SOVIET ATOMIC ENERGY VOL. 41, NO. 3

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• Document Creation Date: January 4, 2017
• Document Release Date: September 23, 2013
• Sequence Number: 3
• Publication Date: March 1, 1977
• Content Type: REPORT

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k
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Russian Original Vol. 41, No. eptember, 1976
Marck1.977
SATEAZ 41(3) 793-866 (1976)
SOVIET
ATOMIC
ENERGY
ATOMHAR 3HEP1-1111
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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Declassified and Approved For Release 2013/09/23: CIA-RDP10-02196R000700080003-7
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physics Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
Soviet Atomic Energy is a cover-to-cover translati,on of Atomnaya
Energiya, a publication of the Academy of '1-3 ciences 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: M. D. Millionshchikov
Deputy Director
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. Vlasov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov
I. N. Golovin
V. F. Kalinin
A. K. Krasin
V. V. Matveev
M. G. Meshcheryakov
V. B. Shevchenko
V. I. Smirnov
A. P. Zefirov
Copyright C) 1977 Plenum Pliblishing Corporation, 227 West 17th Street, New York,
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Published monthly. Second-class postage paid at Jamaica, New York 11431.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
March, 1977
Volume 41, Number 3 September, 1976
CONTENTS
Engl./Russ.
ARTICLES
Measurement of Resonance Escape Probability ?L. N. Yurova, A. V. Bushuev,

and V. M. Duvanov
793
171
Kinetics of Annealing of Radiation Pores in OKh18N9T Stainless Steel, Irradiated by
Neutrons ? V. A. Pechenkin, Yu. V. Konobeev, and V. I. Shcherbak
796
174
Effect of the Interaction of OKh18N9T Steel with the Coolant on the Development of Porosity
in the Fuel Cluster Sheath of the BR-5 Reactor ? V. I. Shcherbak, V. N. Bykov,
V. D. Dmitriev, S. I. Porollo, and A. Ya. Ladygin
802
179
The p-- T Diagram of the Uranium ?Carbon System ? Yu. V. Levinskii
805
182
Thermal Cross Section and Resonance Integrals of Fission and Capture of 241Am, 243Am,
249Bk, and 249Cf ? V. D. Gavrilov, V. A. Goncharov, V. V. Ivanenko,
245cm,
V. N. Kustov, and V. P. Smirnov
808
185
Using Pyroelectric Detectors for the Dosimetry of Pulsed -y Radiation
? L. S. Kremenchugskii and R. Ya. Strakovskaya
813
190
DEPOSITED ARTICLES
Choice of Optimal Dimensions for a Synchrotron Bremsstrahlung Target ? V. A. Vizir',
B. N. Kalinin, V. M. Kuznetsov, and P. P. Krasnonosen'kikh
818
195
The Role of Nuclear Cascades in the Formation of Neutrons in Pb, Cd, Fe, Al and Fission
of Lead Nuclei by the Action of Cosmic Radiation at Various Depths below the Earth
? V. A. Zyabkin and R. M. Yakov'lev
819
195
Effect of Thermomechanical Processing on the Amplitude-Dependent Internal Friction of
Uranium ? A. I. Stukalov, G. S. Gaidamachenko, and A. V. Azarenko
820
197
Two Methods of Determining Fuel Burnup by y Spectrometry ? L. I. Golubev,
L. I. Gorobtsov, V. D. Simonov, and M. A. Sunchugashev
821
197
Singular Equations and Conditions of Solvability of Boundary Problems in the Theory of
Neutron Transfer ? B. D. Abramov
822
198
LETTERS TO THE EDITOR
Interpretation of Instrument Lines of an Ionization Pulse Spectrometer Suitable for
Microdosimetry ? V. A. Pitkevich and V. G. Videnskii
824
199
Planning the Reconstruction of the Active Zone of a VVR-M Reactor ? P. M. Verkhovykh,
V. S. Zvezdkin, G. A. Kirsanov, K. A. Kolosov, K. A. Konoplev, Yu. P. Saikov,
V. N. Sukhovei, T. A. Chernova, and Zh. A. Shishkina
826
201
Analysis of On ?Off Zonal Reactor Control Systems ? E. V. Filipchuk, V. T. Neboyan,
and P. T. Potapenko
830
203
Efficiency of Detection of Fission Fragments by Solid Track Detectors ? A. P. Malykhin,
I. .V. Zhuk, 0. I. Yaroshevich, and L. P. Roginets
832
205
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CONTENTS
(continued)
Engl./Russ.
Limits of Applicability of Weak-Enrichment Approximation for Cascade Separation of
Two-Component Mixtures ? N. I. Laguntsov, B. I. Nikolaev, G. A. Sulaberidze,
and A. P. Todosiev
834
206
Neutron Detection with Hydrogenous Detectors ? E. A. Kramer-Ageev, A. G. Parkhomov,
V. S. Troshin, and M. I. Shubtsov
837
208
Additivity Deviations in the Thermal and Radiation-Induced Embrittlement of Steel under
Neutron Irradiation ? V. I. Badanin and V. A. Nikolaev
838
209
The Transient Response in the emf of a Thermocouple under Reactor Conditions
? M. N. Korotenko, S. 0. Slesarevskii, and S. S. Stel'makh
840
211
Measurement of the Enrichment Factor in Relation to Flow Distribution in a Separation
System ? V. A. Kaminskii, 0. G. Sarishvili, G. A. Sulaberidze, V. A. Chuzhinov,
and B. Sh. Dzhandzhgaba
842
212
Characteristics of Neutron Radiation Reflected from Concrete ? V. A. Klimanov,
A. S. Makhon'kov, and V. P. Mashkovich
iv/Tritium Content in Liquid Media and in Air of Working Locations at Nuclear Power Stations
? Yu. P. Abolmasov
844
845
214
215
Analytic Representation of Ion Energy Loss in Stopping by Nuclei ?V. A. Zybin
arid V. A. Rykov
846
216
C OME C ON NEWS
The Interatominstrument Exhibition ? V. A. Dolinin
848
217
International Symposium on Radioactively Tagged Organic Compounds ? A. K. Zille
849
217
Collaboration Notebook
850
218
CONFERENCES AND MEETINGS
/All-Union Conference on Water Treatment in Nuclear Power Stations? L. M. Voronin,
V. M. Gordina, and V. A. Mamet
851
219
International Conference on Elementary Interactions at Low Energies ? P. S. Isaev
852
220
International Conference on Horizons in Science 1976 ? V. I. Asvrin-
853
221
Conference on the Production of Particles with New Quantum Numbers ? A. D. Dolgov .
856
222
Symposium on Applications of 252Cf ? A. K. Shvetsov
858
223
Seminar on Computer Simulation of Radiation-Induced and Other Defects ? Yu. V. Trushin
860
225
SCIENTIFIC AND TECHNICAL EXCHANGES
Visit of an ERDA Delegation to the USSR ? E. F. Arifmetchikov
862
226
BOOK REVIEWS
Yu. A. Egorov, V. P. Mashkovich, Yu. V. Pankrat'ev, A. P. Suvorov, and S. G. Tsipin.
Radiation Safety and Nuclear Power Station Shielding ? Reviewed by N. G. Gusev .
863
227
V. T. Tustanovskii. Accuracy and Sensitivity Estimation in Activation Analysis
? Reviewed by E. M. Filippov
364
227
G. Hammel and D. Okrent. Reactivity Coefficients in Large Fast-Neutron Power Reactors
(USA, 1970)? Reviewed by G. M. Pshakin
865
228
The Russian press date (podpisano k pechati) of this issue was 8/23/1976.
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
MEASUREMENT OF RESONANCE ESCAPE PROBABILITY
L. N. Yurova, A. V. Bushuev, UDC 539.125.5.173.162.3:539:125.5.162.3
and V. M. Duvanov
One of the most important problems in investigating the neutron cycle in a thermal reactor is the estima-
tion of the resonance escape probability co. In [I, 2] the value of 28(p was obtained by combining some measured
parameters with calculated quantities. The accuracy of the determination was low and did not satisfy an in-
creasing number of requirements, and therefore people began to use the directly measurable parameters
28p, 286, 256, etc. instead of cp.
Now the development of experimental techniques has made_it possible to determine (to rather accurately
from experimental data.
Measurement Procedure. Starting from the balance equation, the probability of resonance absorption
of neutrons in fuel can be written in the form
=
(1+ 28v 25,T1 288)
281 (28ac) exp (x2-7) (1+ 28a epi) exp (x27)
25N (250.4) (5v 286 25//5v 28v-1 +
) 1 ' (1)
28
Rg5V 1+ 2
where 28N/25N is the ratio of the 238U to 235U concentrations in the fuel, 2811c and 28R1 are the cadmium ratios
for the 238U (n, y) and 235U(n,f) reactions, 286 is the ratio of 238U and 235U fission reactions rates in the fuel,
25a epi is the ratio of 235U fission to absorption rates in the fuel for epicadmiumneutronenergies,25vand28v
are the average numbers of neutrons per fission of 235U and 238U nuclei, (280-c) /(250-f) is the ratio of the rates
of neutron captures in 238U and fissions in 235U per nucleus, 143 is the material buckling, T? = Z Tvpi/E (pi ; Ti is the
i
age of neutrons with the i-th energy of the i-th resonance, (pi is the resonance escape probability during slow-
ing down to the i-th resonance.
It is obvious that the terms on the right-hand side of Eq. (1) represent the probability of resonance cap-
ture in 238U and 235U; i.e.,
)
28N (28,3 exp (x27
c)
28,
25N (250f) 28R,5v ( 1+ 28v25v-1 286)
(1+ 25CC epi (exp-x27r)
1 25CP =
28R5V ( 1+ 28Z 1 286)
TABLE 1. Errors in (28crc)/(28of), 28R, and
286 and Uncertainty of Nuclear Data
Parameter
Uncertainty,
Reference
25N/25N*
aRc
2.5,5
25v
28v
For natural uranium.
0,1
1,5
1,5
2-3
0,3
0,7
171
131
151
(6]
181
191
TABLE 2. 28(p as a Function of Water Gap
Thickness
Gap,
RIM
(PLAN A Wilcpo)
Gap'
MITI
ci/wo
A (cPi/TO)
0
2
1,000
1,030
--
0,006
4
6
1,037
1,055
0,007
0,007
(2)
(3)
Translated from Atomnaya Energiya, Vol. 41, No. 3, pp. 171-173, September, 1976. Original article
submitted March 31, 1975.
This material is protected by copyright registered in the name of 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 $7.50.
793
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TABLE 3. 23(p as a Function of Lattice Pitch TABLE
4. 28Ie11 as a Function of Water
ca
Vc/V.0
Gap Thickness
A(q/To)
Gap,
281,4 b
(standard
method [4])
8/eff, b
[by Ect ? (5).1
28Ieff,b [by Eq.
(5) taking ac-
count of anisotropy]
38
. 76
152
1,000
1,092
1,142
mm
-F0,006
+0,006
2
4
6
10,6+0,3
10,6+0,3
10,3-F0,4
10,4+0,4
10,57+0,24
10,55-F0,23
11,36+0,33
11,35+0,32
10,57+0,24
10,17+0,23
10,52+0,33
10,17+0,32
The accuracy with which 28(p can be determined in the measurement of functionals by y spectrometry can be es-
timated. As was shown in [3, 4] this method ensures high statistical accuracy with minimum systematic er-
rors.)28a\ //250f,
) and 28Re were measured with a Ge(Li) spectrometer. and 286 with a scintillation spectrom-
eter.Ci The ratio (280.1)/ ( - 25
af) was determined by calibrating detectors in the thermal column, with the
238U(n, y) and 235U(n, f reaction rates being estimated by the intensities of the 278- and 293-keV radiations
from 239Np and 143Ce, respectively. 28R was measured by using a Cd cover. 286 was determined by the method
of two foils, recording the 1.6-MeV radiation from the fission product 140La.
Table 1 shows the errors in determining these functionals and the uncertainty of the nuclear data used in
Eq. (2). These indicate that the value 28(p 0.85 may be in error by -0.5%.
0.e) r
Measurement and Results. (28/(25a) 28Re, and 286 were measured in a uranium -graphite subcriti-
cal system [4] mounted on the converter of tife horizontal neutron beam of the IRT-2000 reactor. The cell
structure and the composition of the materials were described in [10]. The measurements were performed
in systems with various graphite-to-uranium ratios (Vc/Vu = 38, 76,1.52) and for various thicknesses of the
water gap around the uranium slugs (0= 6 mm). The Vc/Vu ratio was varied by changing the pitch of the
lattice. Foils of natural uranium metal were used in measuring (28 0.c )/(250.f) and 2811c. 186 was deter-
mined by using metal foils of natural uranium and uranium enriched 11 times in 235U. The fuel channels
of the experimental system contained separate slugs, which led to uncertainties in the axial distribution
of the 238U (n, -y) and the 235U (n,f) reactions, and affected the average values of (28 ) (25 0.f) and 28R0.
Approximate corrections were determined experimentally and used in calculating the functionals.
286 was measured in a "dry" lattice with V/Vu =38, and its value was used in calculating (p for all the lat-
tices considered. The assumption that 286 is constant was based on the following facts:
1. The value of 286 obtained in the lattice agrees, within the limits of experimental error, with the cor-
responding value for a single rod in a graphite moderator [6].
2. Surrounding a fuel slug by layers of various materials has little effect on 286 [6].
3. It can be shown that the sensitivity coefficient of 0, with respect to 286 is small ( At.
(2)
In general the difference t5(z) ? t(z) in the actual thermally stressed channel is a function of the longi-
tudinal coordinate z, and if this distance reaches a minimum in the cross section with coordinate z =z0 then
from condition (2) and the condition for the existence of an extremum we obtain the following equations:
zo
got (z)
At 2q0
eV
= ts (z) (z) clz
cb f
0
(z) I2q t90 Of (z) I
aZ lz=z0 IZ='ZO ? CZ aZ lz--=--zo =0
(3)
(4)
where te is the temperature of the coolant at the entrance into the active zone; V is the velocity of the coolant
in the channels of the FEA; p and c are the density and specific heat of the coolant respectively; a is the heat-
transfer coefficient.
Equations (3) and (4) enable us to determine the coordinate of the dangerous cross section zo and the
maximum thermal flux q0.
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The velocity of the coolant was determined from the equation of pressure loss in the active zone
PV2 t j_t, ,,,,, j_t 1
APAz= 2 : a .,---, tout+ t lat 0+ ai,bp ] ,
where APAz are the pressure losses in the active zone; in and gout are the local resistance coefficients at
the FEA inlet and outlet respectively; fr and k tat are the resistances associated with friction and the reactor
lattices.
The t5(z) relationship was determined from the known relationship between the saturaticn temperature and the
pressure (itself depending on the coordinate), viz, ts[P(z)], where
pv2 ?
P (z) =Po-Fpg (Ho+ z)--2? (qn+sfrz/2b+1).
Here g is the gravitational acceleration; Po is the atmospheric pressure; Ho is the depth of reactor pool.
Equations (3) and (4) were solved and 'iv determined from Eq. (1) with the aid of an electronic computer.
Since the functional relationships for the thermal and hydraulic processes in annular gaps and plane-
parallel slots are identical, the results of calculations carried out for plane fuel elements are also valid for
the VVR-M reactor fuel elements of tubular construction.
Figure 1 shows the dependence of the relative increment in the power of the VVR-M reactor on the
geometrical parameters of the fuel elements:
where qv? is the volumetric density of energy evolution (averaged with respect to height in the actual thermally
stressed channel) for an FEA of the VVR-M2 type [1] as at present used in the VVR-M reactor.
The calculations were carried out for a water temperature of 50'C at the entrance into the active zone,
in the absence of rarefaction between the reactor lattices and on the assumption that the maximum wall tem-
perature of the fuel element equalled the water saturation temperature.
Of the whole set of possible tube thicknesses and intertube gaps in the VVR-M reactor we may only
choose those which ensure conservation of the unit cell dimensions of the active zone as determined by the
construction of the reflector and the step of the reactor lattices. Subject to this condition, for a specified num-
ber of tubes in the assembly the.relationship between the-tube thickness and the gap is uniquely determined .
from geometrical considerations. Figure 1 contains a set of lines corresponding to fuel elements with dif-
ferent numbers of coaxial tubes in the set (n),
It follows from Fig. 1 that the greatest gain in reactor power is obtained by rising six-tube FEA with
a fuel-element thickness of 1.2-1.4 mm. We accordingly made some new six-element assemblies of the
VVR-M3 (Fig. 2) and VVR-M4 types consisting of an outer fuel element (a hexagonal tube with a gauge diame-
ter of 33.5 mm), four tubular fuel elements with outer diameters of 11.1, 16.7, 22.3, and 27.9 mm, and a
central rod-type fuel element of diameter 5.5 mm. The diameter of the fuel in the rod was 1.8 mm.
The VVR-M4 type of assembly only differs from the VVR-M3 by having a break of 100 mm in the fuel in
the middle section of the fuel elements in order to increase the flux density of the thermal neutrons in the re-
gion of the individual horizontal channels. As fuel we used a uranium ?aluminum alloy with a uranium con-
tent of 23.5 wt. %. The can material was aluminum alloy SAV-1. The following table gives the comparative
characteristics of the VVR-M2 and VVR-M3 types of FEA respectively.
Thickness of tubular fuel element walls, mm
2.5; 1.25
Thickness of cladding layer, mm
0.9; 0.48
Thickness of active layer, mm
0.7; 0.29
Length of active layer, mm
500; 500
Hydraulic diameter, mm
6; 3.1
Heat take-off surface area per unit volume of the active zone, cm1
3.62; 6.6
Metal/water ratio
0.816; 0.728
Amount of 235U in active zone, g/liter
61.2; 67.9
Amount of 235U per unit heat take-off surface, g/m2
166; 103
Enrichment with 235U, %
36; 90
Year of initiation
1963; 1972 (experimental part)
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The hydraulic characteristics of the VVR-M3 type of FEA were measured in a hydraulic test-bed using
the method of [2]. The average hydraulic resistance of the set of new FEA for a water velocity of 2.5-3.0 m/
sec was 6.85?0.10, which was 1.57 times greater than that of the VVR-M2 type of FEA [2].
Thermal calculations based on the experimental results confirm the possibility of reconstructing the
VVR-M reactor, with its power increased to 30 MW, by using the new FEA and increasing the power of the
heat exchangers and cooling systems; they also show the possibility of installing the new FEA in the active
zone of the reactor together with FEA of the VVR-M2 type.
The efficiency of the new (especially thin-walled) fuel elements is primarily determined by the hermetic
state of the cans. For the VVR-M2 fuel elements the contribution of surface contamination to the activity of
the coolant is negligibly small (-3%), which corresponds to an equivalent amount of 235U per unit surface of
(3?1) . 10 -1? g/cm2 [3]. The increase in 235U enrichment by a factor of 2.5 in the new fuel elements increases
the contribution of the surface contamination by a factor of four as compared with the VVR-M2 fuel elements.
The equivalent 235U content per unit surface of the new fuel elements was determined from the rate of entry
of fission fragments into the coolant of a loop channel of fuel elements with zero burn-up; it amounted to (7 ?2) ?
10-1? g/cm2.
The main contribution to the fragment activity of the coolant arose from the worsening of the hermeti-
city of the fuel elements as burn-up proceeded. Three batches of fuel elements made at different times were
tested. Those of the VVR-M3 and VVR-M4 types were tested in the active zone of the VVR-M reactor together
with VVR-M2 fuel ements at a reactor power of 16 MW. Although 19 FEA were placed in the zone.
? An analysis of the systematic monitoring of the 'nermeticity of the fuel elements in the active zone of the
reactor over the whole period of use of the new fuel elements showed that, on placing VVR-M3 and VVR-M4
assemblies in the active zone to the extent of 8.7% of the total number of assemblies, the fission activity of
the coolant did not increase at all but remained at the usual level (10-8 Ci/liter with respect to?5mKr, 87Kr,
88Kr, 135Xe, 138Xe) for fuel burn-ups of 0-70% in the new elements. Defining the nonhermeticity g a s the ratio
of the fragment leak rate to the rate of fragment formation, we may estimate the upper limit for the new fuel
elements by considering the rate of entry of the fragments into the reactor coolant at the instant at which the
maximum number of new fuel elements occurs in the active zone, allowing for errors committed in measuring
this rate (2a).
By considering the iodine isotopes we find that, if only one assembly is leaking, then f3 =40 ? 10-7; if all
are leaking to the same extent the value is 2 ? 10-7. In the case of four assemblies we traced the changes in
nonhermeticity during the period of burn-up by periodically removing the elements from the active zone and
testing in the loop channel. The results convinced us that the nonhermeticity of the new elements was at the
same level as that of the VVR-M2 type.
Experimental service of the VVR-M3 and VVR-M4 fuel elements in the reactor confirmed their high ef-
ficiency up to the maximumburn-upachieved(7870), which corresponds to a fission density in the interior of the
fuel composite of 1.45 ? 1021 cm-3. The successful reactor tests create a realistic basis for modernizing the
VVR-M reactor by using the new fuel elements and increasing the reactor power to 30 MW.
The authors wish to thank D. M. Kaminker for constant support and also Yu. P. Semenov and B. S.
Razov for constant help in the execution of this work.
LITERATURE CITED
1. D. M. Kaminker and K. A. Konoplev, 3rd Geneva Conference, Paper No.. 235 (1964).
2. G. A. Kirsanov et al., At. Energ., 39, No. 5, 320 (1975).
3. N. G. Badanina, K. A. Konoplev, and Yu. P. Saikov, At. Energ., 32, No. 4, 316 (1972).
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ANALYSIS OF ON?OFF ZONAL REACTOR CONTROL SYSTEMS
E. V. Filipchuk, V. T. Neboyan, UDC 621.039.562:621.039.512.45
and P. T. Potapenko
Constant-speed servodrives are predominantly used in automatic control systems of power distribution
in reactor cores. Speed control is usually hampered by the fact that the servodrive operates under fundamen-
tally different conditions when moving the rods up than when moving them down. For example, all rods of the
RBMK reactor have a constant-speed drive. Thus, technical realization of the required control necessitates
the design of multidimensional on ?off systems.
Here we describe an engineering design method for systems with specified quality characteristics in
reactors with stable power distribution. The system consists of n identical on ?off controllers evenly spaced
in the core region where power is uniformly distributed (in the control region). The detectors and control
rods of local controllers are placed at the nodes of a square or triangular lattice. According to the adiabatic
approximation, the relation between the vector and neutron flux deviations from the specified values (settings)
n =(nn2, nm)T as sensed by the detectors, and the vector of external effects produced by the rods 6,k-----
(Ak1, Ak2, Akm)T is given by the equation
where H(p) is the reactor transfer matrix
n (p) Ak.
H (p) = TV 0 (p) A.
(1)
(2)
The transfer function of a point reactor Wo(p) and the static matrix A are found either experimentally or
calculated.
The analysis of the system in a power distribution stabilization mode can be considerably simplified con-
sidering the limited interaction of local on ?off regulators. Accordingly, local reactivity perturbations,
caused for example by overloading or by the introduction of various instruments into the core, are assumed
to be taken care of only by local controllers adjacent to the point of perturbation. In this case, the number of
interacting controllers is five for a square lattice and seven for a triangular lattice.
Such an assumption is valid for the following reasons. For nuclear safety reasons the number of simul-
taneously shifted rods is restricted by appropriate interlocking. The deformation of the neutron field caused
by a local reactivity perturbation decays with distance from the perturbation point. Because of the presence
of a dead zone, distant local controllers do not take part in control. Thus, the synthesis of the entire system
is reduced to calculating a small number of interacting controllers with central symmetry.
Let the subscript 1 denote the center controller. The, considering the symmetry and uniformity of the
neutron field in the control zone, we have /from Eq. (1):
n C (p) Ak,
where n ?(ni, n2).1 Ak = (Aki, Ak2)T;
? / (P) Ciz (P) (aii a12 (nt -- 1) \ Ivo (p).
C (p) k C21 (p) C22 (p)I 1a21 a22+ 2,123 /
(3)
Figure 1 shows an equivalent block diagram of a control system based on Eqs. (3) , where D1,2(p), Rl, 2
-(p), and B1,2 (p) are transfer functions of the detector, the controller, and the drive with control rod. If the
matrix elements of the linear section of the system have filtering properties, the nonlinear elements Ft and
F2 can be harmonically linearized for transient fluctuations [2]. In consequence, the characteristic equation
of the system becomes
Translated from Atomnaya Energiya, Vol. 41, No. 3, pp. 203-204, September, 1976. Original article
submitted June 23, 1975; revision submitted January 16, 1976.
This material is protected by copyright registered in the name of 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 $7.50.
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02
x2 1-a
'2 j
C,,
Fig. 1 Equivalent block diagram of control
system.
1+D1 (P) R1 (P) {131,P` ( it (P) q (At) +
+B2 (P) q (A2) D2 (P) R2 (p) [D 1C(p22) R(1 3 1) (p)
q (Ai) B (p) (C it (P) C22 (P)- C12 (P) C21 (P)) / =0,
where q(Ai) and q(A2) are the equivalent transfer constants of the nonlinear elements.
(4)
Damped "sinusoidal" fluctuations correspond to the complex roots ofthe characteristic equation. Thus,
to find the attenuation index (A) and the frequency w(A) let us substitute p + jw. An expression relating the
fluctuation amplitudes in the center and peripheral channels, A1 and A2, can be obtained from the equation of
a harmonically linearized system, taking into account that and w change little with time: .
D2 (A) R2 (P) C22 (P)
A2 - "11 D (p) R (II) C12 (P)
+ D2 (P) R2 (P) B (P) , C21 ,P q (Ai) I
C22 (P) Ct (P) C12 ,P) )
C12 (P)
(5)
Equations (4) and (5) completely define the quality characteristics = (A) and w=w(A) as functions of
amplitude. These equations can be used to plot quality thagrams that are very useful in the design of such
systems.
The design technique is quite general. In particular, the technique is applicable to a control system
containing an integral-power controller and several local Controllers symmetrically positioned around the cir-
cumference of a circle of one radius.
It is evident that the complete scheme of controller arrangement is similar to the scheme of interacting
controllers discussed above. Thus, the above design technique can be applied in practice to many variants
of this scheme. The validity of assumptions and of the entire technique has been confirmed by the results of
analog simulation. If the filtering properties of the system are limited to integrating networks, the result of
the synthesis can be regarded as a first approximation which can be corrected, e.g., by digital simulation.
LITERATURE CITED
1. E. V. Filipchuk, P. T. Potapenko, and A. N. Kosilov, At. Energ., 35, No. 5, 317 (1973).
2. E. P. Popov, Applied Theory of Control Processes in Nonlinear Systems [in Russian], Nauka, Moscow
(1973).
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Declassified and Approved For Release 2013/09/23: CIA-RDP10-02196R000700080003-7
EFFICIENCY OF DETECTION OF FISSION FRAGMENTS
BY SOLID TRACK DETECTORS
A. P. Malykhin, I. V. Zhuk, UDC 539.107:621.039.564
0. I. Yaroshevich, and L. P. Roginets
The absolute and relative efficiency of detection of fission fragments by various solid track detectors
must be known for absolute measurement of fission and neutron flux densities, and for comparing the data
published by different authors.
The few published data refer mainly to the detection of fission fragments escaping from thin sources,
i.e., from sources with a width much less than the mean free path of the fragments 11 in the source material.
Practically no data are available for fragments escaping a thick source (d
Accordingly, we have measured the relative detection efficiencies of various track detectors for a thin
and thick source and calculated their, absolute values. Thick sources used for this purpose are polished natu-
ral uranium foils 0.1 mm thick and 5.2 mm in diameter exposed to free air for two weeks. Thin 'ayers were
prepared by vacuum deposition of an ?80 pg/cm2 layer of uranium with a 9g7c enrichment of 235U. All thin
layers were calibrated against the thick sources using fluorophlog,opite as a detectors most convenient for
counting.
The sources were then formed into two kinds of sandwiches for thick- and thin-source measurements.
One type of sandwich consisted of a thick source placed between the studied detector and fluorophlogopite.
After exposure and chemical processing of the detectors, the ratio of track densities on the detectors in each
sandwich and the obtained values were normalized with respect to macrofol-E taken as unity. The second
type of sandwich consisted of a thin source in contact with the studied detector and fluorophlogopite monitor.
According to the readings of monitors all track densities were referred to a single flux and normalized as
before with reference to macrofol-E track density.
TABLE 1. Detection Efficiency of Fission Fragments'by Various Track Detectors
Detector
Chemical
treatment
Thin source
.
Thick source
relative detec-absolute
tion efficiency
detec -
don efficiency
data of other authors
relative detec -
tion efficiency
Macrofol-E
6,25N NaOH;
1
96,2+0,53
(95.2+0,53)%;
1
60? C; 50 min
6.5N NaOH; 20' C; 50hi[1]
Polycarbonate
film
6,25N NaOH;
60?C; 50 min
1,01+0,02
96+2
?
1,06?0,01
Natural(capacitor)
mica
6,8% HF; 60? C;
120 min
0,89+0,01
85+2
0,96+0,01
Synthetic mica
6,8% HF; 60? C;
0,91+0,01
87-1-1
83%; 20%11F; 20? C;
0,888+0,007
(fluorophlogopite)
20 min
10 min [21
Coverglass (GUST
2% HF.; 21? C;
0,43+0,01
40,9+0,9
(42+6)%; 41% HF;
0,527+0,006
6672-59)
30 nun
21? C; 10 min [3]
i
(42+4)1%; 2,5% H1';
19?C; 23 min 12.j
(41?2)%; 2.5% HF;
19?C; 30min [4]
Dacron
6,25N NaOH;
?
?
60?C; 60 min
?
1,032,0,01
Translated from Atomnaya Energiya, Vol. 41, No. 3, pp. 205-206, September, 1976. Original article
submitted June 9, 1975.
This material is protected by copyright registered in the name of 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 $7.50.
832
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Declassified and Approved For Release 2013/09/23: CIA-RDP10-02196R000700080003-7
The sandwiches were irradiated in a rotating plastic disk in the water reflector of one of critical assem-
blies at the Institute of Nuclear Power Engineering of the Academy of Science of the BelorussianSSR. After
chemical processing the central parts of the detectors were photographed under a microscope; the tracks
were counted from photographs with the aid of a marking pen and an electric counter.
The obtained results and the absolute fragments detection efficiency for a thin source, based on the
accepted value e = (95.20 ?0.53) % for macrofol-E [1] are listed in Table 1. The values of E for glass and
fluorophlogopite thus calculated are in quite good agreement with the results of other authors.
Because of the lack of accurate data on absolute detection efficiency of fragments escaping thick sources,
the conversion of measured relative values into absolute is based on the so-called sensitivity constant [5] k=
T/Vd-f. , where T is the track density on the detector irradiated in contact with a thick source, tracks/cm2; (13
is the neutron flux, neutrons/cm2; and df is the average fission cross section for the given neutron spectrum,
cm2. According to [5], k=1.16 ? 1019 tracks/neutron ? cm2 with an error ?8% is valid over a wide range of
neutron energies for various thick sources (including pure 235U and 239U) and detectors (lexan, mylar, etc.).
Comparing the above expression with the one derived in [6] for track density on a detector, we find that
for a_thick source k=0.5 pRe, where p is the source nuclear density, cm-3; and e is the detector efficiency.
For R =10.25 mg/cm2 for 235U [7], corresponding for y =18.6-19.05 g/cm3 to a linear path of ?5.5 p, and for
p =4.8 ? 1022, the detection efficiency of fission fragments of the detector used in [5] (lexan) was about 88%.
Since lexan and macrofol-E have the same chemical composition and to within 1% the same efficiencies for
thin sources [3], the sensitivity constants and absolute efficiencies of our detectors can be evaluated assuming
elex
= emac-E =88%? Then, for polycarbonate film (of macrofol type), natural (capacitor) mica, fluorophlogo-
pite, cover glass, and Dacron we get s=93, 84, 78, 46, 91% and k = (1.23, 1.1, 1.03, 0.61, 1.2) ? 10-5 tracks/
neutron ? b, respectively.
As might be expected, the efficiency of most detectors is lower for thick than thin sources. An exception
is cover glass whose efficiency after such normalization increases slightly. Such anomalous behavior of silica
glass with changing fragment energy is to a certain degree confirmed by data obtained in [8]. However, it
should be noted first that in [8] the detectionefficiency is takentobe the quantity (here denoted as e181) T/n,
where T is the track density on the detector and a is the surface fission density in a source layer with a thick-
ness d if d R, and R if d>R. In our work efficiency is defined as a = T/2rim , i.e., the ratio of the number
of detected fragments to the number of fragments hitting the detector. Here 2n is the number of fragments
formed, and is the fraction of fragments .hitting the detector so that for O. d R, ji0.5[1= ? d/211 ] [6].
Hence, E [8] when d-0 and a = 2 e[8.1ifd=R. Thus, the twofold (2.0 ?0.1) reduction of efficiency of glass
when changing from a thin to thick detector, observed in [8], is associated with fragment absorption within the
source proper and agrees with the unchanging (in our definition) detector efficiency. In this case, the value
=40.g70 for glass in contact with a thin source should be valid also for a thick source. The values obtained
for our set of detectors are respectively (in the order of listing in Table 1) equal to 77.5, 82.1, 74.2, 68.9,
40,9, and 80.8%, i.e., are approximately 12% lower than when normalized in terms of the sensitvity constant.
The standard error of such calibration is about 8%.
LITERATURE CITED
1. R. Gold and R. Armani, Nucl. Sci. and Engng. 21, 13 (1968).
2. A. Kapustsik etal., Pribory i Tekh. Eksperim., No. 5, 72 (1964).
3. H. Khan, Nucl. Instrum. and Methods, 98, 229 (1972).
4. M. N. Kondratiko et al., At. Energ., 27, No. 6, 544 (1969).
5. S. Pretre, E. Tochilin, and N. Goldstein, USNRDL-TR-1098, Oct. 1966,
6. A. P. Malykhin et al., Izv. Akad. Nauk BSSR, Ser. Fiz. Energ. Nauk, No.
7. I. Niday, Phys. Rev., 121, No. 5, 147 (1961).
8. S. N. Kraitor and T. V. Kuznetsova, in; Metrology of Neutron Radiation in
[in Russian], Proc. of the 2nd All-Union Conference, Oct. 14-17, 1974, Vol
Moscow (1974), p. 146.
2, 16.
Reactors and Accelerators
. 1, Izd. TsNHatominform,
833
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LIMITS OF APPLICABILITY OF WEAK-ENRICHMENT
APPROXIMATION FOR CASCADE SEPARATION OF
TWO-COMPONENT MIXTURES
N. I. Laguntsov, B. I. Nikolaev, UDC 621.039.3
G. A. Sulaberidze, and A. P. Todosiev
The development of new methods, and the elaboration and improvement of existing methods, for the
separation of stable isotopic and molecular mixtures, together with the search for means of intensifying the
technological processes occurring in the separating equipment, has led to the creation of apparatus with a satis-
factorily high separation coefficient. For example, when mass-diffusion elements are used to separate iso-
topes of a number of low-mass elements (neon, argon) and mixtures of molecular gases (fine screening of sub-
stances), the separation coefficient for each element exceeds ao = 1.1 [1].
Because of the increase in the separation achieved in the elements, it is no longer possible to assume
that the enrichment at each stage is small, and this is the assumption which lies at the basis of the known
methods for calculations of cascade equipment [2, 3]. As a result, the use of the so-called weak-enrichment
approximation for cascade calculations leads to the accumulation of systematic errors both in determining the
number of stages and in calculating the efficiency of the equipment. Therefore, it is of fundamental importance
to choose the correct calculation procedure, appropriate to the degree of enrichment at each stage.
The theory of cascade calculations for arbitrary enrichment at each stage is now sufficiently well devel-
oped [4, 7]. The region of values of ao in which the theory of arbitrary enrichment should be used can he de-
termined by comparing results obtained in the weak-enrichment approximation and by the arbitrary-enrichment
method. To this end, we analyze a series of calculations for cascades with a given number of stages S, for
cp
97
95
0,4
43
42
41
0 0,25 450 P/Lx102
Fig. 1. Concentration in outflow as a func-
tion of P/L.
Translated from Atomnaya Energiya, Vol. 41, No. 3, pp. 206-208, September, 1976. Original article
submitted June 23, 1975.
This material is protected by copyright registered in the name of 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 $7.50.
834
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15
12
t,-
I 9
6
op
1,0
019
0,8
47
5
44
43
42
30
20
47'
10
0 0
425 450 475 P/LA,102 go glo 475 a0-1
Fig. 2 Fig. 3
Fig. 2. Cascade parameters n (1), cp (2, 3), and Pin q/lnq (4)as a function of
P/L.
Fig. 3. Relative deviation of outflow (1) and separation factor (2) as a function
of ao.
different values of 0/0 and the ratio of the outflow to the flow entering the stage, P/L. This approach allows
us to consider only the simplest case, a cascade of constant width without a waste section.
In the weak-enrichment approximation, the transfer equation in the cascade for the concentration of the
light component c can be written in the form [2]
dc, 2P
ds (cP
where
ec (1 ? c)
is the enrichment function; CpiS the concentration in the outflow.
For stages in which separation takes place along a channel (for example, a mass-diffusion separating
element), the enrichment coefficient e is related to the static separation coefficient a0 and the flux division
coefficient 6 by the following expression [3]
e=(010-1)10-ln I 1 0.
Denoting by CF the concentration in the feeder reservoir, we write Eq. (1) in the form [2]
2
S = ? arcth (c p9)
eq)
(c,P CF) (1+ ) - 2CpCF - 4Cp TcP
(1)
(2)
(3)
where or1 +4P/eL (1 -- 2cp) 4p2/82L2.
For known values of the parameters S, 0, ao, P/L, and cF, Eq. (31 may be regarded as the equation
determining the concentration in the outflow.
For the calculation of the cascade using the method of arbitrary enrichment, the differential equation in
Eq. (3) must be replaced by the difference equation [4]
= L8-108-1 6, 4_ 6_ P (cP?cs-i)
cs?cs-i Ls (1?Os) s-1 s L8 (1-0) ,
where the enrichment function for the case of separation along a channel 6 =670 =6+/1 ? 0 has the form [6]
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(4)
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(1--e)h0-1 (1+
o_
1?cy
(5)
To solve Eq. (4) by computer, an iterative procedure for the determination of cp was composed, using
the balance equation in a cascade cross section between the feeder reservoir and the first stage of the-cacaAe.
Calculations were carried out in the weak-enrichment approximation and by the method of arbitrary en-
richment for several different cascades with various numbers of stages. The value of ao was varied in the
range 1.07-1.2.- In Figs. 1-3, results are shown for a 60-stage cascade separating a mixture with an initial
concentration of the valuable component cp =0.01.
In Fig. 1, the concentration in the outflow is shown as a function of P/L and a0 =l.07 (a) and 1.2 (b). It
is evident that increase in cy0 is accompanied by a marked rise in the difference between the values of Cp given
by the method of arbitrary enrichment (curve 3) and the weak-enrichment approximation (curve 1). Also in
Fig. 1, results obtained for the cascade using Eq. (4) and an approximate enrichment function are shown
(curve 2). Curve 2 permits an analysis of the errors arising in the transition from a difference equation to
a differential equation and the use of the approximate enrichment function in Eq. (2). Thus, the effect on the
calculated results of passing from an accurate finite difference equation ?Eq. (4) to an approximate dif-
ferential equation ?Eq. (1) ? is evident from a comparison of curves 1 and 2. The difference in the calculat-
ed results due to the use of different enrichment functions ? passing from the accurate function in Eq. (5) to
the approximate function in Eq. (2) ? is shown by the relative positions of curves 3 and 2.
It is interesting to note that the divergence of the curves and hence the error in determining the calcula-
ted values of the outflow depend on the value of P/L. Therefore it is worthwhile to compare cascades operat-
ing in conditions optimal in P/L. As the criterion of optimal operation, we may use the efficiency of the mode,
which can be determined in our case as the ratio of the total fluxes of an ideal cascade and a real cascade when
producing the same product. For a cascade with a given number of stages, the dependence of the mode effi-
ciency on the parameter P/L is found to have a maximum. Physically, this may be interpreted in the follow-
ing manner. In conditions of no outflow (P/L =0), as is known, /I =0. With increase in outflow, /I also rises.
However, at a sufficiently large outflow, when the concentration gradient becomes small, the conditions of
separation deteriorate, and the efficiency begins to fall. Thus, for a cascade with a given number of stages,
the dependence?) =f (P/L) should have a maximum.
Dependences of the mode efficiencyn and the concentration in the outflow cp calculated by the various
methods for 04=1.1 are shown in Fig. 2, together with the dependence of the deviation of the separation factor
Ain q/ln q, the value of which is proportional to the error in determining the number of stages. It is interest-
ing that the maximum of the curve for the mode efficiency coincides with the maximum of Ain q. From
Fig. 2 it is apparent that for ao =1.1 the use of the weak-enrichment approximation (curve 2) leads to consider-
able error in determining the outflow and the number of stages.
In Fig. 3, it is shown that, with change in ao, the errors Pin q/In q and AP/P increase according to a
quadratic law; this is evidently associated with the effect in this region of terms ?(cmo ? 1)2, which are neglect-
ed in the approximate method. The curves are drawn for values of P/L corresponding to maximum mode effi-
ciency.
Thus, it is expedient in cascade calculations to use the theory of arbitrary enrichment. Use of the weak-
enrichment approximation is satisfactory only for small values of the static separation coefficient (go -- 1