SOVIET ATOMIC ENERGY VOLUME 22, NUMBER 1

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• Document Page Count: 92
• Document Creation Date: December 23, 2016
• Document Release Date: March 18, 2013
• Sequence Number: 1
• Publication Date: January 1, 1967
• Content Type: REPORT

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. ,
Volume 22, Number 1
, January, 1967
SOVIET
ATOMIC
ENERGY
ATOMHAA 3171EPri4F1
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
`1
CONSULTANTS BUREAU
r
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SOVIET
? ATOMIC
ENERGY
?
Soviet Atomic Energy is a cover-to-Cover translation of'Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An \arrangement:with Mezhdunarodnaya Kniga, the Soviet book
export agency, rnake&available both advance copies of the Rus-
sian journal and original glossy photographs and artwork. This
serves to decreade the necessary time lag betwedn-pukl.ication
of the original and 'publication of the translation and helps to im-
prove the quality of the latter. The translation began with the firat,
issue of the Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: M. D. Millionshchikov
Deputy Director, Institute of AtOrnic Energy
jmeni IV. Kurchatov
Academy Of Sciences of the USSR'
Moscow, USSR
Associate Editors: N. A. KOIckortsov
N. A. Vlasov
t
. A. 12 Alikh'anov
A. A. BochVai.
N. A. Dollezhal'
V. S. F.k.irsov
I. N. Golovin
V. r.Kalinin
A. K. Krasin
A. I. Leipunskii
V. V. Matveev ?
1Meshcheryakov
P. N.?Palei
' V. 'B: Sherchenko
D. L. Sirrionenko
V. I. Smirrlov
A. P. Vinogradov
A. P2 Zefirov
Copyright ? 1967- Consultants Bureau, 'a division of 4plenum Publishing corpora-
tion, 227 West 17th Street, New York, N. Y.. 10011. All rights. reserved. No article
contained herein may be reproduced for any Purpose whatsoeVer without per-
mission of the publishers.
Subscription
(12 Issues): $95
Single Issue: $30
Single.Article:415
Order from:
CONSUITANTS BUREAU '
227 'West 17th Street, New York, New Yori, 10011
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
Volume 22, Number 1 January, 1967
CONTENTS
Study of an Autoresonance Method of Accelerating Particles by Electromagnetic
Waves ? A. A. Vorob'ev, A. N. Didenko, A. P. Ishkov, A. A. Kolomenskii,
Engl./Russ.
A. N. Lebedev, and Yu. G. Yushkov
1
3
Using L. S. Pontryagin,s Maximum Principle in Minimum-Critical-Size and
Maximum-Power Reactor Problems ?T. S. Zaritskaya and A. P. Rudik . , .
5
6
Fast Boiling Reactors with the Fuel in the Form of a Fused Salt ?
Miecislaw Taube
10
10
Sodium Technology and Equipment of the BN-350 Reactor ? A. I. Leipunskii,
M. S. Pinkhasik, Yu. E. Bagdasarov, R. P. Baklushin, V. M. Poplavskii,
A. A. Rineiskii, E. N. Chernomordik, V. I. Sharanov, I. K. Petrovichev,
V. V. Stekolinikov, S. M. Blagovolin, K. B. Grigor'ev, and I. D. Dmitriev. .
14
13
Role of Condensate Decontamination in Single Circuit Atomic Power Stations ?
T. Kh. Margulova
21
19
Study of the Zones of Damage Caused by Fission Fragments of Heavy Nuclei ?
V. K. Gorshkov, L. N. L,vov, and P. A. Petrov
26
24
Radiation Stability of Low-Melting Organic Coolants in the Liquid and Solid
Phases ?V. A. Khramchenkov, I. I. Chkheidze, Yu. N. Aleksenko,
and N. Ya. Buben
30
27
Decomposition of Uranyl Chloride and Its Interaction with Uranium Dioxide in Molten
NaC1 ?KC1 ? M. V. Smirnov, V. E. Komarov, and A. P. Koryushin
34
30
Measuring the Mean Lifetime of Thermal Neutrons from a Small Specimen ?
V. V. Miller
38
33
ABSTRACTS
Accelerator Tubes for Heavy-Current Machines ? E. A. Abramyan and V. A. Gaponov
43
39
The Problem of Maximum Reactor Power ?B. P. Kochurov and A. P. Rudik
44
40
A Correction to the Spherical-Harmonics Method for Solving the Transport
Equation ?V. A. Zharkov, V. P. Terenttev, and T. P. Zorina
45
40
Activation of Spherical Specimens in a Thermal Neutron Field ? V. A. Zharkov
and V. P. Terentev
46
41
Generalization of the Albedo Method ? P. Wertesz
48
42
LETTERS TO THE EDITOR
Parametric Instability Accompanying Interaction of a Modulated Beam with a
Plasma ? V. D. Shapiro
49
44
A Semistatistical Method for Measuring the Effective Delayed-Neutron Fraction ?
A. I. Mogil'ner, G. P. Krivelev, E. K. Malyshev, S. A. Morozov,
and D. M. Shvetsov
52
46
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CONTENTS
Heat Transfer in Free-Convection Sodium Boiling,? V. I. Deev, G. P. Dubrovskii,
L. S. Kokorev, I. I. Novikov, and V. I. Petrovichev
Experimental Study of Acceleration of an Emergency-Shutdown Rod ?R. R. Ionaitis,
and L. I. Kolganova
Some Criteria of the Speed of Neutron-Activation Analysis ? E. R. Kartashev,
0, K. Nikolaenko, I. D. DaniPchenko, R. G. Gambaryan, A. S. Shtant,
and N. N. Bobrov-Egorov
(continued)
Engl./Russ.
56 49
58 51
62 54
Choice of Irradiator for Treatment of Loose Material ?A. V. BibergaP
and V. N. Primak-Mirolyubov
64
55
Correlation Between the Concentrations of Natural and Fission-Fragment Radioactive
Aerosols in the Surface Atmospheric Layer ? A. E, Shemii-zade
67
58
Measurement of Background Exposure to Population of USSR Cities, 1964-1965
Period ? I. A. Bochvar, A. A. Moiseev, T. I. Prosina, and V. V. Yakubik , .
69
59
Relative Natural Radioactivity of FEU-49 Photomultipliers ?Yu, V. Sivintsev,
V. A. Kanareikin, and L. N. Serdyuk
71
60
NEWS OF SCIENCE AND TECHNOLOGY
[International Conference on Isochronous Cyclotrons ?V. P. Dmitrievskii
and V. V. Kol'ga
64]
Ukraine's Second Conference on Ordering of Atoms and Its Effect on Properties of
Alloys ?V, I. Ryzhkov and B. I. Nikolin
75
67
[Uranium Industry of the Capitalist Countries in 1965 ?V. D. Andreev (Based on
European Nuclear Energy Agency, World Uranium and Thorium Resources,
Paris, 1965; USAEC Annual Report to Congress for 1965, Washington, 1966, p.71;
etc.)
68]
[Basel Nuclex-66 International Exhibit of Atomic Industry?Academician
Vikt. I. Spitsyn and A. N. Ermakov
73]
BRIEF COMMUNICATIONS
Conference of COMECON Specialists
76
?76
Polish Summer School on Imperfections in Crystals and Crystal Research
Techniques
77
77
BOOK REVIEWS
78
78
NOTE
This index lists all material that appears in the original Russian journal. Items origi-
nally published in English or generally available in the West are not included in the
translation and are shown in brackets. Whenever possible, the English-language source
containing the omitted items is given.
The Russian press date (podpisano k pechati) of this issue was 1/4/1967.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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STUDY OF AN AUTORESONANCE METHOD OF ACCELERATING
PARTICLES BY ELECTROMAGNETIC WAVES
A. A. Vorob'ev, A. N. Didenko,
A. P. Ishkov, A. A. Kolomenskii,
A. N. Lebedev, and Yu. G. Yushkov
UDC 621.384.62
Aspects of the autoresonance acceleration of particles by fast waves in smooth wave-
guides are considered. The results are confirmed by experiments carried out in the 10-cm
waveband. The maximum energy of electrons so accelerated was about 700 keV.
Existing methods of accelerating charged particles by electromagnetic waves in linear accelera-
tors assume the use of slow waves in diaphragmed waveguides with a longitudinal component of the
electric field. The technological difficulties associated with the manufacture of such accelerating sys-
tems are generally known. In view of this, other methods of acceleration free from this failing and
using a uhf field of high intensity present special interest.
It was shown in [1-4] that it was possible to effect resonance acceleration of particles by a trans-
verse electromagnetic wave by applying a longitudinal magnetic field and selecting appropriate initial
conditions (autoresonance method of acceleration). In this paper we present the results of an experi-
mental investigation into this method of acceleration. We shall only consider acceleration by 10-cm
electromagnetic waves set up inside smooth rectilinear waveguides. This is because as yet there are no
ways of obtaining the strong fields required to produce appreciable 'acceleration over large volumes in
other frequency ranges (including the visible).
If the magnetic field is directed along the z axis, then for a particle of energy 6 moving in the
field of a plane levorotatory electromagnetic TEM wave propagating along the z axis with a phase velo-
city vco the integral of motion is [1-4]
6 (1? const.
Here 13(p=v ,p/c and pz=vz/c, where vz is the component of particle velocity along the z axis.
Condition (1), once satisfied, remains valid on increasing the energy. The condition is satisfied
for both homogeneous and inhomogeneous waves in the transverse plane. Hence the fields of quadrupole
lenses may be used for acceleration. If pc0=1, then the conditions of autoresonance acceleration will
be satisfied in a magnetic field constant along the z axis. If, however, ,3c0 1, then, as shown in [3],
the magnetic field must increase along the z axis in order to maintain synchronism.
In practice it is very difficult to create a rf field satisfying the requirements indicated Firstly,
rf fields of high intensity can only be set up in waveguides in which the waves are not transverse.
Secondly, it is very difficult to excite waves simultaneously traveling in the z direction and rotating to
left or right in waveguides.
In view of this we tried to establishanautoresonance mechanism of acceleration by using simpler
electromagnetic waves such as the H11 wave of a circular waveguide and the structurally-similar H10
wave of a rectangular waveguide. For this purpose we first made some calculations in order to ascertain
what waves existing in waveguides satisfied relation (1). This may be shown most simply for the 1111
wave of the circular waveguide. Let the external magnetic field and the axis of the circular waveguide in which
the Hii wave, (either standing or traveling with respect to z) is excited be directed along the z axis, In this case,
if we write down the equation of motion along the z axis and the energy-balance equation
(1)
Translated from Atomnaya Energiya, Vol.22, No.1, pp.3-6, January, 1967. Original article
submitted September 5, 1966.
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for an H wave traveling with respect to 0 and z, we obtain the relation
).= g(1-13,13) --const,
where kz is the z component of the wave vector.
Relation (2) is an integral of motion analogous to that studied in [1-3] for levorotatory electro-
magnetic TEM waves. If we take an H wave traveling with respect to z and standing with respect to 0,
we may obtain exactly such an integral of motion. This means that the autoresonance mechanism of
acceleration is possible not only on using waves of right- or left-handed polarization but also on using
a superposition of these waves.
If we take an H wave standing with respect to z and traveling with respect to 0, we obtain the
relation
(2)
d = ck, tg kz clW (3)
Tir k?Zi k, dl
We see from Eq. (3) that the integral of motion (1) does not exist for H waves standing with re-
spect to z. This means in particular that the autoresonance mechanism of acceleration is not established
if TEM or H waves standing with respect to z are excited in the waveguide.
Let us estimate the maximum energy to which particles can be accelerated in an autoresonance
accelerator with definite parameters. Multiplying the equation of motion in r by r w/c2 and the equation
in 0 by re 4/c2 and combining them, we obtain
i
c
[(6;)2+ (P.6)9? 6 (i (Er;-+Eoro). (4)
dl
Hence after making some transformations we obtain the following integral of motion
or
172 (.1.2+ r2.02) x2 I'Vc -+('?P2,0)const013
2c2 k2 2 P
V213.1 V0010 x2
2 2 ? 2k2 (V Vo)+V? (1? PC013z, o) ,
OP "'I ye),
?
where ?
r2 r202
[1.21.?
e2 '
Assuming r? re and expressing pi in terms of H; ; and 1-(, =eHr/mc2y), we write the in=
tegral of motion in the following form:
e
eHN)2 rff 2 1 the length of the section in which the energy increased was quite
short. In our case, for an 1111 wave in a circular waveguide, 3 = 2; hence from expression (10) we
find that this length z=3.6 cm. Hence if the length of the
homogeneous magnetic solenoid is greater than 3.6 cm,
the energy should vary periodically along the waveguide.
In order to observe the "beats" of energy, the inner wall
of the waveguide was coated with a thin layer of phosphor.
For an optimum magnetic field, luminous rings appeared
0 on the waveguide walls. The distance between the rings
was 1=6 to 7 cm; i.e., approximately twice the length of
the section in which the energy rise took place. On vary-
ing the magnetic field in the neighborhood of resonance,
slight displacements of the rings along the waveguide took
place. Sharp distortion of the magnetic field at any point
along the solenoid led to the vanishing of the luminous
rings in this region and to a fall in the intensity of x-ray
radiation.
9
Fig .1 . Block diagram of the apparatus. 1)
Magnetron generator; 2) vacuum pump;
3) wave transformer; 4) accelerating sys-
tem; 5) electron gun; 6) rotating magnet;
7) solenoid; 8) rf load; 9) matching plun-
ger; 10) observation window.
The kinetic energy of the accelerated electrons was
determined by passing the electrons through aluminum
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foils; it was E kin=600 keV for an electric field of 3 to 5 kV/cm. This energy is considerably higher
than that attainable with ordinary cyclotron acceleration under analogous conditions.
Detuning the match between the accelerating waveguide and the rf load led to the appearance of
substantial reflections in the channel and to a disruption of acceleration (in this case a ferrite decoupler
was included in the rf channel between the accelerating waveguide and the magnetron generator).
For a more detailed check on acceleration in the systems in question (using a standing wave along
the z axis) we prepared a resonator in which H108 oscillations were excited. In this system no accelera-
tion was recorded. This fact indicates once more that in this case there is no cyclotron acceleration
whereby the replacement of the traveling wave by a standing wave need not change the final energy.
Thus the experimental results indicate the existence of an autoresonance mechanism of accelera-
tion and agree closely with both the theoretical considerations developed in [1-4] and those of the pres-
ent investigation. Electrons accelerated in accelerators of this type may find technological applications
such as the efficient injection of particles into magnetic traps [5,6].
LITERATURE CITED
1. A. A. Kolomenskii and A. N. Lebedev, Dokl. AN SSSR, 145, 1259 (1962).
2. A. A. Kolomenskii and A. N. Lebedev, ZhETF, 44, 261 (1963).
3. A. A. Kolomenskii and A. N. Lebedev, In: Transactions of the International Conference on Accel-
erators, Dubna, 1963 [in Russian]. Moscow, Atomizdat, p.1030 (1964).
4. V. Ya. Davydovskii, ZhETF, 43, 886 (1962).
5. B. S. Akshanov, Yu. Ya. Volkolupov, and K. D. Sinel'nikov, ZhETF, 36, 595 (1966).
6. B. S. Akshanov, Yu. Ya. Volkolupov, and K. D. SinePnikov, ZhETF, 75, 603 (1966).
All abbreviations of periodicals in the above bibliography are letter-by-letter translitera-
tions of the abbreviations as given in the original Russian journal. Some or all of this peri-
odical literature may well be available in English translation. A complete list of the cover-to-
cover English translations appears at the back of the first issue of this year.
r,
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USING L. S. PONTRYAGIN'S MAXIMUM PRINCIPLE IN
MINIMUM-CRITICAL-SIZE AND MAXIMUM-POWER
REACTOR PROBLEMS
T. S. Zaritskaya and A. P. Rudik UDC 621.039.50
L. S. Pontryagin's maximum principle is used for solving problems in which it is
necessary to find the minimum critical size of a reactor for a given power or to find the
maximum power for a given critical size. Recently Pontryagin's maximum principle [1]
has been successfully used both for determining the optimum transient conditions for re-
actors [2, 4] and for finding the optimum spatial arrangement for reactors with prescribed
physical characteristics [1]. In the present study this principle is used in two other pro-
blems encountered in the theory of reactor design.
STATEMENT OF THE PROBLEM OF FINDING THE MINIMUM
CRITICAL SIZE FOR A PRESCRIBED REACTOR POWER
It is assumed that the reactor power W is given and that the structural materials are distributed
uniformly through the reactor. Resonance absorption and neutron absorption and multiplication during
moderation are ignored. The uranium concentration U(z) is considered variable over the volume of
the reactor within the limits:
0 U (z) (-7 max .
The power per unit of reactor volume, p (z) N(z)U(z), is limited:
p = (z) (z) ? D 0,
(1)
(2)
where N(z) is the thermal-neutron density at point z and D is a constant. It is required to find the dis-
tribution U(z) which will yield the minimum critical reactor size for a prescribed power W and under
conditions (1) and (2). The problem is solved in a two-group approximation for a symmetric slab re-
actor. The initial equations describing the thermal-neutron density, [N(z)J, and the moderated-neutron
density [n(z)] , have the usual form [6]
d2N
?(I (z) N ?n?
dz2 '
d2n n
T TE6
(3)
where L is the square of the diffusion length of the medium, where the structural materials are taken
into account but the uranium is not; T is the square of the moderation length (the variation in -r for
different uranium concentrations is neglected); n is the effective number of neutrons produced in fission.
PONTRYAGIN'S METHOD
In order to use the mathematical theory of optimal processes [1], we write (3) in the form of four
first-order equations, introducing the notation x(1)N; x(2)==-dN/dz; x(3)n; x(0-=- dn/dz and adding an
equation for x(5), making use of the fact that the reactor power is specified and is equal to W= N(x)U(z)dz
(where H is the desired half-width of the reactor). As a result, 'we obtain the following system of
equations:
Translated from Atomnaya Energiya, Vol. 22, No.1, pp. 6-10, January, 1967. Original article
submitted July 27, 1966.
5
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ddxdyz((:), x(3)
dz = Lg
.114>
x(4) =
dz
(Lei)= x(3) IP x(1) =
dz TLS
(4)
di(5) UX(') = /(5).
dz
The functions x(i) satisfy the following boundary conditions:
x(1)(H)? x(3) (H) = 0; x(2) (0) = x(4) (0) = 0; x(5) (0) = 0; x(5) (H) =- W. (5)
The Hamiltonian of the system (4) is formed according to the rule [1]:
5
a.i
=*ix(2)+
1-11)3x(4)-F--11)4x(3);
= x(i) (2-.-6) +]
where the auxiliary functions Of satisfy the equations
(6)
aN ap (7)
d z = Tx "Ftr
and the function p is given by formula (2). The function A. is defined as follows: if p 0, we have
W/O
a
U (II ? 8) = Umax ,
Obviously these considerations are valid only when co(h) =0. As
150
will be shown in the following section, q(h) = 0 when we have the op-
t imum arrangement I.
Solution of System of Equations for zpi.
100
??????
We shall write the system of equations (7) for the functions zpi in
explicit form:
50 dth 1+ U ,, , 1U ,. ,
1,5 2,0 25 HA? _
d z L3 11' 2 1" 'TLT 4) i ? 0 4)5 1' r?U ;
Fig.L W/D as a function of 61)2 __ vi;
H/Lo for arrangements 1(a) dz
an 3 ih ? *4 .
d V (b) when dt-
77 =1.07, ' (10)
dz 1"2 T
T/LF) = 0.01, and Umax=35.19
(the x corresponds to arrange- 44 dz ? V3;
ment II.)
=0
dz
*It should be noted that since the function yo(z), according to (6), is the product of a function which
depends only on x(i) and a function which depends only on 01., it follows that 1J0(z) n?The statement
that no such zone can exist means that there cannot be zones U(z ) = 0 in which co(z) = 0.
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In the first zone, according to formula (8), the function A has the form
Fig.2. Graph of cp(z)/x(1)(z)
in the second zone of the re-
actor for arrangement I.
(1P2? V4) +1P5i
i.e., the functions zpi are independent of U. In the second zone A =0,
and the system of equations (10) includes U(z) = Umax.
Figure 1 shows the function W/D=f (H/L0) for arrangements I
and V. As the calculations show, the critical size is even larger for
arrangement II than for arrangement V (Fig.1 shows one of the points
for arrangement II). Figure 2 shows the function cp(z)/x(1)(z) in the
second zone of the reactor for arrangement I. We can see that the
Hamiltonian attains a supremum in this zone. Furthermore, the
analysis shows that the condition A> 0 is satisfied in the first zone.
Thus, arrangement I is in fact optimal.
RELATIONSHIP OF THE MINIMUM-CRITICAL-SIZE
PROBLEM TO THE MAXIMUM-POWER PROBLEM
In the above paragraphs we consider the problem of finding the
minimum critical size for a given reactor power. Now we shall ex-
amine the inverse problem: for a prescribed reactor size and the
assumptions given above, find the arrangement which will yield the maximum reactor power. We shall
show that arrangement I will be optimal in this case as well.
What is the difference in form between the statements of these two problems?
In the minimum- critical-size problem we were looking for the minimum of a functional J=+ dz
for a prescribed value of the functional W= x(1)Udz. In the maximum-power problem the functional J
is given and we must find the maximum of the functional W. The other equations for x(i) in the inverse
problem are exactly the same as in the direct problem.
Let us find how the Hamiltonians and the equations for zpi differ in these two problems. Let us
clenote4(z) by x(?) and W(z) by x(5). In the direct problem the increment added to the Hamiltonian is
while in the inverse problem it is
Vdir =
AVinv = ?11)o x(1)U1'5,
(12)
(13)
i.e., the form of the Hamiltonian is the same in the direct and inverse problems. Hence, according to
Eq.(7), it follows that the systems of equations for zpi are also identical. Let us now compare the boiliid-
ary conditions. In the direct problem x(5) (0)=0; zpo is an undetermined constant [zpo 0, since we are
trying to find the minimum of x(5)(H)]; x(5) (0)=0 and x(5) (H)=W; 05 is a constant found by solving the
equations simultaneously for x(1) and zPi. It is important to note that, according to one of the require-
ments of the maximum principle, the supremum of the Hamiltonian must be a constant positive number,
and so we find that p5> 0.
In the inverse problem x(5) (0)=0 and x(0)(H)=H; i.e., the constant zpo is not determined by the
boundary conditions; x(5)(0)=0; 05 is an undetermined constant [zpo?.. 0, since we are trying to find the
maximum of x(5) (H)]. Thus, the constants zpo and 05 in the direct and inverse problems are not determined
by the boundary conditions but are found as solutions of the systems of equations for x(i) and zp i. Since the
solutions are unique and the systems are identical, all x(i) and zpi (including zpo and 05) are identical for
the two problems. Consequently, if we have solved the problem of minimum critical size for a given
power, we automatically obtain the solution of the problem of maximum power for a given critical size.
The above considerations hold true whenever we are looking for the optimum of any functional for
a prescribed value of a second functional: the solutions of the direct and inverse problems are identi-
cal. However, depending on the signs of the constants zpo and 05, we may have different cases: if zpo 0, then in the direct case we are looking for the minimum of the functional x(0) and in the
inverse case for the maximum of x(5); if zpo > 0 and 15> 0, then we are looking for maxima in both cases;
8
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if zpo< 0 and 05 < 0, we are looking for minima in both cases; if zPo> 0 and 05 < 0, then we are looking for
a maximum in the direct case and the minimum in the inverse case.
In conclusion, it should be pointed out that the use of Pontryaginis maximum principle has made
it possible to findanexact solution of the problem of minimum critical reactor size. The solution pro-
cess is divided into two stages: rigorously defining the type of zones from which the reactor may be
made up, and then making up a reactor from these zones. There is no algorithm for the second stage;
it consists simply in analyzing different variant arrangements for optimality.
The results obtained here can easily be extended to problems with cylindrical and spherical geo-
metry, as well as to multigroup problems. However, if the resonance absorption in the uranium is
taken into consideration, we will obviously have to use numerical calculation methods and cannot obtain
solutions in analytic form.
The authors wish to express their deep gratitude to V. G. Boltyanskii and L. N. Bolt shev for their
interesting explanations concerning the mathematical theory of optimal processes.
LITERATURE CITED
1. L. S. Pontryagin et al., Mathematical Theory of Optimal Processes [in Russian], Moscow, Fiz-
matgiz (1961).
2. Joshikumi Shinohara and Jean Valat, C. r. Acad. Sci., 259, Groupe 6 (1964).
3. Z. Rosztoczy and L. Weaver, Nucl. Sci. Eng. 20, 318 (1964).
4. J. Roberts and H. Smith, Nucl. Sci. Eng., 22, 470 (1965).
5. B. P. Kochurov, Atomnaya Energiya, 20, 243 (1966).
6. A. D. Galanin, Theory of Thermal-Neutron Nuclear Reactors [in Russian], Moscow, Atomizdat
(1959).
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FAST BOILING REACTORS WITH THE FUEL
IN THE FORM OF A FUSED SALT
Miecislaw Taube UDC 621. 039. 526
An attempt is made to classify fast reactors. Versions of a fast reactor with liquid
fuel in a boiling coolant - solvent are considered separately. The advantages of this type
of reactor and the feasibility of its construction are evaluated; the basic characteristics
of the reactor are derived.
A characteristic feature of the current state of development of nuclear power generation is that
in the sphere of fast reactors, solid-fueled (oxide) reactors cooled by liquid metal (sodium) are being
given primary consideration. The main efforts are concentrated on the future improvement and intro-
duction of reactors of this type in energy generation. Nevertheless, the investigations and developments
of other types of reactors are worthy of note, for example with a gaseous and vapor coolant. In part-
icular, it is proposed to use helium (p r=,' 70 atm, T 660?C) [1,2] , and also steam (p 170 atm,
T '&? 540?C) [3]. It is assumed that uranium and plutonium oxides will be used as the fuel in all the pro-
jects mentioned.
There is a significant difference in a reactor with liquid fuel in the form of a three-component alloy
of plutonium (e.g., the LAMPRE-II reactor) [1]. Reactors with liquid fuel in the form of fused
chlorides (UC13, PuC13, NaCl, MgCl2, etc. ) are at the stage of discussion and evaluation. Two different
versions of a reactor of this type are known: a) with indirect cooling (via a heat-exchanger system)
[4-7] and b) with direct cooling, in which the removal of heat by the coolant (liquid lead) is accomplished
by means of contact heat exchange with the liquid chlorides (fuel) [2,4,8].
In considering the possible routes of development of fast reactors, it is possible to see feasibilities
of developing other types of reactors (Table 1). In this paper, we consider the fast reactor with a liquid
fuel and a boiling solvent. In this type of boiling reactor, part of the coolant exists in the liquid state
and part in the vapor state. The existence of several versions of such reactors is possible, in principle
(Table 2); at the end of 1965, two types of fast reactors with boiling coolant were proposed, designated
respectively WARS [15] and SAWA [16].
The basic characteristics of the reactors are given in Table 3. We note the special features which
are common to both versions. The fuel is in the form of fused chlorides U238C13 and Pu239C13; NaC1 as
diluent; melting point of the fuel ?450?C; molar ratio U:Pu=4:1; specific heat ? 0.30 kcal /kg; specific
weight ^,5.0 kg/liter. The coolant enters the reactor in liquid form. Boiling of the coolant takes place
in the reactor core at a temperature of 750-800?C under a pressure of 20-40 atm. The vapor is fed
directly into the turbine or into the heat exchanger; the partial pressure of the uranium and plutonium
chlorides is about six to eight orders less than that of the coolant. The coolant is chemically inert
relative to the fuel components, but reacts with certain fission products.
Part of the fission products are removed by the coolant vapors. The stability of operation of a
fast reactor depends, to a considerable degree, upon the coefficient of thermal expansion of the boiling
coolant, which introduces negative reactivity. This ensures a relatively high reactor stability [17],
although the possibility of transition to the oscillatory conditions cannot be excluded. Reloading of the
fuel can be carried out continuously and part of the fission products can be separated from the liquid
or vapor coolant. The problem of fuel regeneration is solved relatively simply. The problem of
corrosion of the structural materials (for example, an alloy of the INOR-8 type) in a chloride medium
? (in particular, aluminum trichloride in the SAWA reactor or to a certain extent by contact with liquid
mercury in the WARS reactor) requires special investigations; however, this obviously can be solved
positively.
Institute of Nuclear Research, Warsaw-Zeran, Polish People's Republic. Translated from
Atomnaya Energiya, VO1.22, No.1, pp. 10-13, January, 1967. Original article submitted July 16,1966.
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TABLE 1. Principle Versions of Fast Reactors
Fuel
Coolant
Type of cooling
Remarks
Gaseous
Liquid
Indirect
Direct
Gaseous -fueled reactor, cooled by sodium .
Gaseous-fueled and liquid-cooled reactor (technol-
ogically inexpedient)
Liquid-gas(boiling)
Indirect
Direct
No technological advantages
Impossible, because of irreversible mixing of fuel
and coolant
Gaseous
Indirect
Direct
No technological advantages
Impossible, because of irreversible mixing of fuel
and coolant.
Liquid
Liquid
Indirect
Direct
LAM PRE [1] liquid-metal reactor, sodium-cooled.
Liquid-salt reactor, sodium-cooled [4, 7]
Liquid-salt reactor, cooled by liquid lead [2, 5, 8]
Boiling
Indirect
Direct
No technological advantages
Liquid-fueled with boiling coolant (see Table 2)
Gaseous
Indirect
Direct
No technological advantages
Liquid-fueled, with straight-through gas cooling
Solid
Liquid
Indirect
Direct
No technological advantages
Oxide-fueled reactor, cooled by liquid sodium
[1, 9-13]
Boiling
Indirect
Direct
No technological advantages
Solid-fueled reactor with boiling potassium [14]
Gaseous
Indirect
Direct
No technological advantages
Oxide-fueled reactor with gaseous coolant [1,3]
The fundamental differences between the two versions consists in the following. In the WARS
reactor, mercury is used as the coolant and it is almost insoluble in the liquid uranium, plutonium,
and sodium chlorides, as a result of which a heterogeneous dispersion is obtained. The development
of bubbles of mercury vapors can be controlled quite adequately. The possibility of formation of mercury
chloride must be taken into account (the monochloride transforms to the dichloride at a temperature of
560?C). In the SAWA reactor, the coolant is aluminum trichloride, which easily dissolves the uranium,
plutonium, and sodium chlorides with the formation of a homogeneous solution. The development of
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TABLE 2. Fast Reactors with Liquid Fuel and Directly Boiling Coolant
,
Liquid fuel (mp
? 450?C)
Boiling coolant(boil-
ing point ? 800?C, un-
der a pressure of sev-
eral tens of atm. )
,
Fuel-coolant system
Remarks
Metallic*
(alloys of Pu,
Fe, Co, Ce, etc.)
.
Metallic
,Homogeneous
Heterogeneous
Liquid-metal fueled reactor, boiling
coolant - mercury
Liquid-metal fueled reactor, boiling
coolant - sodium
Salt
Homogeneous
Heterogeneous
Impracticable, because of poor
solubility of salt in metals
Impracticable, because of poor
solubility of metals in salts
Salt (fused chlo-
rides UC13, PuC13,
diluted with chlo
rides KC1, MgC12,
NaCl, CaCl2,
etc.)
Metallic
Homogeneous
Heterogeneous
Impracticable, because of poor
solubility of metals in salts
Liquid-salt fueled reactor, boiling
coolant - mercury (WARS type)
Salt
Homogeneous
Heterogeneous
Liquid-salt fueled reactor, boiling
coolant - aluminum trichlo-
ride (SAWA type)
Impracticable, because of mutual
solubility of salts or because of
mutual reaction
The use of uranium is excluded in consequence of the temperature conditions.
TABLE 3. Comparative Characteristics of Fast Reactors
Characteristic
Reactor
BN-350
SAWA
WARS
Cooling
Coolant
Indirect Indirect
Liquid
Direct
Boiling
Fuel
Solid
Liquid
Liquid
(oxides)
(chlorides)
(chlorides)
Thermal power, MW
1000
2500
1000
1000
Core volume, liter
2000
10,000
6,000
10,000
Specific power, kW/liter
500
250
165
100
Fuel concentration,
kg Pu/liter
0.4
0.33
0433
Specific power, kW/kg Pu
1200
580
1000
1000
Coolant
Sodium
Sodium
Aluminum
trichloride
Mercury
Mean specific heat
of liquid coolant, kcal/
kg?deg C
0.30
0.30
0.27
0.033
Heat of boiling of coolant,
kcal/kg
Does not
boil
Does not
boil
37.8
68.13
Coolant supply, kg/sec
1340
3300
Thermal expansion/C
1.3* 10-6
1.5.10-4
2A0-2
2.10-3
(salt)
State of work
To be con-
Prelimi-
Preliminary development
structed
[9]
nary plan-
ning [6]
[15,16]
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bubbles of aluminum trichloride vapor takes place spontaneously and it is very difficult to control. This
problem has been insufficiently discussed in the literature and requires special investigation.
LITERATURE CITED
1. M. Whitman et al. Report No. 3/1 Presented at London Conference on Fast Breeder Reactors,
17-19 May 1966.
2. R. Moore and S. Fawcett, See [1], Report No.1/7
3. R. Mueller et al. See [1], Report No. 1/6
4. L. Alexander, Molten Salt Fast Reactors. Conference Breeding and Safety in Large Fast Reactors,
ANL-6792 (1963).
5. L. Alexander, Ann. Rev. Nucl. Scie. ,14,287 (1964).
6. M. Taube, Symposium Power Reactor Experim. , Report No. SM-21/19. Vienna, IAEA (1961).
7. P. Nelson et al. Trans. Amer. Nucl. Soc. , 8 , 153 (1965).
8. H. Killingback, A Molten Salt Fast Reactor, ?Winfrith AEE. Preprint, April (1966).
9. A. Leipunskii et al. See [1], Report No.3/1
10. A Frame et al. See [1], Report No. 3/1
11. C. Pursel and E. Link, See [1], Report No. 3/5
12. I. Tattersall et al. See [1], Report No. 3/6
13. G. Vendreys et al. See [1], Report No. 1/3
14. A. Fraas, Nucleonics, No.1, 72 (1964).
15. M. Taube et al. Nukleonika, No.9-10, 641 (1965).
16. M. Taube et al. Nukleonika, No.9-10, 639 (1965).
17. M. Taube et al. Nukleonika, No.9, 631 (1966).
18. E. Nesis, Usp. fiz. nauk, 87, 651 (1965).
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SODIUM TECHNOLOGY AND EQUIPMENT OF
THE BN-350 REACTOR
A. I. Leipunskii, M. S. Pinkhasik,
Yu. E. Bagdasarov, R. P. Baklushin,
V. M. Poplavskii, A. A. Rineiskii,
E. N. Chernomordik, V. I. Sharanov,
I. K. Petrovichev, V. V. Stekolinikov,
S. M. Blagovolin, K. B. Grigoriev,
and I. D. Dmitriev
UDC 621. 039. 526+621. 039. 534. 6
Information relating to the installation of a dual-purpose atomic station with a BN-350
reactor on the Mangyshlak peninsula in the USSR was presented in contributions to the Third
International Conference on the Peaceful Use of Atomic Energy (Geneva, 1964), and the
Detroit Conference in 1965. The present paper is devoted to a description of the main tech-
nological equipment and experimental work carried out in the construction process; it also
includes a discussion of certain questions on sodium technology.
CIRCULATION PUMP
A console pump with a free fixed level of sodium, biological shielding, and mechanical sealing
was chosen for the BN- 350 reactor. Adequate experience in the use of such pumps has been gained in
the USSR. The parameters of the pumps of the first and second circuits are shown in the table.
There is no fundamental design difference between the pumps of the first (Fig. 1) and second
circuits. The pump in the second circuit has no biological shielding.
The shaft of the pump has one radial and one radial-thrust slide bearing. The distance between
the axes of the working wheel and lower bearing is 2 m. The biological shielding is situated inside the
pump tank and part of the shielding is in the sodium. Between the roof of the pump tank and the lower
bearing is a cooling belt for reducing the axial flow of heat in the direction of the bearings, and also
for preventing sodium vapor from passing into the bearing cavity of the pump. A sodium-potassium
alloy is used to cool the belt. A system for cooling the shaft, operating from a common oil supply,is
provided, and measures are taken to prevent the passage of oil vapor or the oil itself into the sodium.
The pumping part proper is removed from the tank without cutting the sodium-containing conduits. The
bearings and upper oil seal may be inspected and repaired without withdrawing the removable part of
the pump. The gas cavity is sealed in this case by a special "standing" seal, which operates with the
pump disconnected. Part of the coolant flow is closed "on itself"; the remainder is taken away through
a special overflow line to the pump inlet. No speed regulation is provided, but the pump is able to
operate under different conditions. Three, four, or five pumps may be connected in parallel, and in
addition the pump may operate at one-quarter speed.
Design Parameters of the Circulating Pumps of the First and Second Circuits
Circuit
Rating, m3 /h
Head of sodium
column,m
Shaft speed, rpm
Maximum power of
electric motor, kW
First
Second
3220
3850
110
70
1000/250
1000/250
1'700
1100
Soviet contribution to the Fast-Reactor Conference in England, May, 1966 (abbreviated version).
Translated from Atomnaya Energiya, Vol.22, No.1, pp. 13-19, January, 1967. Original article submitted
July 18, 1966.
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?
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Ce,
Fig. 1. Sodium circulation pump of the first cir-
cuit 1) flow of oil from the shaft gas-sealing
unit; 2) water from shaft gas-sealing unit; 3)wa-
ter for cooling the shaft gas-sealing unit; 4) oil
passing into the shaft gas-sealing unit; 5) gas
for scavenging; 6) oil passing into the upper
bearing; 7) oil passing into the pivot; 8) oil pas-
sing into the shaft; 9) oil from the pivot, upper
bearing, and shaft; 10) oil passing into the low-
er bearing; 11) Na-K for cooling the shaft;
12) oil from the lower bearing; 13) initial lining
level; 14) maximum level.
Experiments in developing the design of the
pump are continuing at the present time.
A 1:4.5 scale model has been used to choose
the geometry of the flow section and the control
apparatus, to determine the number and direction
of internal flows, to carry out cavitation tests, to
determine the degree and direction of hydraulic
forces, and to find the efficiency of the pump (which
turns out to be 70%).
The pump uses sealing of the type used in
hydrogen-cooled generators. The heat from the
friction pairs is transferred to the oil and eliminated
with a built-in cooling system. A special testing
system was set up to develop the construction and
select the materials of the friction pairs. ,Prefer-
ence was given to a combination of graphite and a _-
chromium-plated steel surface.
A full-scale test-bed, comprising the under-
carriage of the pump with all its components except
the rotor (the weight of which was imitated by a
metal disc), was set up to finish the bearings and
to check the thermal state of the shaft, both when
the oil-cooling system and cooling belt were in
operation and when they were switched off.
At the present time a sodium test-bed has
been set up for testing standard pumps. This is
equipped with all necessary measuring and control
systems. The test circuit contains about 20 m3 of
sodium. The test-bed will be used to test pumps
under conditions similar to those found in practice
and also to test the electric motor and its auxiliary
systems, the fittings, the reverse valve, the level
gage, and the flow meter. The main purpose of the
test-bed, however, is the all-round "capability
testing" of earlier-developed principal components
of the pumping system and the pumping system as
a whole.
The test-beds for the pumps of the first and
second circuit are placed together; by setting up a
connection between them, it is proposed to carry
out tests on the reverse valve under conditions
simulating the shut-down of one of the pumps in the
BN-350 reactor.
INTERMEDIATE HEAT
EXCHANGER
The intermediate heat exchanger (Fig.2 ) of
shell-and-tube construction consists of two parallel
sections. Each section is made in the form of a
horizontal rectangular tank with three heat-transfer
pipe beds immersed in it. Each bed consists of 343 U-shaped pipes 28mm in diameter and 2 mm thick
with a spacing of 35 mm along the front and in depth. Kh18N9 steel is used. The beds in each section
are connected in series. The sodium of the first circuit passes into the inter pipe space, where it
transfers heat to the sodium of the second circuit moving inside the pipes. The vertical U-shaped pipe
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Sodium of the
first circuit
Sodium of
the second
circuit
Fig. 2. Intermediate heat exchanger.
bed has a cylindrical form; hence, in order to ensure
a uniform distribution of the coolant over the width of
the body, the pipe system of each bed is filled out to
rectangular form with a set of stationary, nonoperating,
straight pipes.
In order to create a uniform flow of the sodium of
the first circuit, an equalizing grid is placed at the
entrance to the first bed. Any bed of the heat exchanger
may be taken out and replaced by a new one. In order
to ensure access to the entrance and exit chambers,
biological shielding, with special channels for passing
the sodium of the second circuit, is provided.
At the present time the following experiments
have been carried out:
1. The hydrodynamic characteristics of the
interpipe space of the heat exchanger have been
studied (on a 1:2.5 model).
Principal Characteristics of the Heat Exchanger
Thermal power 200403 kW
Temperature of first-circuit sodium
at the entrance 500?C
at the exit 300?C
Temperature of second-circuit sodium
at the entrance 273?C
at the exit 453?C
Heat-transfer surface 1120 m2
Hydraulic resistance of first circuit 0.146 kg/cm2
Hydraulic resistance of second circuit 2.24 kg/cm2
The results of the tests showed that the configuration of the input part of the model failed to ensure
uniform flow of the sodium around the first pipe bed.
By suitable remodeling, this nonuniformity was eliminated. The experimentally determined over-all
hydraulic-resistance coefficient of the heat exchanger, equal to 2.8, agreed closely with calculation.
2. Vibrational tests of the heat-exchanger tubes with transverse coolant flow were conducted on the
model. The geometry of the bed, its lay-out, and its materials, were similar to those in the design.
The tests were carried out with water. The experiments indicated that the dynamic stresses arising
in the tubes under the influence of a transverse coolant flow were small for the design in question and
could not have any marked effect on the efficiency of the heat exchanger.
In addition to the model tests, vibration tests were carried out on a full-scale heat exchanger, with
the circulation of water through both the first and second circuits at the rated flow velocities.
3. A sodium test-bed of 3000 kW thermal power was also assembled and tested in order to secure
an experimental verification of the thermotechnological characteristics of the heat exchanger.
STEAM GENERATOR
The steam generator (Fig.3) consists of two sections connected in parallel with respect to the
sodium and water-steam circuits, a gas vessel, and connecting tubes. Each section contains one
evaporator and one steam super-heater.
The evaporator is made in the form of a vertical vessel, with natural circulation of water inside
Field tubes and separation of the steam in the steam space of the body. Sodium passes into the evaporator
from the superheater and moves upward through the interpipe space, giving up heat to the water.
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Fig. 3. Principle of the steam generator.
The boiler water from the water space of the evaporator
passes into the inner, downcoming channel of the
Field tube, moves downward, and passes into a ring-
shaped gap, where it receives heat from the sodium,
and, partly evaporating, again moves upward. The
water-steam mixture thus formed is brought out
through the steam exhaust pipes into the steam space
of the evaporator.
The tube panel separates the body of the
evaporator into two cavities: the upper, (steam-water)
and the lower, (sodium). In the upper space or cavity
are the collector of the feed-water supply, the
scavenging collector, lines for the emergency removal
of water from the evaporator, a jet-quenching sheet
with downcoming tubes, and separation systems.
The lower (sodium) space may be arbitrarily
divided into three parts: the entrance chamber, the
working part, and the exit chamber with the gas space. In the entrance chamber is a double perforated
sheet intended to produce a uniform distribution of the flow of sodium over the cross section of the
evaporator. The working part consists of a body 1400mm in diameter with a wall thickness of 24 mm.
In the body are 816 Field tubes arranged in a triangular lattice with 44-mm spacing. Each Field tube
consists of an outer tube of diameter 32 x 2 mm and an inner tube of diameter 16 x 1.4 mm. The lower
end of the former is lapped and sealed, and the latter is fixed by its upper end in a steam waste vessel
600mm high set in a socket of the tube panel. In the upper part of the exit chamber is a gas space for
the withdrawal of gaseous products of the reaction between sodium and water in the case of accidental
unsealing of the tube system.
The steam superheater is a vertical U-shaped heat-exchange system with the sodium and steam
entrance and exit chambers in an upper position. The heat-transfer surface is made up of 805 U-shaped
tubes 16 mm in diameter and 6 x 2 mm thick. The ends of the tubes are fixed into tube panels with
apertures arranged in a triangle with a 23-mm spacing.
The components of the evaporator and steam superheater are made of 1 x 2M steel.
The gas vessel is a cylindrical vessel with hemispherical ends; it is intended for the partial
trapping of sodium which may be thrown out together with hydrogen from the steam-generator space if
there is any significant unsealing of the heating surface.
In the line of each evaporator is a feed regulator and a fast-acting irreversible cut-off valve, which
operates if any leak appears in the steam generator. In order to secure rapid elimination of the
dangerous state if substantial leaks of water into the sodium occur, an emergency line is provided for
ejecting the water from the evaporators.
For removing reaction products there are tubes linking the gas cavities of the evaporator with the
gas vessel. The latter is connected to a reaction-product separator installed outside the steam-genera-
tor room by means of a system of pipes incorporating a safety device.
Principal Characteristics of the Steam Generator
Steam-production rating
Superheated-steam pressure
Pressure in evaporator
Temperature of superheated steam
Temperature of feed water
Temperature of sodium at entrance to steam superheater ? ?
Temperature of sodium at exit from steam superheater
Temperature of sodium at exit from evaporator
Resistance of steam generator with respect to steam
Resistance of steam generator with respect to sodium
276 tons/h
50kg/cm2
52 kg/cm2
435?C
158?C
453?C
416?C
273?C
1.5 kg/cm2
0.93 kg/ cm2
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Evaporator heating surface 820 m2
Steam-superheater heating surface 455 m2
Circulation in evaporator 4-pass
A number of experiments have been carried out at the present time. The effects of interaction
between sodium and water on failure of the heat-transfer tube have been studied. So has the effect of
the composition of the gas blanket on the mechanism of the interaction, and the effect of the velocity
and direction of the sodium flow on the temperature change at the point of contact of the reagents and on
the propagation of the gaseous reaction products. The stability of the pipe bed of the evaporator when
one of the pipes breaks and a large quantity of water passes into the sodium has been studied. The
experiments were made on a model made of the design materials. The experimental test-bed constituted
a closed sodium circulation circuit including a model of the evaporator, an electromagnetic pump,
transport and drainage vessels, fittings, and conduit pipes.
In order to measure the pulsations in pressure at the point of breakage and in the gas space of the
model, tensomanometers were used in combination with the appropriate amplification and supply systems
and a loop oscillograph. The change in the temperature of the sodium at the point of contact and the
temperature variation over the height of the interpipe space of the section was recorded with special
low-inertia KhA microthermocouples.
Among the most important measurements, we also note the time variation in the position of the
piston of the water dispenser in the course of injection. Five experiments were made in all. Up to
3 kg of water were fed into the sodium, the test volume of sodium being 100 liter. The injection time
varied between 3 and 4 sec. The results were approximately the same in all the experiments.
At the moment of breakage, the pressure at the point of injection rose momentarily to 40 or
50 kg/cm2; then there were a few pulsations, and the pressure fell. The flow of sodium through the
model practically ceased, and the temperature at the injection point rose briefly to 700 or 800?C. The
pressure in the gas cavity first rose, falling after the breakage of the safety membrane; the change in
pressure was determined by the capacity of the reaction-product ejection system. In all the experiments,
almost all the sodium enclosed between the injection point and the gas blanket flowed out into the ejection
system.
There was not a single case of breakage in the neighboring tubes filled with water under a pressure
of 50 to 60 kg/cm2. The bending of the central and neighboring tubes was negligible. A characteristic
graph giving the change of parameters in one of the experiments is shown in Fig.4 and the form of the
damage in Fig.5.
18
3
60
"E 40
C.)
tzo
(g20
/
/
/\
\
\
\ ,1
V
/
/
/
/
/
\
\
\
\
3 \
/
\
800
600
400
200
0 2 6 Time, sec
Fig. 4. Change in the principal parameters on
injection of water into the sodium. 1) Tem-
perature of sodium at the point of breakage;
2) weight of water passing into the sodium;
3) pressure at the breakage point.
Fig. 5. Failure of the central tube.
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The circulation characteristics of the Field tube were studied over a wide range of thermal loadings,
and water-chemical tests of the evaporator elements were carried out. A special test system with a
single Field channel was set up for this purpose.
A sodium test-bed of 3000 kW thermal power was set up and put into action in order to secure an
experimental verification of the thermotechnological characteristics in the models of the evaporator and
steam superheater. The models were full-scale structures as regards length, but had a number of heat-
transfer channels corresponding to the power of the test system.
As a result of the experimental work it has so far been found that:
1) The experimental data on heat transfer and temperature distribution agree satisfactorily with
computed data;
2) stable flow hydrodynamics in the Field tubes is obtained under a variety of operating conditions;
3) the separating systems of the evaporator model work reliably with respect to their output of
steam of the required quality for two methods of extracting the steam-water mixture, namely, under the
water level and directly into the steam space;
4) the individual components of the structure (the fitting of the tubes into the tube panels, the
sealing, the welds, and so forth) operate satisfactorily. At present the models have operated for more
than 2000h, and experiments are continuing.
AUXILIARY SYSTEMS
The heat from the BN-350 reactor is eliminated or discharged by means of six parallel loops, of
which five operate continuously and the sixth is held in reserve. Each loop of the first circuit has in-
dependent feed lines to the reactor and may be cut off from the rest of the system by slide valves.
The necessity and desirability of using a cut-off system is determined mainly by two considerations:
first, the possibility of cutting out the loop and running off the sodium in it in case of any fault, and,
secondly, the fact that there is then no need to enclose the whole primary circuit in a protective sheath
in case of a break in the walls of the structure or the conduit pipes and tubes.
Only the body of the reactor and part of the piping (up to the slide valves) are enclosed in a
casing filled with inert gas. Filling the space between the reactor body and casing with sodium does
not lead to any break in the flow of circulating sodium or overheating of the core.
Sealing of the coupling rod of the principal slide valves is effected by means of solidified sodium
cooled by a eutectic sodium-potassium alloy.
A characteristic feature of the construction of the slide valves is an arrangement by which their
working components may be extracted for repair or replacement by remote control. This operation does
not therefore necessitate cutting the conduits of the first circuit or going into the room in which it is
situated; the operation may even by carried out without draining the sodium from the circuits, since the
two slide valves are positioned approximately at the level of the upper part of the reactor. Access to
the demountable joints is facilitated by built-in biological shielding as in the pump and intermediate
heat exchanger.
The efficiency of the installation as a whole is ensured by a number of auxiliary systems. The
most important of the auxiliary molten-metal systems include a system for purifying the sodium of the
first and second circuits and indicating the oxide content, overflow tanks for the first and second circuits,
and a system for preparing the coolant.
The filtration and oxide-indicating systems serve to determine the quantitiative sodium-oxide
content in the coolant of the first and second circuits and also to purify the latter.
In the first circuit there are six cold traps. The number of working traps will depend on the degree
of contamination of the sodium. As a rule, one or two traps are connected simultaneously; the trap-cooling
system, however, is designed for four. In addition to this, two oxide indicators (of the plug-gage type)
are provided; the sodium in these in air-cooled.
Each loop of the second circuit has its own independent system, including a cold trap and indicator.
One cold trap is calculated for a sodium flow of 10 m3/h. The circuit traps are identical in construction
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Ate
Ala MO
Fig. 6. Cold trap
of the first cir- The overflow tanks of the second circuit (four tanks at 50 m3 each) are
cuit. 1) Bypass; designed for the simultaneous overflow of any two loops out of the six. The first
2) cast-iron and second circuits are filled from the overflow tanks by means of linear electro-
shield; 3) ther- magnetic pumps. The overflow of sodium from the circuits is free.
mal insulation; Means are provided in the BN-350 reactor for facilitating the repair and
4)filling(chips ); replacement of the sodium equipment of the principal circuits. The removable
5)regenerator; parts of the pumps, the heat-exchanger pipe beds, and the working parts of the
6)NaK-contain- principal slide valves are taken out of the circuit into pressurized vessels filled
ing sleeve; with an inert atmosphere. The pressurized vessels enable equipment to be
7)NaK-contain- replaced without draining the sodium from the circuit. A special sluice valve
ing coil. prevents the inner cavity of the circuit from coming into contact with the
atmosphere in this process. The same pressurized equipment is used to take
components into the washing system, in which any units taken from the circuit may be washed free from
residual sodium (with water and steam), and if necessary treated with deactivating solutions. After
such washing, the components are taken to the repair section.
(Fig. 6) and constitute vertical cylindrical vessels about 6m high and lm in
diameter. These are placed in special electric furnaces and all feed lines to them
are placed at the top. The first-circuit traps with their furnaces are arranged in
a concrete shield. From above, the traps are closed with a layer of cast iron,
ensuring access to the tubes should replacement be required.
The special sodium-potassium system carrying heat away from the cold
traps includes two electromagnetic pumps rated at 150m3/h each and two air heat-
exchangers. No reserve is provided in this system, and if any component of the
system goes out of order some of the traps will be cut off.
An analogous but independent sodium-potassium system is provided for
cooling the seals of the fittings and pumps. In this case, continuous trouble-free
cooling is important, and 100% reserve equipment is therefore provided.
The overflow tanks of the first circuit (10 tanks at 50m3 each) are designed
for the overflow of sodium from the whole circuit. The tanks are connected in
pairs. Each pair is placed in a separate box. In addition to this, in each box are
two similar tanks constantly connected to the gas cavity of the reactor; thanks to
these, the fluctuations of gas pressure in the reactor on changing the volume or
temperature of the sodium are kept within tolerable limits.
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ROLE OF CONDENSATE DECONTAMINATION IN
SINGLE CIRCUIT ATOMIC POWER STATIONS
T. Kh. Margulova UDC 621. 039. 517.6.
It is shown that the principal impurities in the supply water of single-circuit atomic-
power stations (APS) are corrosion products. In view of the high solubility of these im-
purities in saturated steam, the efficiency of their removal with the scavenging water is
relatively low, and decontamination of the whole condensate in ion-exchange filters be-
comes necessary. This condensate decontamination also ensures continuous deactivation
of the condensate-supply tract and frees the circuit from hardness-producing salts passing
into the condenser as a result of indrafts of the cooling water together with the corrosion
of the condenser tubes. Of no small importance is the protective effect of condensate decon-
tamination in any possible emergencies which may develop. Under condensate-decontam-
ination conditions, the filtration velocities may be relatively high, and this demands filters
of small dimensions.
The supply water for the reactors of single circuit APS comprises the condensate with the addition
of desalinated water. Under these conditions the principal impurities are oxides formed in the circuit
as a result of the corrosion of the structural materials. Also of no small importance are the hardness-
producing salts arising from indrafts of cooling water in the condensers. In order to keep the concen-
tration of these impurities at a level ensuring reliable operation of the active zone of the reactor, it is
of prime importance to organize the water system in such a way that corrosion and indraft in the con-
densers may be reduced to a minimum. However, in view of the impossibility of stopping impurities
from reaching the circuit altogether (at all events, after prolonged service), suitable means of with-
drawing them from the circuit must be provided all the same. One such method is scavenging the
circuit. For a single-circuit APS, this means the continuous removal of a proportion of the water
(usually 1 to 2% but in rare cases 4%) to the purifying plant. However, analysis of the behavior of
individual impurities in the technological circuit of the APS and an estimate of their acceptable concen-
trations leads to the conclusion that the scavenging method by itself is insufficient. For single-circuit
APS this method must be supplemented by ion-exchange condensate decontamination for a 100% flow of
condensate. Reasons for this requirement are set out below.
BEHAVIOR OF THE OXIDES OF CONSTRUCTION
MATERIALS IN THE CIRCUIT
It has been frequently noted in the boilers of ordinary thermal power stations that there is a great
tendency for corrosion products to be carried away with the vapor rather than to be condensed in the
scavenging water. An analogous situation occurs in single-circuit APS. Thus it has been pointed out,
in connection with the water system of the Dresden APS, that scavenging the reactor only removes 20%
of the iron oxides entering with the supply water. This means that a large proportion of the iron is
carried out of the reactor with the saturated vapor. A large number of papers published over the past
ten years by 0. I. Martynova, D. G. Tskhvirashvili, and others, under the direction of Academician
M. A. Styrikovich, on the solubility of various substances in saturated steam enable us to estimate the
quantities of impurities passing into the steam. Figure 1 shows the so-called distribution ratio K as a
function of the ratio of the densities of the water and the steam (pw/ps) for different impurities in the
water, i.e., the ratio of the amounts of dissolved substances in the saturated steam and the boiler water.
The behavior of the iron oxides is characterized by data for magnetite. It follows from Fig.1 that the
solubility of magnetite in steam is much greater than that of the other impurities, and it is considerable
even at low pressures. At the same time, the solubility of magnetite is less dependent on pressure
Translated from Atomnaya Energiya, Vol. 22, No. 1, pp. 19-23, January, 1967. Original
article submitted June 14, 1966.
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10`2
10-4
than that of any of the other impurities. At a pressure of
70 abs. atm. the value of K for magnetite is about 10%,
i. e., it considerably exceeds the ordinary scavenging
factors for the reactors of single-circuit APS.
The balance of any impurities for the steam-gener-
ating plant is
IV
'Vt1 1
1111
al
MI
IC
I
WI
u 0
Co0 0344e
Wel
he
10-5 - (100 p) S.W.= (K p) S sc. w (1)
4 10 40 100 400 1000 PW /Ps
220 160 100 60 30 15 7 3
I I' , ' Nabs. atm.
.224 200 120 BO 40 20 10 5
Fig. 1. Graph of distribution ratio of var-
ious impurities in the circuit water.
where p is the scavenging factor in % and Ss. w. and
Sse.w. are the concentrations of the impurity in the supply
and scavenging water respectively.
Strictly speaking, for corrosion-product calculations,
Eq. (1) should contain two or more terms; on the left-
hand side there should be a term allowing for the arrival
of oxides as a result of the corrosion of the construction materials in the reactor, and on the right-hand
side there should be a term allowing for the loss of corrosion products associated with deposition inside
the reactor. For a single-circuit APS, however, these terms are small in comparison with the principal
terms in Eq. (1), and may therefore be neglected, especially in view of the fact that they are of similar
magnitude and enter into opposite sides of the equation.
If we take the quantity of impurity carried in with the supply water as 100%, then the amount of
this impurity carried away with the scavenging water is
P -L SSC ? 100%;
100+p
and with the dry saturated steam
Ssc
100 p
The ratio of the impurities carried away by the scavenging water and by the saturated steam
depends on the scavenging factor and K. The scavenging factor, however, varies very little, while the
distribution ratios differ by an order of magnitude for different impurities (see Fig. 1). Hence for
substances with a large value of K scavenging may not be an effective means of eliminating impurities.
In order to illustrate this, Fig. 2 shows the ratio of the amounts of dissolved impurities carried away
with the steam and the scavenging water for p = 1% and p = 2% on varying the distribution ratio K from
0 tO 20%. It follows from Fig. 2 that , if K = p, as much impurity passes off with the steam as with the
scavenging water. If K< p, then scavenging is the principle means of removing impurities. If, however,
St%
90
80
70
60
50
40
30
20
to
0
-
K Ssc\
\
K Ssc \
100?p-ss.w\
_
\\.\\100+p-ss.w\
):
\
-
.
-
_
p Ssc
. S
,forp: s ,s . v
/100/+pv?Ss. .1 /
0 5 10 15K
a
0 5 153 15 K,Y
Fig. 2. Ratio of the amounts of dis-
solved impurities carried away
with the steam and the scavenging
water for p = 1% (a) and p = 2%
(b) as a function of K.
22
K> p, and especially if K>>p, then the impurity in question
passes off principally with the saturated steam, and increasing
(e.g., doubling) the scavenging factor makes comparatively
little difference in the amount of the impurity removed from
the circuit with the scavenging water. If as before we take a
K of about 10% for Fe304 at 70 abs. atm., then for p = 2%
only 18% of the impurity passes off with the water, and the
other 82% remains in the steam! This means that, in order
to secure efficient elimination of the corrosion products from
the circuit (these products being in the truly dissolved state),
the whole condensate flow must be treated (condensate
decontamination must be calculatedfor a 100% steam rating).
The solubility of the oxides of other construction materials
and individual metals composing the alloys employed has been
studied less extensively. However, existing data suggests
that cobalt and zirconium oxides are carried out as well as
silicon okides. Hence the effective removal of these from the
circuit also requires supplementing the reactor scavenging
operation with 100% condensate decontamination, especially
when we consider that cobalt and zirconium (and to a lesser
extent iron) are carriers of activity under single-circuit
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APS conditions. Hence the removal of these elements from the part of the circuit in which the vapor
is replaced by water is extremely important from the point of view of the continuous deactivation of the
whole succeeding tract and that of ensuring its accessibility for use and repair.
The treatment of 100% of the condensate flow in ion-exchange filters does not eliminate the
necessity of continuously scavenging the APC circuit. After condensate decontamination, the concen-
tration of iron oxides in the supply water will rise again owing to the corrosion of the condensate-supply
tract and may exceed the values corresponding to the truly dissolved state, so that a corrosion scum
appears in the water. This is all the more likely in view of the fact that the solubility of iron oxides in
water falls as temperature rises. The effective removal of this iron oxide scum, dangerous from the
point of view of its possible "scaling-on" to the fuel-element cans, is only possible by means of
scavenging water, and this constitutes the main purpose of continuous scavenging in the reactors of
single-circuit APS.
INDRAFTS OF THE COOLING WATER IN THE CONDENSERS AND
COMBATING THEM
The causes of indrafts of the cooling water may be of a technological character (leaky tube rolling,
technological defects in the tube material), but may also arise in the course of use (failure of vacuum-
tightness at the rolling points as a result of vibrations, corrosion cracking in the tube material). These
factors mean that we cannot count on the creation of a condenser free from such indrafts. The smallest
value of indraft guaranteed by the factories is q = 0.005% of the flow of steam through the condenser.
For a powerful condenser with tens of thousands of tubes and 900 tons/h of steam passing through them,
this corresponds to a transferred flow of 45 liters/h of cooling water. If we consider that it is almost
impossible, with existing test methods, to observe such an indraft, so that it is very hard to discover
the points of indraft, and the reactor has to be shut down or its power sharply reduced in order to remove
an inaccessible indraft, it' becomes clear how important it is to take precautions against indrafts and
to eliminate their consequences. The first problem is solved by a number of constructional measures
and the second by desalinating part or all of the condensate flow.
The constructural measures include: 1) use of corrosion-resistant alloys; 2) use of thick-walled
tubes; 3) setting up of double tube panels; 4) setting up of the so-called salt compartments in regions
near the tube panels and desalination of the condensate passing through these spaces (30 to 40% of the
total flow); 5) smearing the rolling points with sealing pastes of the liquid Nairit ( = Neoprene) type.
Thermal-power experience shows that a combination of the first and last measures is the most
promising. The setting up of double tube panels complicates the manufacture and repair of the con-
densers and only removes the effects of indrafts at the rolling points. The same may be said of salt
compartments. A study of the condensate quality in a condenser with salt compartments in the Lugansk
Thermal Power Station (in pg/kg sodium) give the following results:
Condensate of salt compartments (flow 30 to 40%) after ion-exchange filters 5 to 7
Main flow of condensate (60 to 70% ) 65 to 70
Mixture of main condensate flow and desalinated condensate of the salt
compartments 50 to 60
Hence this method also fails to give a very high quality of condensate.
Considering the extremely well-developed surface of the tubes in condensers, it should be pointed
out that an indraft associated with the corrosion of the tube material is entirely commensurate with an
indraft at the rollingpoints, or may indeed exceed this, as shown by experimental results.
Regarding the corrosion of brass condenser tubes in the Melekesse single-circuit APS, there is
a continuous flow of copper and zinc ions (associated with the dezincification of the brass) into the
condensate. Experience in the use of double tube panels in this APS also shows that the removal of the
effects of indraft at the rolling points cannot entirely eliminate the deleterious influence of indrafts.
All this makes desalination of the condensate of prime importance. Considerations of economy
alone would suggest partial (rather than 100%) desalination of the condensate in regions near the rolling
points (salt compartments). The flow of condensate, however, is still large, and this complicates the
assembly of the plant and fails to reduce the dimensions of the system. It is therefore better to change
over to 100% desalination of the condensate with increased filtration velocities. Thus for a condenser
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100
90
80
70
.x
60
er 50
u
40
_c ?,,) 3030
20
10
100
90
80
iao
x 70
.,: 60
a)
, 50
ts3
40
v)
m g-
/kg 20
/kg
10
g-equiv./kg
Stlc = 12p g -
equiv./ kg
he = 25?
equiv.
c =12 ii g-equiv.
with a steam flow of 900 tons/h, at filtration
velocities of 30 m/h, the filter diameter equals
6.2m, while for filtration velocities of 120m/h
(quite acceptable for the condensate) the filter
diameters are only 3,1m. The indraft of
cooling water in the condenser is also a source
of silica, chlorine ions, and hardness-pro-
ducing salts.
Limitation of the concentration of silica
is
superheated
only necessary when using
steam at high temperatures and pressures.
Inadmissible
of chlorine ions
concentrations
arise in the condensate when the indraft in the
ch 5 0 ch 5 , 10
'cool 'cool mg -equiv. / kg
mg-equiv. /kg condenser leads to inadmissible concentrations
a b of hardness-producing salts. Hence the in-
fluence of indrafts of cooling water on the
Fig. 3. Hardness of the water in the circuit as a func- water system of the reactor of a single-cir-
tion of the indraft in the condenser; a) p = 1%; b) p = cult APS is only a consequence of the influence
2%. of the hardness-producing salts. Heat-exchange
conditions without either scaling or scum
formation must be ensured in the reactor.
There can thus be no talk of phosphating the reactor water, i. e, , the water system must be correction-
free. Thus normalization and testing of the water system should be based on the hardness of the
scavenging water of the reactor. It follows from Fig. 1 that we may neglect the solubility of the salts
in the steam up to extremely high pressure (K =? 0), Hence scavenging is an effective method of
removing hardness-producing salts from the circuit (see Fig. 2), The balance of impurities for hard-
ness-producing salts is simpler:
(100 + p) S
The impurity concentration of the supply water is given by the expression
S s. w = S cool,
where Scool is the impurity concentration in the cooling water of the condenser,
(2)
(3)
Figure 3 shows the results of calculating the hardness of the water in a reactor as a function of the
adinissible degrees of indraft in the condenser and scavenging of the reactor. The hardness of the
cooling water is taken as the mean value for river water; desalination of the condensate is not carried
out. Figure 3 also shows the admissible hardness of the water in the reactor corresponding to scale-
free operation (12 pg-equiv./kg for constant use and 25 pg-equiv./kg for short term use). It follows
from the figure that it is only permissible to omit desalination of the condensate (at any rate for cooling
water with a hardness up to 100/4-equiv./kg) for indrafts of the order of 0,001% in the condenser,
which is certainly an unrealistic value for prolonged service, When the indrafts are 0,005% (even more
if they are 0.01% or over) desalination of the condensate is essential.
Considering that it is impossible to guarantee that indraft should only at the rolling points, and
that it probably arises at arbitrary points in the tubes (for example, slight corrosion cracks), we
must be wary of desalinating only part of the flow of condensate. We must remember futhermore that
the purity of the condensate is only tested periodically, and that between samplings there may be an
increase in the indraft, not large enough to be reflected in the degree of vacuum, but dangerous from the
point of view of reliable reactor operation. For example, an indraft of 0.05% is regarded as being the
upper admissible limit from the thermotechnical point of view, but as Fig. 3 shows it is quite unaccept-
able for ensuring reliable operation of the reactor water system. This means that condensate decon-
tamination with 100% flow of condensate fulfils yet another important function in protecting the reactor
from possible emergency situations associated with damage to the condenser tubes.
Thus we may conclude from the present discussion that for single-circuit APS the setting up of
ion-exchange filters for the total quantity of condensate is absolutely essential. This: 1) removes iron
oxides and the oxides of other construction materials from the coolant; 2) ensures proper accessibility
of the equipment of the condensate-supply tract; 3) removes hardness-producing salts arising from the
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indraft of cooling water in the condenser and hence enables the scavenging of the reactor to be reduced
without danger of scale deposition; 4) frees the condensate from copper and its oxides and also certain
other metals (e.g., zinc) arising in the circuit as a result of the corrosion of the condenser tubes, and
protects the reactor from possible emergency situations associated with condenser-tube damage.
The main purpose of scavenging the reactor of a single-circuit APS with 100% condensate decon-
tamination is the removal of corrosion scum and the maintenance of the hardness of the reactor water
at an acceptable level. In view of this the degree of scavenging may be somewhat reduced, thus
achieving increased economy in the running of the installation.
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Declassified and Approved For Release 2013/03/18: CIA-RDP10-02196R000700050001-2
STUDY OF THE ZONES OF DAMAGE CAUSED BY
FISSION FRAGMENTS OF HEAVY NUCLEI
V. K. Gorshkov, L. N. LTvov, UDC 621.039.553;546.799.6
and P. A. Petrov
This study is based on the well-known anomalous fall in the evaporation rate of thin
sources containing the isotope CM244. The anomaly is apparently due to local surface
damage induced by fission fragments. The mean diameter of the local damage zones de-
pends on the pressure of the medium containing the source; it lies between 0,1 and 1 ?
The irradiation of a solid by fission fragments of heavy nuclei produces local damage both inside
the solid and on its surface. This is confirmed by electron-microscope examination of single crystals
and polycrystalline material [1-3]. In order to explain the nature of this interaction, experimental
measurement of the dimensions of the damaged zones as a function of the surrounding conditions is of
interest.
In the present investigation, the zones of surface damage were studied by measuring the evaporation
rate of atoms and molecules from the surface of a solid under the influence of fission fragments [4, 5].
It was found in [6] that thin sources (thickness less than 1? ) containing spontaneously evaporating
isotopes of curium evaporated predominantly wider the influence of the fission fragments along the surface
of the source. Evaporation occurred from a region of relatively small radius (about 100 A) around the
track, the number of evaporated atoms per fragment being independent of the substance. Hence the
evaporation should only be determined by the relief of the source surface. In other words, evaporation
will be the greater, the more even the surface over the path of the fragment. Hence the character and
extent of the surface damage induced by fission fragments may be judged from the variation in the
evaporation rate.
ARRANGEMENT OF THE EXPERIMENTS
In all, five sources of different strengths (see table) consisting of a mixture of CM244 and certain
rare-earth elements were studied. The sources were prepared by evaporating an acetone-alcohol
solution of the nitrates of the mixture in question and cellulose (photographic plate dissolved in amyl acetate),
deposited on aluminum substrates, with subsequent annealing at about 500?C. This gave strong layers
less than 0.1j thick, which were almost unaltered on treatment with alcohol-moistened pads. The area
of the active layer for all the sources was 0.12 cm2, and the uniformity of the curium distribution was
5 to 8%.
Relative Strengths of Different
Sources
Number of source
Relative strength of
source
1
2
8.0
3
1.9
4
1.0
5
0.58
Note. By relative strength of the source
we mean the number of fragments emitted
from its surface per unit time.
We studied the time variation of the evaporation rate of
the sources in vacuum (pressure of the order of 102 mmHg),
at atmospheric pressure, and also under the influence of
fission fragments from an additional source. Some time after
preparation, all the sources (except No. 2) were fixed in a
special apparatus for measuring the degree of evaporation
(Fig. 1) and placed in a vacuum chamber. The relative number
of evaporated atoms was determined from the a-activity (due
to the a-decay of the Cm244) of the collectors, which were
periodically replaced.
In the experiment at atmospheric pressure, after sources
Nos. 3 and 4 had been taken out of the apparatus for a consider-
able time, it was difficult to measure the evaporation rate,
owing to the low energy of the evaporated atoms; hence the
Translated from Atomnaya Energiya, Vol. 22, No. 1, pp. 24-27, January, 1967. Original
article submitted June 16, 1966.
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ill'a'
II
lir AM
ii
8 111?1111MW N
:.'11.111111.111. ?&%. it
Fig. 1
Fig. 2
Fig. 1. Apparatus for measuring the evaporation of the sources: 1) base;2)cen-
tering rod; 3) clamping plate; 4) source substrate; 5) active layer; 6) collector
for evaporated atoms (aluminum foil 0.1mm thick); 7) disc with standard ap-
erture; 8) separating spacers.
Fig. 2. Layout of experiment involving the supplementary irradiation of source
No.1: 1) supplementary source; 2) A1203 film; 3) source No.1; 4) active layers
of sources.
change in the evaporation rate was deduced on the basis of measurements carried out in a vacuum before
and after the experiment.
In the experiments involving prolonged irradiation of the source (Fig. 2) an A1203 film served to
prevent the evaporated atoms from the supplementary source from striking the surface of source No.1.
The relative strengths (see table) were measured by counting the number of fragments revealing
traces on the surface of the glass after etching in hydrofluoric acid [71. Periodic measurements showed
that the strength remained constant during the whole experiment; this was because of the comparatively
long half life of CM244 (T1/2 = 17.6 years).
RESULTS
The time variation in the evaporation rate of sources Nos. 3 and 4 is shown by the curves in Fig. 3:
AB, CD, EF, HI, KL, MN, PQ, correspond to vacuum measurements and DE, LM to measurements
500
400
g 300
RMkR' ? chain termination.
Thus, two radicals are consumed for the formation of a molecule of an HB product consisting of
n = k + 2 units: one to initiate the chain, the other for its termination.
As can be seen from the data cited in the table, the ratio [Grhici[Gr]sol is 1-4,i.e., considering
the extremely approximate nature of the calculation, in practice
[Cr] [GrIsoi.
liq
However, the fact that for all the cases cited [Grliie [Gr]sol evidently is an indication of the contribution
of nonradical processes to the formation of the HB products. It may be that dimer products are formed
both in the recombination of radicals, and in reactions of excited molecules.
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0, vi> 0, v2 0, (1) (1)
where X = 0 for v > 0; v = 0 and v2 = 0 for 0 Lstus 110. The function 0 must be continuous and satisfy the
? ),.?7," Op
equation ?p = - x
Analysis of condition (1) leads to the following result. If G9 (z) decreases rapidly enough, then
W = (H) , and at the reactor coolant outlet there must exist a region with u = 0 (in this case the
conditions of transversality for 0 must be formulated in a special way so that 3(H)50.0 If co (z) is con-
stant or falls off sufficiently slowly, for example, maxi(/' (z) co (z) (etH - 1 - tH)-1, the reactor is
optimum when the regions 0 sz hi and h2:sz:sH contain the maximum allowable concentration of
uranium u = u0 (h1> H - h2) while the central zone has a value given by the heat engineering limitation,
i. e., v = 0. If (pis constant the ratio of the maximum power to the power corresponding to a uniform
distribution of uranium lies within the limits 0 -(Wmax/Wuni) -.5- 22-r. depending on the values of t and 110.
*Cf. L. S. Pontryagin et al. ',Mathematical Theory of Optimum Processes," Moscow, Fizmatgiz,
1961, (Theorem 23).
Translated from Atomnaya Energiya, Vol. 22, No, 1, p. 40, January, 1967, Original article
submitted March 31, 1966, abstract October 3, 1966.
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Declassified and Approved For Release 2013/03/18 : CIA-RDP10-02196R000700050001-2
A CORRECTION TO THE SPHERICAL-HARMONICS METHOD
FOR SOLVING THE TRANSPORT EQUATION
V. A. Zharkov, V. P. Terentlev, UDC 621. 039. 50
and T. P. Zorina
A solution of the one-velocity transport equation in spherical geometry by a modification of the
spherical-harmonics method is discussed. Even in the lower pne approximations the accuracy is
appreciably greater than in the ordinary PN approximation. The results may be used to solve problems
related to the behavior of localized absorbers in neutron fields.
The essence of the modification consists in taking into account the effects of the higher harmonics
in the exapansion of the solution in Legendre polynominals - the harmonics which are discarded in a
given PN approximation. A correction factor is introduced based on the use of a fictitious source of
the form
Fict
UN (r, = IN P N+1 (P),
2.0
10
1.5
08
\
.?4
1.0
0.6
s
8
a
0.5
,-9
24
0
-010
0.2
_Jr
OS 0 05 ji
0
Fig. 1
1
2
3
____..,..
-' --
..- -.,--..---
--.1'-
...-,...
,.......-?---
_.-5-
_. ..-?!'-'..
3
1
2
Fig. 2
3 4 (2-; )-/-x(2)R
Fig. 1. The angular distribution of the neutron flux 4 (R,?) at the surface of a sphere
placed in graphite (4 is the value of the unperturbed neutron flux; negative values
of /.4 correspond to directions into the sphere) --- -ordinary Pi approximation;
-? -.ordinary P3 approximation; ? ? modified P1 approximation (on the scale used
it is identical with the curve obtained in the modified P3 approximation).
Fig. 2. Expansion coefficients of the function 4.(R,?) in a power series for a spherical
absorber placed in graphite:
t (, -1)
-aFR
(13
;
(13 (R, -1)
4a
I
020
(R'
2'4,1)- 1 cm
(13 (R , -1)
;
2- z
=3cm -1, 3-
-_ oo;
X 1"3a (?.+1tr)?
Subscript (1) refers to the absorber and subscript (2) to the surrounding medium;
Za and Ztr are respectively the macroscopic absorption and transport cross sections.
Translated from Atomnaya Energiya, Vol. 22, No. 1, pp, 40 - 41, January, 1967, Original
article submitted April 11, 1966, abstract October 15, 1966.
45
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Declassified and Approved For Release 2013/03/18: CIA-RDP10-02196R000700050001-2
where r is the distance from the center of symmetry, II the cosine of the angle between the direction from
the center of symmetry and the direction of motion of the neutron:
N?1 d N (N +1) (PN (r)
f N (r) 2 dr TAT ?ri? 2 r
where yoN(r) is the Nth expansion coefficient of the angular flux in terms of Legendre polynominals
determined by solving the transport equation in the ordinary PN approximation, and PN+1 is the
Legendre polynominal of order N + 1.
A solution is investigated which is a superposition of an ordinary solution in the PN approximation
and of a solution corresponding to the fictitious source. The latter is given by the relation
r) r?-1 dl
(I) A (r, = exp [? Et (V r2 y2? 2ruP) IN (V r2 +12 ?2r10 PN+1 ( V r2 12 -2r1p,
0 0
where Zt is the total macroscopic cross section;
Angular distributions of the neutron flux for spherical absorbers having various absorption and
scattering cross sections placed in various diffusion media were calculated on a BESM - 2 computer.
It was found that the error in the angular distribution of the neutron flux at the surface of an absorber
amounted to a few percent in the modified P1 - approximation, and that the calculational procedure was
rather simple and did not require a large amount of machine time.
Figure 1 shows the angular distribution of the neutron flux at the surface of a sphere of radius 1 cm
with Zt = co placed in graphite.
An approximate analytic expression, in the form of a Taylor series in powers of ? + 1 about the
point 43(R, -1), for the inwardly directed angular neutron flux do (R,p) on the surface of an absorber is
presented and discussed.
Figure 2 shows the coefficients in the expansion of the angular neutron flux in a power series for a
spherical specimen in graphite.
The modification of the spherical-harmonics method developed in this article may also be used
for systems with any geometry.
ACTIVATION OF SPHERICAL SPECIMENS IN A
THERMAL NEUTRON FIELD
V. A. Zharkov and V. P. Terentev UDC 539. 172.4
The problem of neutron-induced activity has many important practical applications: the production
of radioactive isotopes in nuclear reactors, activation analysis, the measurement of neutron fluxes,
etc. The main difficulty in calculating the activity of specimens irradiated in a diffusion medium has
to do with the description of the perturbation of the neutron flux incident on the specimen. The theory
of neutron activation for foils, which correctly takes into account the effect of the perturbation of the
flux, has been worked out in considerable detail, see e.g., [1]. However, an analogous theory for
"three-dimensional" specimens such as spheres or cylinders, while of great practical interest, cannot
be regarded as complete.
Translated from Atomnaya Energiya, Vol. 22, No. 1, pp. 41-42, January, 1967. Original
article submitted April 11, 1966; abstract November 12, 1966.
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Declassified and Approved For Release 2013/03/18: CIA-RDP10-02196R000700050001-2
t-p
1.5
1.0
0.5
05 1.0 1.5 20 R, cm
Fig. 1. The quantity p/(1-p) as a func-
tion of the radius of the specimen, R,
for water. ) analytic expression;
?) Monte-Carlo method.
1/[1+0 - P)]),P
emitted isotropically from the specimen will return to the surface of the sphere after a series of colli-
sions in the diffusion medium. The probability of back-scattering was calculated by the Monte-Carlo
method for several directions of emission from the surfaces of spherical specimens of various radii
irradiated in water. These data gave the probability, p, for isotropic emission. Values of the function
if which do not depend on the properties of the diffusion medium have been tabulated for specimens with
absorption cross sections obeying the 1/v law. All numerical calculations were performed on a BESM -
2 computer.
A combination of the modified spherical-harmonics method and the back-scattering probability
method is used to obtain an analytic expression for the function p1(1 - p) in ordinary water, heavy
4 water, and graphite. The values of p/(1 - p) calculated by the Monte-Carlo method and from the analytic
solution are in good agreement (cf. Fig. 1).
The buildup of activity with time for a specimen whose absorption cross section obeys the 1/v law
is also discussed.
Relations are obtained in the present article for cal-
culating the activity of three-dimensional specimens irrad-
iated by thermal neutrons, taking into account both the
effect of self-shielding and the effect of the perturbation of
the flux by the specimen: for example,a sphere. The effect
of the flux perturbation is described in terms of the proba-
bility of back-scattering, calculated by the Monte-Carlo
method, and also on the basis of a solution of the transport
equation using the modified spherical-harmonics method [2].
It is shown that the relation for the number of neutrons
captured per unit time, Q, by a three-dimensional specimen
irradiated by thermal neutrons in a diffusion medium may,
within a few percent, be written in the form
cps
Q TH,
where is the unpertubed neutron flux, S the surface area
of the specimen, if the probability, averaged over the
Maxwellian spectrum, of the absorption of neutrons in the
specimen for isotropic incidence, taking into account self-
shielding, and H the flux perturbation coefficient (H =
the probability of back-scattering, that is, the average probability that a neutron
LITERATURE CITED
1. R. Ritchie and H.? Eldridge, Nucl. Sci. and Engn. , 8, 300 (1960).
2. V. A. Zharkov, V. P. Terentlev, and T. P. Zorina, present issue, p. 45.
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Declassified and Approved For Release 2013/03/18: CIA-RDP10-02196R000700050001-2
GENERALIZATION OF THE ALBEDO METHOD
P. Wertesz UDC 621. 039. 51. 12
Albedo boundary conditions for a layer* are considered as integral operators of general form. The
kernels of these operators are Green functions for the transport equation, i.e., if (I)? (r, v, 52, vo, ac,)
in the layer (r?, r-) satisfy the transport equation with the boundary conditions
v, Q)= (v? v0) (5 (52?Q0), -? B052 > 0;
(I)? v, S2)=0, ?
Bo
where 7I.Bo
BoQ