Kozlov,
0 V. Komissarov, E. V. Koryagin,
A. G. Kostromin, N. I. Lagosha,
1V1 A. Lyutov, M. E. Minashin,
K. N. Mokhnatkin,A. P. Pantko,
Yu. F. Taskaev, V. N. Sharapov,
and A. I. Shtyfurko.
UDC 621.039.524.2621.039.519
As already reported [1], the Bilibinsk Nuclear Power Station will consist of four units with reactors
of the same type. In the period from 10 to 31 December, 1973, physical startup of the reactor of the first
unit was effected* and on January 12, 1974 the Bilibinsk Nuclear Power Station produced electric current
for the first time.
During startup of the reactor of the first unit, detailed investigations were undertaken of the physical
characteristics of the active zone in order to introduce, if required, any necessary changes in the loading
of the reactors of subsequent units. The startup program, therefore, in addition to determining the
characteristics of the reactor necessary for operation, provided for a number of other measurements, in
particular, determination of the parameters of critical assemblies which was necessary for verification of
the accuracy of the design procedures used in planning.
*The second unit of the nuclear power station was brought on stream at the end of 1974.
TABLE 1. Physical Characteristics of As-
semblies
Assembly
Critical number of
FC-3
Material parameter,
m-2
experiment
calcula-
tion
experiment
calcula-
tion
I
II
III
IV
38,3+0,2
55,2+0,2
50,8+0,2
63,5?0,2
39
55
46
58
6,5?0,6
4,7+0,5
4,4?0,5
?
5,9
4,6
4,5
3,9
TABLE 2. Change of Reactivity on With-
drawal of FC-3 with Water (ApFC) and with
the Water Removed from It OpH2o)
Coordinates ApFC.103
Assembly
of cell*
APH2o. 10'
LII
?4,4?0,2
?3,9?0,2
?2,9?0,2
?2,7?0,2
?1,52?0,08
?0,41?0,02
?0,65?0,03
?0,67?0,03
?0,25?0,02
*Here and in future, the first two figures signify the
number of the row and the next two figures signify the
number of the cell in the row (see Fig. 1, a).
Translated from Atomnaya Energiya, Vol. 39, No. 1, pp. 3-8. July, 1975. Original article sub-
mitted September 13, 1974.
?1976 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.
571
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Number of row
21
20
19
18
17
16
15
14
13
12
11
10
09
08
07
06
05
04
03
02
01
1:1-> 0-2 ? -5 ? -4 o-5 A-6
P2111
Kir
01111CIMICIIIMMIC1111121100110
IIMMMIIMIIIIIIMMIIIIIIIIIIIII
IIMDMICIIIIICIMC1111131110M11
111111111111111:111111MMMIIIII
121111B111:110111CIMEIMCJIMC
MMIIIIIIIMMIIIIIIIMM1111111
121MCIIIICIMCIMCIIIICIMCIMEI
IMEICIIIMMMEMIRMMIll
CIMCIMCIIIDMOINCIIMOMO
MMIIMMIIIIIMMIIIIIIIMMIM
CIMILIMEMICIMCIMOMMIIIICI
111111111M111111121MIIMMIWIIIII
IIMEIMCIIIICIWCIIIKIMallM
MIIIIIIMMEMIIIIIIMMMIll
P2MCIMIZIMCIMC111101111CW2
0802 03 04 05 06 07 08 09 0 1 2 13 415 16 17 18 19 20 21
Number of cell in row
a
14 ?
?
15
? 14
?
NM
MM.
13
12'
11
10
13
12
? 11
10
111111111MOM
11111?111MIIMIN
?
?
111?11111EMIll
09
09
os
?
08
MEM
? 07
? ?
?
08 04 10 11 12 13 14 07 08 09 10 11 12 13 14 15
a
16
15
MA
ME
15
14
1110111121M
14
0
?
13
13
12
MCIMIZIMOM1211111
12
0
0
0
0
11
0 1111111111MMEM
11
10
111311113MOMOM
10
0
0
0
09
1111111111MMEMM
04
08
MCIMCIM
08
?
0
0
?
07
ME
ME
07
06
07 08 09 10 .11 12 13 14 15
C
07 08 09 10 11 12 13 14 15 16
Fig. 1. Record chart of the reactor (a), transverse sections of a fuel channel (b) and
a control and safety rod channel (c): 1, 2) Cells with fuel channels FC-3 and FC-3.3;
3, 4, 5) Automatic control rods (ACR), scram rods (SR) and manual control rods
(MCR); 6) Neutron flux sensors; 7) Graphite brickwork;8) Fuel element;9) Steel tube;
10) Opening for control and safety rod.
Fig. 2. Record charts of critical assemblies I-IV (a-d): 0) Cell with fuel channel FC-3;
?, ? , C) Channels for scram rods, ACR and MCR.
TABLE 3. Change of Reactivity on With-
drawal of the Control and Safety Rod Chan-
nel with Water (ACS), and the Graphite
Plug (NA) from cell 12-12
Assembly
S
ApC ? 103
Apg .103
III
2,8+0,2
?0,74?0,04
IV
2,4+0,2
?0,87?0,04
accordance with the characteristics
Power station reactor.
Measurements on critical assemblies were made for the purpose of investigating the physical prop-
erties separately of the central and peripheral parts of the active zone. The difference between the prop-
erties of these parts of the active zone is because the control and safety rod channels, which occupy
separate cells, are located in the central part of the active zone and not in the peripheral section (Fig. 1).
The following units were mounted in the center of the reactor for these measurements: assembly I repre-
sented the control lattice (200 x 200 mm) of fuel channels filled with water and there were no control and
safety rods in the active zone of the assembly; assembly II was similar to assembly!, but without water in
The condition of the reactor and the emergency
protection was monitored by means of a highly-sensitive
startup equipment, the sensors of which-were located in
the peripheral cells of the active zone. This equipment,
with the presence in the active zone of a startup neutron
source with a strength of ?107n/sec, enabled the
neutron flux in the reactor to be monitored reliably from
the instant of loading of the first fuel channels up to
emergence at the power generating level. The effects of
reactivity were measured by a "Pamir-M" analog
reactimeter [21, whose kinetic simulator was made in
of the effective groups of delayed neutrons of the Bilibinsk Nuclear
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50
75
100
125 r, cm
Fig. 3. Dependence of efficiency of water in the control and safety rod channels
and the square of the neutron flux on the distance to the center of the assembly:
CS
*) Ap ; X)
H20
Fig. 4. Dependence of change of reactivity Lp, by filling an opening for a fuel
channel with graphite, on the distance to the center of the assembly:., ? )
Assemblies I and II.
TABLE 4. Efficiency of Water in Control and
Safety Rod Channels
Position of rod in con-
trol and safety rod
channel
Presence of
waterinfuel
channel
Average change of
reactivity on --
removal
Fully withdrawn
Yes
No
6,1?0,3
8,0?0,4
Fully inserted
Yes
No
4,3+0,2
5,7?0,3 .
the fuel channels; assembly III represented the fuel
channel lattice, evacuated, with control and safety rod
channels and fuel channels filled with water; assembly
IV was similar to assembly III, but without water in the
fuel channels.
In order to form assemblies I and II, 12 regular
control and safety rod channels were removed from the
central part of the reactor and fuel channels were
installed in their place. The entire assembly was
loaded with fuel channels having a 3% uranium enrich-
ment (FC-3).
During the measurements on the assemblies, the
minimum kinetic loadings, fuel channel efficiency and the efficiency of the control and safety rod channels,
and the neutron flux distribution along the radius and height of the assemblies were measured. The
measurement results are shown in Tables 1 to 3 and the record chart of the assemblies is plotted in Fig. 2.
Comparison of the calculated and experimental data (see Table 1), shows their quite good agreement.
The greatest difference (? 9%) in the critical number of channels is observed for assemblies III and IV.
The effect of water in the cooling tubes of the control and safety rod channels on the reactivity of the
assembly was determined. The data obtained (Fig. 3), show that the effectiveness of the water in the con-
trol and safety rod channels (412S0), positioned at a different distance from the center of the active zone,
to a first approximation is proportional to the square of the thermal neutron flux (41). This confirms that
the effect of the water in the control and safety rod channels is due mainly to an increase of thermal neutron
absorption. The overall decrease in reactivity, when the cooling tubes of the 12 central control and safety
rod channels of assembly III are filled with water, amounted to 5.2 ? 10-3.
In the experiments on the assemblies, the opening for the fuel channels, located outside the active
zone, were not filled with graphite. In order to estimate the reduction of efficiency of the reflector due to
the presence of these openings, the change of reactivity when certain openings were filled with graphite and
located at a different distance from the boundary of the active zone (Fig. 4) was determined. The data
showed that by filling all openings of the reflector with graphite, the reactivity is increased by 9.6 ? 10-3
and 7.6 ? 10-3 respectively for assemblies I and II.
573
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TABLE 5, Efficiency of Fuel Channel and Control and Safety Rod Channels
"8
a)
4-1
CtS
Reactor
change
Measurable effect
Change in reactivity, Ak/k. 104
cell 11-11
cell 11-14
cell 11-17
cell 11-19
cell 11-21
269 FC with
FC-3 with water
7,3?0,4
7,4?0,4
5,5?0,3
6,1?0,3
5,8+0,3
water
FC-3.3 with water
9,0?0,5
8,8?0,4
6,6?0,3
7,8?0,4
7,5?0,4
FC-3 filling with water
1,23?0,06
0,33?0,02
0,95?0,05
1,66?0,08
1,06+0,05
FC-3.3 filling with water
1,66?0,08
0,60?0,03
1,26+0,06
2,3?0,1
1,52?0,08
Removal of CSR channel
with water
?
2,4?0,1
2,5?0,1
3,0?0,2
?
269 FC
FC-3 with water
10,0?0,5
10,2?0,5
5,6?0,3
4,6?0,2
4,2?0,2
without
FC-3.3 with water
12,5+0,6
11,5?0,6
7,1?0,4
6,4?0,3
5,6?0,3
water
FC-3 filling with water
2,5+0,1
0,40+0,02
1,39?0,07
2,2?0,1
1,13?0,06
FC-3.3 filling with water
3,3?0,2
1,00?0,05
1,72?0,08
2,9?0,2
1,46?0,07
Removal of CSRchannel
with water
?
3,4?0,2
3,0?0,2
3,5?0,2
?
1,00
0,95?
go-
485-
460
0 20 40 . 60 . BO r, cm
Fig, 5. Dependence of the neutron if
on the distance to the manual control
Measurements with the Full Reactor Charge, After
carrying out the experiments on the assemblies, the reactor
was loaded completely with fuel channels filled with water. A
total of 217 FC-3 and 56 channels with 3.3%-enriched uranium
(FC-3.3), which were installed in the peripheral cells of the
active zone, were loaded into the reactor. The reactor was
compensated at a minimally controlled power level by the
total insertion of 40 manual control rods (out of 48) and 4 auto-
matic control rods were located in the central position. In
this state of the reactor, the efficiency of all the standard
scram rods (8 rods) was Ak/k =1.3 . 10-2, which coincided
satisfactorily with the design value of 1.24 . 10-2. On raising
the scram rods and all the inserted manual control and auto-
matic control rods, the subcriticality of the reactor was equal
to Ak/k = -1.1 ? 10-2. The value obtained for the total reacti-
vity reserve of the reactor (Ak/k = 0.11?0. 015) coincided with
the calculated value.
In the Bilibinsk Nuclear Power Station, reduction of the
water density in the fuel channels leads to a drop in reactivity.
It was determined in the experiments that the complete re-
moval of water from all of the 273 fuel channels reduces the
reactivity of the reactor by 3.1 ? 10-2. The corresponding calculated value is Ak/k = 2.75 ? 10-2. The
experiment showed that water in the fuel channels at 30-50 cm distant from the boundary of the active zone
and located in regions where there are no control and safety rods, has the greatest efficiency. The change
of reactivity on removal of water from the fuel channels is due mainly to an increase of neutron leakage
from the reactor. Analysis of the results of measurements of the efficiency of the rods in the case of a
complete loading of the reactor with fuel channels without and with water, shows that the efficiency of the
first case is greater by a factor of 1.4 approximately than in the second case. The removal of water from
the tubes of the control and safety rod channels leads to a small increase of reactivity of the reactor. This
effect was measured when the reactor was loaded with fuel channels without water, and fuel channels filled
with water (Table 4).
The data given show that the efficiency of water Ak/k in the control and safety rod channels depends
on the position of the absorbing rods in these channels and the presence of water in the fuel channels. In
the control and safety rod channels, the efficiency of the water on withdrawal of the rods, is higher by a
factor of 1.4 approximately than in channels with inserted rods.
During operation of the reactor at 100% power (62 MW), the average water density in the fuel channels
is ? 0.6 g/c m3 and ? 0.9 g/c m3 in the tubes of the control and safety rod channels. As, at the start of the run, the
number of control and safety rod channels with inserted rods is 30 (out of 60), the overall increase of reactivity as
a result of the complete removal of water from the control and safety rod circuit in this case amounts to
3. 5 ? 104.
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The increase of reactivity by the removal of water from the control and safety rod channels is
caused mainly by a change of the multiplication properties of the active zone. The efficiency of the rods
in this case is changed only very insignificantly. The effect of water in the control and safety rod channels
on the efficiency of the rods was investigated for both complete loading of the reactor and by the critical
assembly II. With complete loading of the re'actor, no effect of the water in the control and safety rod
channels on the efficiency of the rods was detected, within the limits of measurement error (?5%). On
assembly II, measurements were conducted in the. control and safety rod channels (12-06 and 12-04),
located in the reflector at distances of 40-80 cm from the boundary of the active zone of the assembly.
The measurements showed that, in this case, the presence of water in the tubes of the control and safety
rod channels reduces the efficiency of the rod by 8-10%.
The effects of reactivity on the setting up of the fuel channels (FC) and the control and safety rod
channels were measured in cells of the eleventh row (see Fig. 1, a) for two states of the reactor: with
the FC filled with water and without water (Table 5). The effects being considered are significantly dif-
ferent for different cells which is due, in the first place, to the shape of the neutron field and to the
presence of lattice inhomowneities created by the control and safety rod channels. On loading the reactor
with fuel channels with water, the arrangement of fresh FC-3 (with water) increases the reactivity of the
reactor on an average by 6.4 ? 10-4, and the arrangement of FC-3.3 by 7.9 ? 10-4. In this state of the
reactor, the increase of reactivity on filling anFC-3.3 channel with water is greater by a factor of 1.4
approximately than on filling an FC-3 channel with it and the replacement of one manual control channel by
an FC-3 channel increases the reactivity of the reactor by 9.2 ? 10-4 on an average. Replacement of FC-3
by FC-3.3 gives the least gain of reactivity in the cells located in the row with the control and safety rod
channels and in the peripheral cells with two faces adjacent to the side of the reflector.
The neutron flux over the height of the reactor and along the radius near the manual control rods and
the empty cell was measured with miniature fission chambers when the reactor was loaded with fuel chan-
nels without water. The measurements showed that when 8 absorbing rods are in the active zone in the
central position (up to 4 scram rods and manual control rods), the neutron flux nonuniformity coefficient
in the region of the active zone located around these rods and over the height Kz is equal to 1.50. Even
when there is no rod in the intermediate position in the zone, Kz =1.34. These results confirm the design
data concerning the significant increase of Kz in the presence of eight or more absorbing rods in the
intermediate position in the zone. Measurements on the reactor showed also that the insertion of manual
control rods into the zone reduces the neutron flux in the fuel channels located in series with the rod
approximately 18% (Fig. 5). The presence of an empty cell leads to an increase of the neutron flux in the
fuel channel adjacent to it by 7? 3%.
The misalignment of the neutron flux in the fuel elements of the fuel channels located in a cell, which
was situated between an empty cell and a cell with an inserted manual control rod, was determined experi-
mentally. The maximum difference between the neutron fluxes in the fuel elements of this channel amoun-
ted to 8 ?2%.
Monitoring of the Energy Release in the Fuel Element Channels. A system for monitoring the heat
release in the fuel channels is provided in the Bilibinsk Nuclear Power station, consisting of 24 rhodium
sensors for the neutron flux [3]. The sensors are connected to an interpolating device and their currents
are recorded by a multipoint pen-recording potentiometer. In addition to this, the energy release in the
fuel element channels can be determined by measuring the efficiency of identical sections of the manual
control rods as described in [4]. In these methods, the energy release in each fuel element channel is
determined by linear interpolation of the neutron flux values at the measurement points and by the intro-
duction of coefficients which take into account the change of the neutron flux in the vicinity of the command
and control rods, empty cells and at points of installation of peripheral sensors, and also the uranium
enrichment in the fuel element channels. In determining the energy release by the efficiency of sections of
the manual control rod, a coefficient defining the reduction of the neutron flux at the periphery of the active
zone also is used. In order to refine the values of these coefficients, the neutron flux was measured in all
fuel element channels and at points of location of the sensors for monitoring the heat release, with a full
reactor charge of fuel element channels without water, by fission chambers. On the basis of these mea-
surements, values of the coefficients were chosen for which the values of the neutron flux in the fuel
element channels obtained by linear interpolation, differed to the minimum degree from the values ottained
by direct measurement in these fuel element channels.
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For the coefficients chosen in this way, the mean-square error in determining the energy release
in the fuel element channels by means of the regular system of monitoring the energy release amounts to
?79c, and by measuring the efficiency of sections of the manual control rods it is ?5%. The small error is
due to the fact that the number of manual control rods is greater by a factor of two than those of the
energy release monitoring sensors. With the combined use of both procedures, the error is reduced to ?4%:
Measurements during startup showed that the principal physical characteristics of the reactor of the
first unit of the Bilibinsk Nuclear Power Station correspond with the design values. The planned control
and safety rods provide compensation of the reserve of reactivity equal to 119i and create the required
subcriticality for the safe startup of the reactor. Therefore, the introduction of any corrections to the
loading record chart of the active zone and to the reactivity compensation system is not required.
By means of the manual control rods, the energy release field along the radius of the reactor can be
smoothed. The coefficient of nonuniformity does not exceed the design value of 1.5. The reactor has a
negative steam reactivity effect, which makes its operation stable and safe.
In conclusion, the authors express their sincere thanks to all staff of the Bilibinsk Nuclear Power
Station, participating in the preparation and execution of the physical startup.
LITERATURE CITED
1. V. M. Abramov et al, Atomnaya Energiya, 35, No. 5, 299 (1973).
2. B. G. Dubovskii et al, Atomnaya Energiya, 36, No. 2, 104 (1974).
3. E. N. Babulevich et al, Atomnaya Energiya, 31, No. 5, 465 (1971).
4. I, Ya. Emeliyanov et al, Atomnaya gnergiya, 30, No. 5, 422 (1971).
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BOOK REVIEWS
V. G. Zolotukhin, L. R. Kimeli,
A. I. Ksenofontov, et al.
THE RADIATION FIELD FROM A POINT UNIDIRECTIONAL
SOURCE OF GAMMA QUANTA*
Reviewed by B. R. Bergellson
In order to calculate the effects due to the interaction of y ?radiation with a substance, namely the
quantity of energy released, dose intensity, instrument readings, biological effects, etc, it is necessary to
have available comprehensive data on the space-energy and angular distribution of the radiation in every
specific case. However, the problem of determining the y-radiation spectrum presents considerable com-
putational difficulties. Even modern computers, in many cases cannot provide the required volume of
calculations. An alternative for carrying out the cumbersome calculations is a procedure in which the
required spectra can be set up by means of tabular data obtained for elementary sources. A point uni-
directional source can be considered as the most elementary source, the radiation field of which has
maximum information content. In the light of this approach, and also taking into account the applied nature
of the problem, the monograph by V. G. Zolotukhin et al.should be considered; this is devoted to the com-
putational-experimental investigation and tabulation of spectral data from point, unidirectional y -radiation
sources in an infinite medium. The book consists of six chapters. In the first chapter, definitions are
given of the principal characteristics of the sources and field and also methods of transforming the spectral
distribution.
The methodology for the experimental study of the energy and angular radiation spectra of a point
unidirectional source is described in the second chapter.
The authors pay particular attention to problems associated with the possibilities and special features
of the use of the Monte Carlo method for calculating the transfer of y radiation to large distances from the
source. These sections are written in a condensed form and, in contrast from others, postulate defined
skills and knowledge of the subject by the reader.
In the fourth chapter, the results are given of calculations of the differential characteristics of the
radiation field of a point unidirectional source, and also data on the spectra, energy flux, absorbed
energy and dose intensity for infinitely homogeneous media of H20, Al, Fe, Sn, W, Pb and U for source
energies of 0.1 to 10 MeV.
The present monograph is a unique publication in the diversity of the information given in the section
on the characteristics of the y-radiation field of a point unidirectional source.
In the sixth chapter, data are given which are essential for engineering calculations on building
factors of scattered y radiation for anisotropic point sources. Unfortunately, the authors have confined
themselves in this section to only a single medium ? water, although the necessary data for other media
also were available.
In conclusion, it should be emphasized that on the whole, the problem of finding the spectral distri-
bution of scattered y radiation can be solved only by improvement of the appropriate algorithms and pro-
grams for machine calculations. A knowledge of the entire problem for studying a unidirectional point
source is scarcely feasible, in consequence of the diversity of the parameters of the source-medium-
detector system, the complexity of presentation of the information in compact form and time consumption
*Atomizdat, Moscow, 1975.
Translated from Atomnaya Energiya, Vol. 39, No. 1, p. 8, July,1975.
?1976 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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for reconstruction of the spectra. However, for the simplest case of point and surface anisotropic
sources and a homogeneous infinite medium, this approach is competent and undoubtedly useful.
The book reviewed will be used widely by engineers and scientific workers in their practical
activities,
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ARTICLES
SOME PROBLEMS OF THE ECONOMICS OF A RESEARCH
NUCLEAR REACTOR
V. I. Zelenov, S. G. Karpechko, UDC 621.039.55:003.12
and A. D. Nikiforov
Recently, more attention is being paid everywhere to problems of the economics of a research nuclear
reactor and the planning of experiments on it [1-61. Procedures are considered in the papers for estimating
the cost of an experiment on the reactor and certain efficiency indexes for its utilization. In determining
the cost of the experiment, the total reactor costs are distributed between the experiments proportionally
with the efficiency of the experimental apparatus [11, depending on the product of its volume and the neutron
flux.
This approach to the distribution of expenditure, in our opinion, is in need of refinement. For ex-
ample: part of the total reactor costs, depending slightly on the power, is more suitable distributed
equally between all experiments and the remaining part, which is directly dependent on the reactor power,
is more suitably distributed proportionally with the efficiency of the experimental facility.
In this paper, a procedure is proposed for assessing the cost of an experiment on a research nuclear
reactor, taking account of this refinement. In addition, an attempt is made to explain the effect of the
index of efficiency of utilization of a research reactor (in particular, the power utilization factor and the
average operating power) on the cost of neutrons in the experimental facility.
Procedure for Assessing the Cost of Experiments
on a Research Nuclear Reactor
We define the total costs on a research nuclear reactor in the following way:
Etotal =Econst+ Evar
where E is the total annual expenditure on the reactor; E
total const is the constant component of the total
(1)
expenditure and Evar is the variable component of the total expenditure.
We relate to the constant expenditure, those costs which depend only slightly on the reactor power :
Econst= Earn+Esal Eint Eadrry
(2)
where Earn is the annual funding of amortization deductions on production buildings and power plant; Esai
is the annual funding of working salaries of the staff; Et is the expenditure on the energy requirements for
the intrinsic needs of the reactor and Eadm is the expenditure on salaries of the administration?manage-
ment staff. We relate to the variable expenditure, the costs which depend directly on the power, in partic-
ular the fuel costs :
qCf ?
Evar Nkpuf8760 ,
(3)
where q is a coefficient which takes into account the consumption of fuel in the generation of one unit of
thermal energy; Cf is the specific fuel costs in manufactured products; cp is the relative average burnup of
the discharged fuel; N is the average operating power of the reactor and kpuf is the power utilization factor
of the reactor, defined as the ratio of the time of operation of the reactor at any level of power to the
calendar time.
Translated from Atomnaya Energiya, Vol. 39, No. 1, pp. 9-11, July 1975. Original article sub-
mitted August 8, 1974,
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, NY. 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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,1 42 43 44 45 46 47 48 49 PN/N
Fig. 1. Variation of cost of neutrons
in experimental facilities with in-
crease of average reactor power.
The cost of an experiment is determined by both the constant and variable components of the total
expenditure on the reactor. As the constant component depends only slightly on the reactor power, then
it should be distributed equally between the experiments without taking account of their individual charac-
teristics (volume of the experimental facility, and the neutron flux in it). This distribution allows the
minimum cost of an experiment in a given reactor to be obtained. We shall call it the support cost. The
distribution of the variable component of the total costs between the experiments, which is proportional to
their efficiency, allows individual special features of the experimental facility to be taken into account and
the supplementary cost of the experiment to be obtained. We shall call this the physical cost. Thus, the
total cost of the experiment will be determined by the support and physical costs.
Taking account of what has been said, we write the total cost of a specific experiment on the reactor
in the following form:
Evar
C e.. .___Econst _i_ (Its,
n
(4)
where Ce. I. is the annual cost of the i-th experiment; 71,-1 is the unperturbed specific neutron flux in the cell
of the active zone, intended for installation of the experimental apparatus [1]; Si is the working surface area
of the experimental facility (immediately adjoining the active zone). Here, in place of the working volume
in the expression for the efficiency of the experimental facility [1.1, the working surface is used, which
equates the degree of effect of the physical (neutron flux) and geometric (diameter of the experimental
facility) components of the efficiency, to the cost of the experiments.
Cost of Neutrons in Experimental Facilities
From the cost of an experiment in the reactor and the number of neutrons created by the reactor in
the experimental facility during the year, it is easy to determine the cost of the neutrons for a given ex-
perimental facility:
_
Ce.i.
_
(DiSiNkp1f8760
(5)
where Cn.1. is the cost of neutrons in the i?th experimental facility. With calculation (4)
Econst qCf
_ (6)
n N kpuf 87 MI ,S n ?
E (DiSi
The structure of the neutron cost is determined by the structure of the cost of the experiment. The cost
of the neutrons also has two components:
Econst
(7)
n. const
nN kpuf 876001Si
qCf 1
n ? (8)
v.
CD'S,
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This definition of the neutron cost shows that, in experimental facilities of a different type (channel in a
"catcher," in the heat release assembly, in the reflector and beyond the reflector),It is different. The
constant component of the neutron cost in the i-th experimental facility depends on the utilization ef-
ficiency index of the reactor (R, kpuf) and on the characteristics of the experimental facility Si) and
?
the variable component depends on the productivity of the reactor (II Si, on the fuel cost and the depth
of burnup of the discharged fuel. Let us consider the effect of the utilization factor of the reactor on the
cost of the neutrons in experimental facilities.
Simple mathematical transformations show that :
ACjj.j, 2i
Ln. Var TI 1+ AAT- E (-s? )
EconsttizSi
(9)
where 71-i Si is the efficiency averaged over the entire experimental facility; ACn. 1, /Cn.i. is the relative
reduction of the neutron cost in the experimental facility for a relative increase of the average operating
power of the reactor by AFT/FT with change of the other reactor characteristics.
Figure 1 shows the dependence of ACn.i. /Cn. on AR/FT for various ratios of Evar/Econst with con-
stant value of 41 Si/oli Si = 1.0. It follows from the figure that the maximum effect when the average reactor
power is increased is achieved with small values of the ratio of these quantities.
The absolute magnitude of the economic effect, when the average power of the reactor is increased,
amounts to
AN/A7
AC E
-const 4/V ?
1 -'
,
(10)
Consequently, the nature of the dependence of AC/Econst on AR/R. is identical for all reactors, and the
economic effect is determined by the constant component of the reactor costs, other parameters being con-
stant ( , Cf, cii, Si). It is obvious that an increase of the reactor utilization factor gives an economic
effect which is determined by the expression:
41cpuf /kpuf
AC =_Econst
I Akpuf gr.puf ?
The graph?of the dependence of AC/Econst on Akpuf/kpuf for all reactors will also be identical.
Thus, in the case of costs distribution according to the proposed procedure, the concept of the sup-
port cost of the experiment is introduced (defined by the constant component of the cost and the number of
experimental facilities), which is the minimum cost of the experiment in the reactor. It is obvious that the
cost of any experiment on a research reactor cannot be lower than the support cost, It has been shown
that the ratio of the variable and constant cost components on the reactor, depends strongly on the re-
duction of the cost of neutrons in the experimental facilities with an improvement of the utilization efficiency
index of the reactor. In particular, it is most advantageous to increase the power characteristics of the
reactor with respect to the variable and constant cost components within the limits of 0.1 to 0.5.
The economic effect, when the utilization efficiency index of the reactor is changed, depends only on
the constant component of the costs and is independent of the other reactor characteristics ((p , Cf Si).
LITERATURE CITED
1. V. A. Tsykanov, Atomnaya t nergiya, 14, No. 5, 469 (1963).
2. A. S. Kochenov, Atomnaya Energiya, 21, No. 2, 97 (1966).
3. A. N. Erykalov and Yu. V. Petrov, Atomnaya Energiya, 25, No. 1, 52 (1968).
4. V. A. Tsykanov, Atomnaya Energiya, 31, No. 1, 15 (1971).
5. G. A. Bat', A. S. Kochenov, and L. P. Kabanov, Research Nuclear Reactors [in Russian], Atom-
izdat, Moscow (1972).
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6. V. V. Batov and Yu. I. Koryakin, Economics of Nuclear Power Generation [in Russian],
Atomizdat, Moscow (1969).
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BOOK REVIEWS
A A. Vorob'ev, B. A. Kononov,
and V. V. Evstigneev
BETATRON ELECTRON BEAMS*
Reviewed by P. S. Mikhalev
Interest in accelerators as radiation sources for medicine, biology and industry continues to grow.
One of the simplest and cheapest of the accelerators in operation over the range of energies 5-50 MeV is
the betatron, which has been in series production for many years. The authors have attempted to eluci-
date the buildup of experience in relation to the characteristics of electron beams during injection, accele-
ration and, mainly, their extraction and utilization.
There are five chapters in the book. The first two are devoted to the theory of the classical betatron
with a time-variabie azimuthal-symmetrical magnetic field, and the dynamics of electrons on injection and
during acceleration.
In the third and fourth chapters, various methods are considered for extraction of the electron beam,
problems of stabilization of the electron beam parameters and instruments used during operation with the
beam.
Problems of the practical application of betatronelectron beams are described in the fifth chapter.
The authors have attempted to cover a quite wide circle of problems involving the motion of the elec-
tron beam in the betatron. The principal value, in our opinion, is the experimental data assembled during
the construction and operation of the betatrons in the Tomsk Polytechnical Institute and the engineering
approach developed for the construction of beam extraction devices, The third and fourth chapters com-
prise the basis of the book, However, these data are discussed very concisely and the theoretical part
preceding it (chapters 1 to 3) is, in essence, an account of other well-known manuals on the theory of the
betatron. It would be more valuable to give examples in more detail of the practical application of theory
in approximate engineering calculations. The fourth chapter is overloaded with data which could be the
subject of a separate and detailed consideration (this refers, first and foremost, to the sections on detec-
tion and spectrometry, where only a brief listing is given of the methods and instruments for beam diag-
nostics).
Unfortunately, future improvements of the betatron beam characteristics are considered almost not
at all in the book. It is true, the authors make an attempt to describe, from their point of view, future
trends in this order: a betatron with a constant guiding field, a betatron with a spiral magnetic field, the
application of superconductors, linear induction accelerators and a plasma betatron, Consideration of the
prospects, in essence, reduces to the listing mentioned. However, a linear induction accelerator has
been used for a long time in a number of investigations and, on the basis of the experience built up, judge-
ment on the prospects for its utilization can be justified; an induction cyclic accelerator with a constant
field, well-studied theoretically and on model experiments, permits the beam intensity to be increased by
comparison with the normal betatron by an order of two to three, and now it should be possible to assess
the prospects for its utilization. The other trends listed are in the experimental stage (plasma betatron)
and the first theoretical proposals (spiral field), and no reference would be made in this book.
Despite the shortcomings mentioned, the book can be useful to specialists in the development of beam
extraction devices for betatrons of various applications. Moreover, the bibliography contained in the book
*Atomizdat, Moscow, 1974.
Translated from Atomnaya Energiya, Vol. 39, No.1, p. 11, July, 1975.
?1976 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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(126 references) and the brief description of the experiments enables those so desiring to become
acquainted in detail with the work carried out in this field.
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ARTICLES
SYNTHESIS OF A DIGITAL SYSTEM FOR CONTROL OF
NEUTRON FLUX DISTRIBUTION
E. V. Filipchuk, P. T. Potapenko,
V. G. Dunaev, N. A. Kuznetsov,
and V. V. Fedulov
UDC 621.039.515
In recent years, data-transmission and data-handling systems based on "objective" computers are
being used ever more extensively at nuclear power stations. The traditional path for computer use is the
creation of a system of centralized control followed by its use as an "adviser" with the possibility of per-
forming certain control functions in proportion to the accumulation of operating experience. It is consider-
ed that one of the basic automatic control functions of such a system is control of the distribution of energy
release in the core. '
We discuss several problems involved in the construction of a control system for a neutron field using
an objective computer.
Formulation of the Problem. For spatial control, we divide the reactor into m control zones with a
detector and control rod in each zone. We introduce the local neutron fluxes vi and the settings (4.. The
aim of control is minimization of the quadratic quality index
[(p? (nT) ? w (nT)1T [cp? (nT)? (ID (nT)].
n=1
In contrast to [1, 21, we consider here fast motions of the system for a reactor with a stable power
distribution. For a formulation of the problem, one can assume that the iodine and xenon concentrations
are independent of time and the dynamics are satisfactorily described by a one-group diffusion equation.
It is further assumed that the total power is stabilized by a supplementary high-speed automatic control
system or by internal effects.
A block diagram of the control system is shown in Fig. 1. Here, the Diare intrazone neutron flux
detectors; K are commutators which provide a connection between the computer and each channel; the DMi
are constant-velocity drive mechanisms.
11,
r?
D2
BM
DM2
DMI
Fig. 1. Block diagram of control system.
Fig. 2. Structural diagram of pulse-
height system.
Translated from Atomnaya Energiya, Vol. 39, No. 1, pp. 12-16, July, 1975. Original article sub-
mitted June 13, 1974.
?1976 Plenum Publishing Corporation, 227 West 17th Street, New York, NY. 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.
585
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Kamp'
46
45
44
43
42
4015
4010
go
45 46 47 go oto 1,0 1,1 1,2 1,3
1,4 T, sec
nT, sec
Fig. 3. Dependence of threshold amplification factor of an open circuit on quantization time:
?) one channel; ---) two channels.
Fig. 4. Transitional processes in the system parameters :T = 1.4 sec; rate of introduction of
reactivity, 1.7?10-5 sec -1; static accuracy, 0.5k; correction coefficientb= 0(a), 1 (b), and
2 (c).
A feature of this system is that the control computer, or machine for centralized control, is included
in a closed control circuit, i.e., the controlled coordinates are quantized with respect to time and level.
Introducing the appropriate lattice functions and considering that each of the m control channels is
connected by commutators to the computer in a definite time period c = T/m after the (m-1) -th channel
(quantization time T is identical for all channels), we obtain a structural scheme for this multi-dimensional
relay, pulse-height system (Fig. 2). Here, W(q, c) is a matrix of transfer functions for the continuous por-
tion shown, which joins detectors, drive motors, and object of control; x, f, and cl) are m-dimensional vec-
tors for error, external effect, and characteristics of nonlinear elements.
We assume that the digital control device, which is realized with a specialized or general-purpose
computer, has a sufficiently large digital mesh and therefore quantization with respect to level in the com-
puter can be neglected in the calculation.
Stability. Since the range of possible perturbations is ordinarily rather large, there is particular
interest in a study of the absolute stability of this system.
We use theorems on absolute stability [31 for analysis of the stability of multiply-connected nonlinear
pulsed systems. This method is similar to the well-known Popov method for the determination of the stab-
ility of continuous nonlinear automatic systems and yields results which are associated with the concept of
frequency response; what is more important, the method yields general sufficient conditions for stability
which are applicable to systems of arbitrary order in this class.
Note that the frequency criteria yield only sufficient conditions for absolute stability. However, these
qualitative results are extremely useful in the initial design stage of the system.
We consider an autonomous multiply-connected pulsed system (see Fig. 2). The system has m non-
linear (in this case, relay) elements. 4)i (xi) is the output of the i-th nonlinear element; the input is the
i-th component of the vector x[n, c1. We assume the nonlinear functions belong to the sector (0, K):
(Di [0]=0; 0 0; (4)
ei"
12
[Re (I + er4_? I a) WI` (j7, 0)] ?
ei1?
?0,25
(e'?-1

1 a) (Fo, 8) +
+11 + (I ?0,7) a] W` (? jw,
V (0.o).
Setting a. 0 (see [41), we obtain the simpler forms
Re (Fo, 0)+-J->0;
[Re WT (j(7), 0) + _7]2_ 0,25 I 147 e) e-i0+
+ TV! (? jc,C. e) 12 > 0, V (0.. 0 and Tkj 0 the equilibrium state (3) of system (1) in the case of weakly
connected cores (Oki 0) is "totally" asymptotically stable, if there exist for each of the subsystems in Eq.
(4) an infinitely large Lyapunov function which is positively defined throughout all phase space in the form
Vk = vik(nk) v2k (zik zmkk) and in addition the inequality 0 9vik/ank/nk < 6k -s 00 is satisfied.
THEOREM 2. Let the function zkw satisfy correlqtion (2) and each subsystem in Eq. (4) be subject
to the conditions in Theoreml, then for any arbitrary (Vk)(4) the evaluation
Translated from Atomnaya Energiya, Vol. 39, No. 1, pp. 48-53, July, 1975.
?1976 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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Mh
(Vk)(4) Wikk IZikk 123
Ik=1.
M,
will be true, in which yk and (pikk are positive numbers. If the inequalities yk/Ok > ck,k = 1,... M;
M;
j= k are satisfied, then for all akj > 0 and Tkj a 0 system (1) with nonlinear delayed connections is "totally"
asymptotically stable.
LITERATURE CITED
1. F. Bailey, SIAM Contr. , 3, 443 (1966).
2. N. A. Babkin and V. D. Goryachenko, in: Problems of Atomic Science and Technology, Series: Dy-
namics of Nuclear Energy Reactors, Vol. 2, Izd. TsNllatominform, Moscow (1972), p. 67.
3. Y. Asahi, S. An, and A. Oyama, Nucl. Sci. Technol. , 4, No. 6, 49 (1967).
Original article submitted March 4, 1974.
FREQUENCY CRITERION FOR. THE STABILITY OF A
CIRCULATING-FUEL REACTOR
V. D. Goryachenko and V. V. Mikis.hev UDC 621.039.514
Frequency criteria for reactor stability have been obtained only for fixed-fuel reactors. We propose
a frequency condition for the asymptotic stability of a circulating-fuel reactor. As initial equations we take
the kinetic equations of a circulating-fuel reactor from [1] and the linear feed-back equations in integral
form. Proper transformations reduce the initial system to a single nonlinear integro-differential equation
dx
? (1 + f ? u) x (u) du 13L[E?x ? ki ? u) x (u) du] ,
v dt c
(1)
in which x is the relative deviation of the reactor power, T is the time measured in fractions of T*, the
transit time of the fuel through the core, pi and j are the fraction and the importance [2] of the i-th group
of delayed neutron emitters, p=1,1 pi, v = 1/pT*, 1 is the neutron lifetime, f(T) is the kernel for linear
feedback which can be either lumped or distributed, and the k1(r) are the kernels generated by the equations
for delayed neutron sources.
The steady state of a circulating-fuel reactor is described by the solution x = 0 of Eq. (1). We denote
by Ki(p) and F(p) the Laplace transforms of the kernels lq (r) and f (r). On the basis of the results of [2, 3]
we prove the following. Suppose the function F(p) has no poles for Rep a 0 and F(0) > 0, and for all real
values of co the inequality
F(to) Re F > 0
v 2 K (P)1
(2)
is satisfied.
Then the zero solution of Eq. (1) is asymptotically stable for all initial conditions.
This statement is analogous to the criterion obtained in [4] for fixed-fuel reactors and lumped linear
feedback.
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LITERATURE CITED
1. V. D. Goryachenko and E. F. Sabaev, Atomnaya Energiya, 23, No. 4, 295 (1967).
2. V. D. Goryachenko, Stability Theory Methods in the Dynamics of Nuclear Reactors [in Russian],
Atomizdat, Moscow (1971).
3. V. D. Goryachenko, in: Problems of Atomic Science and Engineering, "Dynamics of nuclear power
installations," No. 2 (6) [in Russian], TsNIIatominform, Moscow (1974), p. 75.
4. W. Baran and K. Meyer, Nucl. Sci. and Engng. , 24, No. 4, 356 (1966).
Original article submitted April 3, 1974.
ESTIMATION OF THE EFFECT OF PHYSICO-GEOMETRIC
FACTORS ON THE DISTRIBUTION OF DELAYED
FISSION NEUTRONS IN A BOREHOLE
Yu. B. Davydov UDC 550.835
In order to determine the uranium content by delayed neutrons, the fission reaction of natural uran-
ium nuclei under the action of primary neutron radiation is used [1, 2]. The purpose of this paper is to
estimate the effectofphysico-geometric factors on the distribution of delayed fission neutrons in a borehole.
A quantitative estimate of the effect of the hole diameter and the water saturation of the breeding medium
on the distribution of fast and thermal delayed neutrons is obtained by a numerical method.
The problem is solved concerning the distribution of delayed fission neutrons, induced by a point
source of fast neutrons in a two-layered infinite medium with a cylindrical boundary of separation.
The calculations are carried out for the case when the breeding medium is composed of porous rock
of carbonate composition, the pores are filled completely with fresh water and the content of natural uran-
ium in the rock is constant. The energy of the primary neutrons from the source is assumed equal to 14.1
MeV.
The results of the calculation allow the following conclusions to be drawn: the flux of fast delayed
neutrons decreases monotonically with increase of the hole diameter for probes of any length; the nature
of the effect of the hole diameter on the magnitude of the flux of thermal delayed neutrons depends on the
length of the probe. In the region of small probes of t 20 cm, an increase of the hole diameter causes
a decrease of the thermal neutron flux. In the region of large probes, an increase of the hole diameter
leads to the appearance of a local flux maximum of thermal delayed neutrons, which is attained when the
depth of the water layer in the hole is equal to 2 to 3 cm. With further increase of the hole diameter, the
buildup process is replaced by a process of absorption of thermal neutrons in the water and the flux de-
creases.
An increase of the moisture content of the breeding medium leads to a reduction of the flux of de-
layed fast fission neutrons in the hole. The nature of the effect of water-saturation of the rock on the
magnitude of the thermal delayed neutron flux depends on thebole diameter and the length of the probe. In
the region of small probes, the magnitude of the thermal neutron flux decreases, for large diameters,
with increase of the water-saturation of the medium and has a local maximum for small hole diameters
when the moisture content reaches 10-20%. For large probes of / a 30 cm, an increase of the moisture
content leads to a monotonic reduction of the magnitude of the thermal delayed neutron flux for any hole
diameter.
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LITERATURE CITED
1. S. Amiel and M. Peisakh, Atomnaya Energiya, 14, No. 6, 535 (1963).
2. Yu. B. Davydov, Izv. Vuzov. Gornyi Zhurn. , No. 6, 8 (1972).
Original article submitted May 20, 1974.
SPATIAL D.ISTRIBUTION OF FISSION NEUTRONS IN
A BREEDING MEDIUM, CROSSED BY A DRILL HOLE
Yu. B. Davydov UDC 550.835
The solution is considered of the problem concerning the spatial distribution of fission neutrons, in-
duced by a point source of fast neutrons in an infinite homogeneous uraniferous medium, crossed by a drill
hole [1-4].
The numerical calculation is carried out for the case when the breeding medium is composed of a
dense rock of carbonate composition containing uranium ore of natural isotopic composition and with a
density of the medium of 2.7 g/cm3. A source of primary neutron radiation is located in the hole, filled
with fresh water ? a borehole generator of neutrons with energy equal to 14.1 MeV. The initial energy
of the prompt fission neutrons is assumed to be 2 MeV and the neutron yield 2.5 n/event.
In order to estimate the effect of the hole on the magnitude of the flux of fast 4>21k(r, z) and thermal
4)22k(r, z) fission neutrons, the results of the calculation are presented in units of magnitude of the fast
4321(0, 0) and thermal 4)22(0, 0) fission neutron fluxes in an infinite breeding medium, in the case of a
negligibly small effect of the hole.
The spatial distribution of the flux of fast and thermal fission neutrons is shown in Fig. 1. The re-
sults of the calculation confirm that the fission neutron flux reaches a maximum magnitude in the breeding
medium in regions subjected to the most intense irradiation. The moderation length of the fast neutrons
exceeds the diffusion length of the thermal neutrons, and therefore data concerning the moderating proper-
ties of the breeding medium are obtained from the more distant regions.
Fig. 1. Spatial distribution of the flux of fast and ther-
mal fission neutrons in units of the maximum flux mag-
nitude in an infinite breeding medium: a)
z)
/.1321(0, 0); b) 4)22k(r, z)/422(0, 0).
LITERATURE CITED
1.
S. A. Igumnov, Izv. Vuzov. Gornyi Zhurn. , 2, 3 (1966).
2.
Yu. B. Davydov, Izv. Vuzov. Gornyi Zhurn. , 6, 8 (1972).
3.
Yu. B. Davydov and A. T. Markov, Atomnaya Energiya, 33, No. 1,
574
(1972).
4.
J. Czubek, Report N. 732/PH, Cracow Institute of Nuclear Physics (1971).
Original article submitted May 20, 1974.
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VARIABLE MECHANICAL STRESSES, INDUCED
IN THE FUEL ELEMENT CLADDINGS OF THE IBR-30
REACTOR BY POWER PULSES
V. S. Dmitriev, L. S. Il'inskaya,
G. N. Pogodaev, V. V. Podnebesnov,
A. D. Rogov, V. T. Rudenko,
and 0. A. Shatskaya
UDC 621.039.55:621.039.526
During the development of power excursions, the active zones of pulsed fast reactors and boosters
are subjected to the action of thermal shocks. This phenomenon, due to exceeding the rate of rise of tem-
perature above the rate of expansion of the material, is accompanied by the stimulation in the fuel elements
of alternating deformations and stresses, which are transmitted to the claddings and supporting structures
of the core [1j. The action of the thermal shocks is aggravated by their high repetition frequency, which
creates an accelerated wear of the active zone elements due to material fatigue. Damage of the fuel ele-
ments might also occur when the tensile strength is exceeded, either during a single power pulse or from
wave interference from the stresses of several pulses in the case of a too high repetition frequency.
On the pulsed fast reactor (IBR) of the Joint Institute of Nuclear Research in Dubna, this phenomenon
has been investigated over a number of years for the purpose of finding the optimum fuel element design
and for determining the permissiblepulsed loading [2, 3]. -
The paper describes the procedure and gives the results of measurements of the alternating me-
chanical stresses which are induced by power pulses in the fuel element claddings of the IBR -30 reactor.
The relative deformations were determined by means of high-temperature wire teuso-resistors with a
base of 10 mm. Wire with a diameter of 30M made of NM23 x 10 alloy is used as the material for the
tenso-sensitive lattice and VN-15T organo-silicon cement is used as the binding and insulating material.
The principal measurements were conducted during operation of the IBR-30 in a cycle of widely-spaced
pulses at a repetition frequency of 0.2 Hz and an average reactor power of up to 15 kW. Longitudinal and
transverse oscillations were detected, with a frequency of ?5000 and ?1000 Hz respectively (Fig. 1).
The amplitudes of the oscillations increased with increase of the pulse energy, and the time of damping did
not exceed 10 msec. With power pulse energies of 2 ? 1015 fissions (average rise in temperature of the
plutonium fuel elements of the active zone was 20?C per pulse), the maximum stresses in the cladding,
created by the longitudinal and transverse oscillations amounted to 7.105 and 5. 105 N/m2 respectively.
Fig. 1. Signals from the tenso-resistors
installed on the cladding of a fuel ,element
of the working fuel assembly; below: pulse
power. The pulse energy was 2 ? 1015 fis-
sions; pulse frequency 0.2 Hz.
LITERATURE CITED
1. I. Randles and R. Laursma, EUR-3654-1 (1967).
2. V. T. Rudenko, Preprint OIYaI 13-764, Dubna (1971).
3. V. D. Anan'ev, OIYaI 13-4395, Dubna (1969).
Original article submitted July 10, 1974.
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CORRECTION OF THE GROUP CONSTANTS BY THE
RESULTS OF EXPERIMENTS ON THE BFS
CRITICAL ASSEMBLIES
A. A. Van'kov and A. I. Voropaev UDC 621.039.519
The following problems are considered in the paper:correction of the group constants on the basis
of integral experiments on critical assemblies (measurements of the ratio of the average cross-sections
of different reactions and the ratio of the reactivity of samples at the center of the active zone for three
BFS assemblies); determination of the constant error of the principal characteristics of a fast reactor
of the OK-5 type (parameters ofcriticality and breeding, reactivity coefficients) before and after taking
account of the Integral experiments; determination of the bias of the numerical values of these character-
istics, due to taking account of the integral experiments.
A statistical method has been used for the correction, in linear approximation, of the coefficients
of sensitivity. Part of the results obtained is given in Table 1.
The conclusion consists in, the following: the bias of the constants with a correction based on the
integral data, depend significantly on the assumptions about the dispersions and also on the form and mag-
nitude of the initial correlations for both the group constants and the integral data. In order to obtain
physically plausible results of the correction, it is important to estimate correctly the error of the group
constants and of the integral quantities associated with the approximations of the numerical model (re-
quirement of adequacy of the conditions of the calculation and of the experiment). Taking account of cor-
relations between the measured quantities is of considerable importance. The bias in the calculated
reactor parameter is stable, if the choice of the integral quantities is sufficiently informative relative to
this parameter.
TABLE 1. Bias and Error Keff of the Total Coefficient of Breeding KB and of the active
zone KBaz, the Doppler (DKR) and Sodium (NKR) Coefficients of Reactivity
BFS-22
BFS-23*
BFS-27t
.0H-5
Keff
KBaz
Keff
KBaz
Keff
Keff
KB
DKR
NKR
Go, %
1
5,5
3,7
9,2
4,1
4,2
6,2
80
60
all %
0,9
4,4
1,4
5,3
1,5
1,6
4,4
50
55
6, %
0,0
?4,5
1,6
?8,5
2;7
3,8
--6,0
35
15
*Model of fast reactor with uranium (BFS-22) and plutonium (BFS-23) fuel.
t Assembly without U-238, with large dilution with graphite.
*Breeder-reactor with oxide fuel, volume of active zone 5 m. Calculated values: KB = 1.39; DKR = ? 4.4.10-4
(Keff/AT). T? from 900 to 1500?K; NKR = 1.1% (Keff/Keff) with 50% of sodium removed from the reactor.
00 and oi are the errors, with and without taking account of the integral experiments respectively;
.5 is the bias relative to the values calculated by the BNAB-70 system of constants; BFS = Fast Physics Assembly.
Original article submitted August 23, 1974.
THE INFLUENCE OF BEAM NOISE ON THE CRITICAL
CURRENT OF LINEAR ELECTRON ACCELERATORS
I. N. Mondrus UDC 621.384.64
This paper deals with the development of the transverse beam instability in a single section of a
linear electron accelerator, taking into account the fluctuations in transverse displacement Y1 (s) and
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transverse velocity Y2(s) of the center of mass of the beam bunch. At the section input the time-series
Yi(s), Y2(s) constitute a normal stationary process and are described by the spectral density matrix f(co).
The variance a2n and the mean An of the transverse displacement of the n-th bunch at the section output
(Yn) can be expressed by the elements fik(w) of this matrix and the fundamental solutions of the transverse
instability problem rii(s), rj2(s) by the relation [1]
Y.=
[Y1 (s) ? )72 (s) 112 (n s)]
s=o
The probability that the displacement of the last (n-th) bunch in the pulse does not exceed the section
aperture a at critical current is given by
P (lYni