THE SOVIET JOURNAL OF ATOMIC ENERGY VOL. 7 NO. 6
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THE SOVIET JOURNAL OF
Volume 7, No. 6
April, 1961
OMIC ENERGY
CONSULTANTS BUREAU
ATOMIla51
1-leprlisi
F'ROArk 741:SSANcl
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-o
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the latest Soviet techniques.'
CONTEMPORARY EQUIPMENT
for WORK with
RADIOACTIVE ISOTOPES
A comprehensive review of the Soviet methods and, tech-
nological used in the production of isotopes and
the preparation of labelled compounds fromthem. The shield-
ing and manipulative devices are described as well as illus-
trated in detail. It is an excellent -guide for all scientists
and technologists concerned with.radioactive isotopes.
CONTENTS
Some* technical and technological aspect? of the production
of isatopes and labeled compounds in the USSR.
INTRODUCTION
Development of remote handling methods in the radiochem-
ical laboratories- of. the Academy 'of Sciences, USSR.
Shielding and manipulative devices for work with radio-
'- activeisotope?:
INTRODUCTION
Development' of Shielding Techniques in
, ?Radioprepas9.tive Operations
Mechanical Holding Devices
Remote PneurnatiC Manipulators
Liquid Dispensers
Radiocheinical Hydroinanipulatorg?
Radiopreprative Pneumatic flydromanip-
ulators
CHAPTER I.
CHAPTER II.
CHAPTER III.
CHAPTER IV.
CHAPTER V.
CHAPTER VI.-
CHAPTER VII.
Toothed Mechanisms for Manipulative De-
vices
CHAPTER VIII. Non-Destructive Methods. of Amptile In-
,
sPection
CHAPTER IX. Some Decontamination Methods
CONCLUSION
durable paper 'covers 67 pages illus.. $15.00
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101
CONSULTANTS BUREAU ?
227 W. 17th ST., NEW YORK 11, N.Y.
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EDITORIAL BOARD OF
ATOMNAYA gNERGIYA
A. I. Alikhanov
A. A. Bochvar
N. A. DollezhaV
D. V. Efremov
V. S. Emel'yanov
V. S. Fursov
V. F. Kalinin
A. K. Krasin
A. V. Lebedinskii
A. I. Leipunskii
I. I. Novikov
(Editor-in-Chief)
B. V. Semenov
V. I. Veksler
A. P. Vinogradov
N. A. Vlasov
(Aasietant Editor)
A. P. Zefirov
THE SOVIET JOURNAL OF
ATOMIC ENERGY
A translation of ATOMNAY A ENERGIY A,
a publication of the Academy of Sciences of the USSR
(Russian Original Dated December, 1959)
Vol. 7, No. 6 April, 1961
CONTENTS
Design Principles and Basic Data of Betatron Facilities at the Moscow Transformer Works.
PAGE
RUSS.
PAGE
B. B. Gel'perin
969
509
Simulation of Control and Temperature Variation of Water Density in Intermediate-Neutron
Uranium-Water Reactors. V. B. Klimentov and V. M. Gryazev
977
519
Utilization of Natural Uranium in a Homogeneous Reactor. Vatslov Bartoshek
981
524
Determination of the Solubility of Metals in Lithium. Yu. F. Bychkov, A. N. Rozanov,
and V. B. Yakovleva
987
531
Identification Tables for Use in the Analysis of cx and 8 Activities. A. A. Lbov
and L. I. Serchenkov
993
537
Morphological Types of Industrial Uranium Deposits and Methods for their Prospecting.
D. Ya. Surazhskii
1003
539
LETTERS TO THE EDITOR
? External y -Radiation Dosage Due to Fallout of Several Fission Products. V.P. Shvedov,
G. V. Yakovleva, M. I. Zhilkina, and T. P. Makarova
1007
544
Calculation of the External y -Radiation Dosage Due to Fallout of Radioactive Fission
Products. L. I. Gedeonov, V. P. Shvedov, and G. V. Yakovleva
1008
545
The New Isotopes Sb112 and Sb"4 and the Identification of SbII5 and Sb115. I. B. Selinov,
Yu. A. Grits, Yu. P. Kushakevich, Yu, A. Bliodze, S. S. Vasil'ev, and T. N. Mikhaleva. .
1011
547
Stability of a Charged Beam in Storage Systems. A. A. Kolomenskii? and A. N. Lebedev. . . .
1013
549
The Albedo of)' Rays, and the Reflection Build-Up Factor. B. P. Bulatov and 0.I.Leip?nskii
1015
551
Application of Mass-Produced Scintillation Equipment in Radiometric Control of Boundaries
of Petroleum Product Mixtures in Piping. L. N. Posik
1016
553
Improved Deposition of Uranium and Thorium Layers by the Method of Atomization
in an Electrical Field. Yu. A. Selitskii
1019
554
About the Single-Stage Separation Coefficient of Lithium Isotopes by the Ion-Exchange
Method. G. M. Panchenkov, E. M. Kuznetsova, and 0. N. Kaznadzei
1021
556
Creep in Hot Rolled Uranium. G. Ya. Sergeev and A. M. Kaptel'tsev
1023
558
On the Parameters of a Reactor with Minimum Critical Loading. V. Ya. Pupko
and L. I. Ermakova
1025
560
NEWS OF SCIENCE AND TECHNOLOGY
Fourth International Conference on Ionization Phenomena in Gases. L. Kovrizhnykh
and N. Sobolev
1028
562
The IX International Radiological Congress. K. K. Aglintsev
1031
565
Annual subscription 75.00 .@ 1961 Consultants Bureau Enterprises,'Inc., 227 West 17th St., New York 11, N.Y.
Single issue 20.00 Note: The sale of photostatic copies of any portion of this copyright translation is expressly
Single article 12.50 prohibited by the copyright owners.
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CONTENTS (continued)
The Linde Approach to the Production of Heavy Water by Low-Temperature Distillation
PAGE
RUSS.
PAGE
of Hydrogen. K. Sakodynskii
1033
566
The Atomic Energy Section at Poland's Industrial Exhibit in Moscow. Yu. Koryakin
1034
567
A Trade Enterprise Unique in Its Own Way. Yu. Koryakin
1036
569
(Brief Communications
5711
BIBLIOGRAPHY
New Literature=
1038
572
INDEX FOR 1960
Tables of Contents for Volume 7
1041
Author Index
1053
NOTE
The Table of Contents lists all material that appears in Atomnaya nergiya. Those items
that originated in the English language are not included in the translation and are shown en-
closed in brackets. Whenever possible, the English-language source containing the omitted re-
ports will be given.
Consultants Bureau Enterprises, Inc.
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DESIGN PRINCIPLES AND BASIC DATA OF BETATRON
FACILITIES AT THE MOSCOW TRANSFORMER WORKS
B. B. Gel'perin
Translated from Atomnaya Energiya, Vol. 7, No. 6, pp. 509-518
December, 1959
Original article submitted February 14, 19591
The present article gives the principles underlying the design of betatron accelerator facilities for nondestructive
testing, medical, physical, and other research uses. The conditions under which azimuthal asymtnetry of the
betatron magnetic field may take shape, and methods for coping with it, are considered. The multiyoke electro-
magnet design for betatrons, developed at the MoscoW Transformer Works (MTZ), is described; this design confers
improved azimuthal homogeneity on the magnetic field. Data are also provided on specialized betatron designs
of the following types at MTZ: a stationary 4-yoke model with accelerated-electron energies from 20 to 50 Mev,
a rotating suspended-type betatron, 25 Mev, for medical purposes, a movable rotating 25 Mev model for nondestruc
tive testing, and a 15 Mev pendulum-type tilting betatron, for medical purposes.
Introduction
Betatrons are being employed in an increasing num-
ber of applications for research in the physics of the
atomic nucleus, in medicine (for therapy in malignant-
tumor cases), and in industry (for nondestructive testing),
etc.
The increasing use of betatrons in the national
economy has thrown new light on the need to develop I
not only stationary installations, but also those facilities
which can be moved or adjusted to a desired position:1
rotating and pendulum-type facilities, etc.
The principal requirement to be met by stationary
betatrons is reliability of output parameters (energy and
intensity of 5 - or y -radiation). A necessary factor in I
the design of movable betatrons must, in addition, meetsuch
requirements as minimized weight, size, and noise level.
It is obvious that the donut chambers in movable beta-
trons must also be sealed off.
Basic Requirements for Betatron Electro-
magnets
To obtain maximum radiation intensity, a high
degree of azimuthal homogeneity must characterize
the magnetic field established in the air gap of the elec-
tromagnet. The magnetic field of the betatron always
suffers from a certain azimuthal inhomogeneity in pracl-
tice, since the orbital path of the accelerated electionsl
will not be a circle, because of distortions in the mag-
netic-field homogeneity, but some form of a closed I
curve.
It is a familiar fact from betatron theory ? that the
deviation of a perturbed orbit from the ideal orbit xo I
is expressed by the relation
Co
xo hi
?
ro 12+n? 1 cos (10 +
t=i
where 1.0 is the radius of the ideal orbit; hi is the re-
lative magnitude of the 1 -th harmonic obtained by de-
composing the magnetic field in a Fourier series; a/ is
the phase of the 1 -th harmonic.
Let's consider in greater detail the reasons for the
azimuthal inhomogeneity of the field and measures for
coping with it. The field intensity H1 at a point (01, ro)
will differ from the intensity H2 at a point (0 2, ro) both
in amplitude and in phase. Let H1 = Hoi sin wt, and
H2 = H02 sin (wA+ .5), where H01 and H02 are the ampli-
tudes of the field intensities at points 01 and 02 and
6 is the phase shift. Since 6 is usually a small angle,
we have
112?Ht 6 _L. HO2 ( 1
Hi =tan cot H01
The magnitude oftanoau may be neglected, com-
pared to unity, since as a rule cot, >> 6 at the time of
injection. Then
rtan cot) ?
112 --HI 6 1112-1101
Hi ?tan cot ' Poi '
Accordingly, the inhomogeneity of the magnetic
field at two points may be broken down into two com-
ponents: phase inhomogeneity I
s=cot
-1102? Hot
and amplitude inhomogeneity: Va ? yei ?
The nature of these two components of field in-
homogeneity is different. Phase inhomogeneity is due
to the nonuniformity of active currents coupled to the
tubes of force of the magnetic field at different azi-
muths, i.e., it is due to the nonuniformity of energy
losses in the magnetic materials of the electromagnet.
*D. Bohm and L. Foldy, Phys. Rev. 70, 249 (1946).
969
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The amplitude inhomogeneity, on the other hand, is due
to the difference in the reluctance of the tubes. Since
the reluctance of the tubes is determined principally
by the reluctance of the air gaps and spacers between
components, y a is due to the difference in dimensions
of individual tubes of the field.
It is clear from Fig. 1 that yp is a vector perpendi-
cular to the field intensity Hoi, while ya is a vector
coinciding with it.
At the initiation of the acceleration cycle, while
6
wt is still small, y has a large value, since is
tan wt
practically 8-1/0. at the time of injection, whereas ya
is about 2-3/0. At the end of the acceleration cycle,
yp will be insignificant, its value tending to zero. The
time to combat field inhomogeneity is therefore prima-
rily at the beginning of the acceleration cycle, when
y p is large compared to the injection field. This pro-
blem is approached on the one hand by designing azi-
muthal symmetry into the electromagnet, to minimize
'natural' inhomogeneity, and on the other hand by set-
ting up a bank of coils to compensate for any "natural'
inhomogeneity on the part of the field.
An example of symmetrical design in the magnetic
circuit may be seen in the multiyoke design developed
at MTZ (a 4-yoke design is shown in Fig. 2). The en-
tire periphery of the pole piece is broken down into a
large number (some 200-250) of segments, each of
which is assembled from an identical number of steel
laminations forming a portion of the pole piece and the
yoke at the same time (Fig. 2a). The thicknesses of
these segments azimuthally are so consigned that the
pole is densely packed when all of the parts are assem-
bled in place, while the segmental parts forming the
yoke, also arranged radially, have a smaller stacking
factor. The yoke portions of all of these segments are
in turn broken down into m equal parts (4 parts in Fig.
2b), which are compressed to form m symmetrical
yokes, identical in design. They are identical, mag-
netically speaking, except for the fringe segments (at
Fig. 1. Diagram of
phase and amplitude
inhomogeneities of
the magnetic field.
970
the sides of the yokes), through which the fringing mag-
netic flux leaks. The shape of the curve for the azi-
muthal phase inhomogeneity distribution is found to be
a consistent one with characteristic humps corresponding
to the edges of the yokes. Figure 3 shows the approxi-
mate curve for the magnetic field distribution across
the gap of a 4-yoke electromagnet. The fourth harmonic
in the curve is the fundamental. However, its contri-
bution to the distortion is limited, since its amplitude
is divided by a factor less than the square of the har-
monic number (at n = 0.7 by 15.7). In Table 1, we
have the values for the harmonics of the curve, and
their contribution to the distortion of the orbit. The
'natural' azimuthal inhomogeneity of the magnetic
field is thus held at a minimum in multiyoke-type
magnets, because of symmetry in design.
We see a completely different pattern in the conven-
tional two-yoke design for the magnetic path. It is
clear from inspection of Fig. 4, for instance, that the
pole piece is in this case assembled from a radial array
of steel laminations, while the yokes and columns are
assembled from parallel-stacked steel laminations. It
Single
piece
Fig. 2. Diagram of 4-yoke design of magnetic leads
to betatron.
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TABLE 1
Harmonic Analysis of the Curve in Fig. 3
Number of harmonics
Amplitude
1
2
4
hi
hi
0,29
0,517
0,14
0,995
?0,435
0,141
0,0161
0,0635
12?n-1-1
is readily seen that the segments arranged closer to the
center will saturate more strongly (see area abed) than
segments farther out (see area efgh). Specific energy
losses in different segments of the yokes will not be the
same, for that reason. It is evident that the curve for
the azimuthal magnetic-field intensity distribution will
in that case exhibit a clearly defined second harmonic
(Fig. 5). Table 2 shows that the 'natural" yp will be
much larger in that case.
The compensation for ya is usually brought about
by equalizing the gaps in the magnet (by inserting ad-
ditional spacers, or reducing the thickness of existing
ones).
The phase inhomogeneity is offset by means of
coils, through which flows current shifted 90 in phase
to the principal magnetizing current of the magnet.
When these coils are properly positioned and connected
up, the first and second harmonics of the azimuthal
phase variation, of whatever magnitude, can be com-
pensated for. Higher-order harmonics need not be
cancelled out, as a rule. since their contribution to
distortion of the orbit is negligible. The compensation
circuit of the first harmonic in the four-yoke electro-
magnet design is shown in Fig. 6. In the two-yoke de-
sign, used in the betatron, the compensation coils are
TABLE 2
Harmonic Analysis of the Curve in Fig. 5
Number of harmonics
mplitude
1
2
3
6
0,23
3,0
0,064
2,25
h1
0,345
0,82
0,0074
0,144
12+n-1
wound around segments of the yokes and columns (the
medium and extreme segments), in corresponding
manner. The ventilation ducts provided in the yoke
columns are used for accomodating the compensation
coils. The compensation system remains the same as
described.
The advantage of this type of compensation system
is that the compensation current may be controlled by
the operator from a control console while the betatron
is in operation, and the magnetic field of the facility
is subject to control, to obtain peak y -radiation inten-
sity.
Design of Electromagnets in Stationary
and Movable Betatrons
The considerations mentioned above provide grounds
for the conclusion that a multiyoke design is in some
ways superior to the two-yoke design in betatron ap-
plications. The stationary betatron facilities built at
MTZ,,and designed for 20 Mev energy and higher, are
therefore based exclusively on the multiyoke design.
When magnetic field intensities are equal throughout
the air gap, the weight of multiyoke magnets shows
little difference from that of two-yoke magnets.
Min
?7
I .1,1.I,I,I
180 160140120100 80
it 1.1
60 40 20 0 340 320 30,0 280 260 240 220 200 160
Azimuth
Fig. 3. Azimuthal phase variation of the magnetic field across the gap M. a 4-yoke
electromagnet.
971
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Development work on movable betatrons demon-
strated the need to reduce greatly the weight of the
movable portion of the facility, i.e., the electromagnet.
As we know, the weight of a betatron electromagnet is
approximately proportional to the cube of the orbital
radius. For some specified energy of accelerated elec-
trons, the radius of the orbit may be reduced solely by
increasing the magnetic field strength at the orbit. In
addition to weight reduction, reduction in the radial
dimensions of the electromagnet air gap may be a-
chieved by reducing the radius of the orbit, since dis-
tortions of the orbit due to azimuthal field inhomo-
geneity are propUrtional to the radius of the orbit. The
accelerator donut chamber is therefore made more com-
pact and sturdier.
It was decided to employ cold-rolled steel in
movable betatrons, to increase the magnetic field
strength. The improved magnetic properties of this
steel permit the field strength in the electromagnet air
gap to be brought up to 5 kilo-oersteds, while only 3.3
kilo-oersteds are attained by the use of hot-rolled steel.
The orbital radius may accordingly be reduced by 330/0.
Fig. 4. Arrangement of steel laminations in a two-yoke
electromagnet.
However, cold-rolled steel shows greater anisotropy in
its magnetic properties. When the magnetic flux is
directed along the rolling direction of the metal, the
magnetic properties are excellent, but when the mag-
netic flux is directed at some angle, particularly Be
and 90', magnetic properties deteriorate abruptly.
Since the shape of the blank is punched from sheet
steel to form the pole pieces and yoke simultaneously
in multiyoke designs (Fig. 7), the magnetic flux will
proceed partially along the rolling direction (sections
1 and 2), partially at right angles to the rolling direc-
tion (section 3), and partially off at different angles
(sections 4 and 5). In that case, the improved magnetic
properties of the cold-folled steel will not be realized
in practice.
In the two-yoke design, the magnet yoke and core
may be assembled from metal cut only along the direc-
tion of rolling. The electromagnets used in movable
betatrons are therefore made from the cold-rolled steel
used in the two-yoke design.
Cooling Systems for Stationary and
Movable Betatrons
The length of time a betatron may be operated
depends on the field in which it is being used. In
physics research and training demonstration applica-
tions stationary betatrons are generally employed, and
the duty cycle is insignificant. Natural air coo' ling is
used in such betatrons. In chemistry and biology, sta-
tionary betatrons are also used, but a certain dose of
exposure is required here, so that the betatron duty cycle
may take on significant proportions. Some approach to
Min
1- 20
/9
?18
?17
?16
?15
?14
?13 ?
?12
?11
?10
?9
?8
jIIiliItlIil
180 160 140 120 100 80 60 40
5
4
3
2
ill 1 If I
20 0 340 320 300 280 260 240 220 200 180
Azimuth
Fig. 5. Azimuthal phase variation of the magnetic field across the gap of a two-yoke
electromagnet.
972
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artificial cooling must be resorted to in these cases.
Forced air cooling is employed as a rule.
Movable betatrons for medical applications and
flaw detection have large duty cycles. In medical
therapy, the duty factor is 60, and in flaw detection.
10C10. Forced-ventilation cooling arrangements are
needed for movable betatrons.
The parts subject to greatest heating are exposed
to the full force of the air blast: the inner bushing with its
high magnetic saturation, and coils having comparative-
ly high current density. In stationary betatrons, cooling
Fig. 6. Arrangement of compensation coils in a
four-yoke electromagnet.
Fig. 7. Arrangment of
segments in stock metal
for a four-yoke electro-
magnet, prior to
machining.
Fig. 8. Path of cooling air in electromagnet.
air is drawn by suction from the betatron hall and driven
through the electromagnet, to be discharged outside.
This direction of air flow protects the rooms where
people are working from contamination by radioactive
air. Figure 8 shows the path of air flow through the
electromagnet, which is used in stationary betatrons.
The fan for the stationary betatron is usually installed
In an underground room, to minimize fan noise in the
betatron hall.
In movable betatrons, the fans are installed within
the betatron enclosure. In this case, air from the beta-
tron gains admittance to the room housing the betatron
facility, thus putting a premium on good cross ventila-1
tion arrangements for the room. The speed of air flow
in the ventilation ducts of the betatron varies 5-20
meters/ sec. '
Choosing the Frequency for Betatron
Current Supply
In choosing the frequency for the current supplied
to the betatron, one must keep in mind that the corn-
Arrows indicate path of air flow
Flange for air
ducting
Grounded
sector
A cz,
Tapped
sector
Fig. 9. Stationary 4-yoke betatron, 20 Mev,
973
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Not less than
C".:?
Movable
carriage
Counterpoise
Betatron pilot wheel
,
Fig. 10. Ceiling-suspended rotary
Winch
/. /// ///:/:////2i//-24",;'12.'Z?-?;.2,--Z!="
Raising and
lowering controls
Detachable beam-
' position indicating
probes
974
Cooling fans
10
betatron, 25 Mev, for medical applications.
580
1070
Stuffing box
for supplying
cables
625
1000
to
target
6
Detachable beam-position
indicating probes
Pilot wheel for rotating
betatron, scale range ?45?
(2)
1560
1160
900
Fig. 11. Rotating 25 Mev betatron, for nondestructive testing.
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plexity of the arrangement is increased as the frequency
increases, with lessened reliability in performance and
a pronounced weight penalty with respect to the electro-
magnet, since the allowable flux density in the steel
decreases as the frequency is stepped up. On the other
hand, the intensity of the betatron radiation increases
as the frequency. Although a high radiation intensity
is required in movable betatrons, industrial line fre-
quency (50 cps) has been accepted for those applications,
requiring less complex equipment; all the more so
since the personnel who will be operating the facility
will not be very highly skilled technically in this area
(e.g.,doctors, nurses). In the case of stationary facilities,
where low weight is not such a prime consideration, the
equipment used may be more complicated and higher
weight may be tolerated, with an associated gain in
radiation intensity. MTZ has devised a stationary beta-
tron facility with supplied frequencies of 150, 300, and
600 cps. The high-frequency generator used is a
vacuum-tube oscillator or a static frequency tripler.
Parameters of MTZ Betatrons
The following basic betatron designs have been
evolved at MTZ:
1. The 20 Mev 4-yoke betatron (Fig. 9).
2. A ceiling-suspended rotating betatron for
medical purposes, 25 Mev (Fig. 10). The suspension
design makes it possible to position the magnet for both
horizontal irradiation (with the target placed at 1050
cm from the floor) and vertical irradiation. The de-
sign provides for 600 mm displacement vertically and
rotation of the electromagnet 120? about the horizontal
Cable car
Suspension
frame
Electromagnet
///////////////////////1//
Fig. 12. Crane-suspended 25 Mev betatron, for nondestructive testing.
tHt_
Roll axis
Controls for angle
of swinl/g
TaW_e siporting patienti
N.= 950
rL
-e-
Range ? swing
0-240
R 380
GLI
Fig. 13. Pendulum-type tillable betatron, 15 Mev, for medical applications.
975
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TABLE 3
Betatron Characteristics
Parameters
Betatron type
stationary,
4-yoke
(Fig. 9)
suspension,
rotating,
medical
(Fig. 10).
rotating
platform,
flaw de-
tection
(Fig. 11)
traveling-
crane-sus-
pension, flaw
detection
(Fig. 12)
pendulum-
type,
tillable,
medical
(Fig. 13)
stationary,
research
Energy of accelerated
electrons, Mev
20
10-25
10-25
10-25
6-15
10-50
Weight of active steel, kg
4750
1625
1625
1625
420
15,000
Weight of electromagnet, kg
6600
2700
2700
2700
650
18,500
' Weight of upper removable
part, kg
3000
1200
1200
1200
300
9000
Cooling system
Forced air
Forced
Forced
Forced
Forced
Forced air
circulation
air
air
air
air
circulation
Fan capacity,
meterss/hr
3000
2 x 500
2 x 500
2 x 500
600
5000
Current supplies
frequency, cps
150
50
50
50
50
50
Intensity of y radiation,
at 1 meter from target,
r/ min
100
30
30
30
4.5
200-250
Weight of lead shielding,
kg
?
585
?
?
400
?
Donut chamber ,
Evacuated
Sealed-off
Sealed-off
Sealed-off
Sealed-off
Evacuated
axis, with the beam position variable over a range +90?
to ?30? from the vertical. All of the vertical displace-
ments are controlled by a motor drive, and angular ad-
justments are controlled manually.
An array of diaphragms and equalizing filters
allows for the following irradiation dose fields at a dis-
tance of 1 meter from the target: round 40 and 80 mm
diameters and rectangular 100 x 150 rum, 80 x 100
mm, 60 x 80 mm, and 50 x 180 mm (the dose field
over the ranges can be stabilized to within 1050).
The betatron is lead-shielded on the patient's side.
The thickness of the lead shielding is based on the dose
rate of unused y radiation,not exceeding 0.5% of the
dose rate at the beam axis (with a filter in use).
3. A 25 Mev betatron for nondestructive testing;
one model on a rotating platform, another crane-sus-
pended. The rotating betatron (Fig. 11) can vary its
beam axis to 30? off horizontal. The crane-suspended
betatron (Fig. 12) can be moved to a distance of 20 meters
from the location of the controls, and the beam axis
can be lowered to 90? below or raised to 30? above the
horizontal.
976
4. A pendulum-type tillable betatron, 15 Mev, for
medical applications, (Fig. 13). The betatron electro-
magnet may be swung through any angle to 210?. This
provides a maximum dose of exposure at the center of
the tilt excursion (at the tumor), with a much smaller
dose rate at the surface of the healthy skin (at the
points where the beam enters and leaves the body).
The distance from the center of the swing ex-
cursion to the target is 800 mm. The betatron is
equipped with the same array of diaphragms and filters
as is the 25 Mev medical betatron, with the further ad-
dition of one 70 x 30 mm diaphragm. The lead shield-
ing cuts the dose rate of unused y radiation down to
0.5% of the dose rate at the beam axis (with filter in
use). The motion of the betatron is controlled by two
remote-control facilities (from a control desk) and also
directly from the room where the betatron is installed.
5. The 50 Mev research betatron. This betatron
is of the 2-yoke design, made of cold-rolled steel, and
is in the production stage at the present time.
The basic characteristics of the betatron types
described herein are presented in Table 3.
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SIMULATION OF CONTROL AND TEMPERATURE
VARIATION OF WATER DENSITY IN INTERMEDIATE-
NEUTRON URANIUM-WATER REACTORS
V. B. Klimentov and V. M. Gryazev
Translated from Atomnaya Energiya, Vol 7, No. 6, pp 519-523
December, 1959
Original article submitted March 12, 1959
This article deals with the results of experiments on the physical simulation of control and of the temperature
effect due to changes in water density in intermediate-neutron uranium-water reactors. The values of control
rods of different types were determined, and the dependence of the critical size of uranium-water reactors on
the density of the water filling the reactor core was found.
Introduction
The physical simulation of various processes in
nuclear reactors may be achieved by simulation pro-
cedures carried out on critical facilities. This makes
available much information needed in the design and
construction of nuclear reactors, and is a much cheaper,
variant than carrying out criticality experiments during,
the reactor start-up. Physical simulation makes it
possible to arrive at a highly accurate estimate of the 1,
optimum reactor loading at peak power operation,
better than that obtainable from theoretical calculations.
? Specially heightened interest is focused in studies
of the temperature effect due to variation in water den-
sity, and problems connected with the control of inter-
mediate-neutron uranium-water reactors. The authors
of the present article have performed investigations of
these problems on the critical assembly of a uranium-
water multiplying system. The design of the facility and,
several of the experiments performed on it are described
In detail in a report submitted to the Second Geneva I
Conference on the Peaceful Uses of Atomic Energy [1].
? The possiblity of altering the configuration and
composition of the core and reflector, and arrangment
of control rods, was provided for in the design of the
critical assembly.
The working components of the critical assembly
were plates 250 x 70 x 2.7 mm, compacted from a
mixture of uranium dioxide and trioxide (90% U235)
plus polyethylene. The plates were assembled.5-8 units
each in a stainless steel cell. The cells were mounted
on a scale-model table forming a core of the required
size and shape. The volume of a single casing was 0.62
liter. The ratio of the number of hydrogen nuclei to
number of U235 nuclei (p H 4235) varied from 17 to 50.
Two hollow cadmium automatic-control rods and two
scram rods were positioned near the core. The critical I
facility was lowered into an aluminum tank 3 meters
across and 1.6 meters high. The tank was instrumented
for controlled loading of water and rapid discharge. The
water level was indicated by a water gauge. The critical
facility was fully instrumented for reliable control and
monitoring of the process during all phases of its per-
formance. While experiments were in progress, parti-
cular attention was devoted to radiation hygiene prob-
lems.
1. Control Rod Value Studies
Empirical determinations of control rod worth are
not difficult and may be carried out with ease on a
critical assembly of the type described at a power level
no higher than 1 w. A solid boron rod (134C) measuring
60 mm in diameter and a hollow cadmium rod of the
same diameter, wall thickness 1 mm, were studied. The
Fig. 1. Diagramof annular uranium-water system, with
graphite lateral reflector (pH/p2 = 31): The blank
rectangles are working cells, while the hatched area is
the graphite; P are control rods; A are scram rods;
? indicates a movable cell.
977
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length of the rods was 400 mm,with the height of the
core of the multiplying system equal to 250 mm.
Measurements were carried out for systems with water
reflector and graphite lateral reflector 210 mm thick and
400 mm high. Rods placed at distances of 35, 70, and
140 mm from the reactor core were studied. Water was
used in all instances as the upper and lower reflector.
The measurements were performed on a ring multiplying
system, with an interior cavity, 140 X 140 mm, for water.
A diagram of this system, illustrating the case with a
side reflector,of graphite, is seen in Fig. 1. The scram
rods could be relied upon to shut down the facility at any
given position of the control rods or test rods. Neutron
spectrum energy was determined from the ratio pH/p235 =
= 31. According to the paper mentioned earlier (1], the
fraction of fissions of U235 due to neutrons of energies
above 0.4 ev is about 30% for this type of arrangement.
The procedure employed in the measurements in-
cluded prior calibration of the control rods P, by using
a removable working cell. A special setup with a lead
screw was used to move the cell. The worth of the cad-
mium and boron rods, and that of the working cell,
was determined by this means. The experiment was as
follows. An automatic controller was started and the
test cell was removed from the core. Control rods P
were automatically raised. The worth of the extracted
portion of the control rods was tentatively estimated
from the reactor doubling time. Similar operations
were repeated until the test cell had been completely
withdrawn from the core. Control rod displacement was
shown by a synchro position indicator.
The effectiveness or worth A p of a single working
cell in the mutiplying system of 25 cells, with aawater
reflector, was 0.015, and was found to be 0.021 for the
system of 20 cells with graphite side reflector. The cali-
bration curve for two cadmium rods inserted together
and placed in the graphite side reflector flush to the
core is seen in Fig. 2.
Lip
403
0,02
0,01
if
7
100
200
300 400
H, mm
Fig. 2. Calibration of control rods: I) core; II) top
and bottom water reflectors.
978
The worth of the boron and hollow cadmium rods
was found to be virtually the same. Their relationship
to the arrangement of rods about the core was determined
from the distribution of thermal neutrons in the reflec-
tor, as shown in Fig. 3.
Liquid absorbers may prove useful in the control
of pressurized uranium-water reactors. Controllers with
liquid absorbers have no moving parts, which entails an
appreciable simplification of the reactor design.
An estimate of the effectiveness of a mercury ab-
sorber placed at the center of the core of a uranium-
water system with water reflector was obtained by ex-
perimental means. A diagram of this system appears
In Fig. 4.
The energy spectrum of the neutrons in the multi-
plying system was determined from the ratio pH 4235 =
= 25. The number of fissions caused by neutrons of
energies higher than 0.4 ev amounted to not less than
50% [1]. The mercury absorber consisted of 12 copper
tubes filled with mercury (2.7 kg of Hg). It replaced
two withdrawn test cells. The outer and inner diameters
of the tubing were 10 and 8 mm, respectively, and the
height 400 mm. The tubes were placed along the peri-
meter of a square of sides 53 mm. Corrosive attack by
the mercury on the copper presented no hazard, since
the rods were not used for any period in excess of a few
days. Gradual withdrawal of the mercury absorber was
effected as part of the reactor automatic controls, the
variation in reactivity being compensated by introducing
control rods and withdrawing peripheral cells. For a rod
filled with mercury, Ap' = 0.088, and without mercury
Ap "= 0.023. Accordingly, the effectiveness of 2.7 kg
of mercury for the given rod design in the system is
A p'"--Ap.= 0.065.
lip
0,015
0,010
0,005
50 150
R,cm
Fig. 3. Effectiveness of absorber rods as a function of
their position around the core: 1) reflector (210 mm,
graphite); 2) reflector (water).
100
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2. Physical Simulation of Temperature
Variation of Water Density
Temperature-induced changes in water density
result in increased neutron migration length and greatly
modify the physical characteristics of uranium-water
reactors. Variation in water density in the core of a
nuclear reaction was simulated by introducing special
layers into the space between working plates. These
layers were made from a thin resin film on a copper
base and were filled with air. The volumes of air and
layering material were determinedby the volume of
water displaced by them. The distance between work-
ing plates was small compared to the neutron diffusion
length in water, and remained within 3-4 mm, while
the thickness of the air-containing layers was about 2
mm. Experiments aimed at calculating the degree of
heterogeneity of uranium-water systems with plate-type
fuel elements such as described in [1] showed that such
systems may be viewed as homogeneous systems at
pH /p235 C'.1
II) If)
CS 0. .
COC') sl,
-a. co oo
Lf) if) in
0" 0. ' g
ac.,
0
?,-, 01
co t-
..,-.
II
. ? 4
9. L
C.)
E,
milliwatt-
days/ ton
,
co to
0-../i
in...I?
00
co
oo
co
CV 00
0-> cs1
cq t--
co cq
8 .0
o.
11)t?????
ca, -.
..
C)... 0
CD
Co
0..
..... If)
co oo
0.. c:7
8
C.)
N
cl ,c
00 00
.....?
II
01' *d
C.)
E ,
milliwatt-
days/ ton
0 0
C \IC \I
CO If)
co Lo
0
If)
N.
',V
,0 .0
0170 t?-?
0 CI
..7... CO
8 .0
00 CO
co ca)
0- 0-
00
-,
0-
InCV
-a. t--
-
c; co
E
0
c0)00co
-.10
00 ..?-??
C,; 11
11 ?-?
F.4
9- Q
E.
milliwatt-
days/ ton
oin
co c..?
c
co
? Co LC)
-..1,
Cl
co
...../.
o. co
.../. cy.
co co
CO Cl
8 ,0
CO CO
N. C)
????7' If)
0; C)..
N.
Cr)
If)
C).-
0....14
N. 53
If)
CS. C)
788
Rcrit ?172 CM
E,
milliwatt-
days/ ton
CC CO
Cl .../I
Cr LC)
00 cc
Cl
CV
..r.
in
0
.....1r
t?-?
co Cl
8 .0
a,
-4, ????-?
co 0
C; 0...
0
..5.
O.
N t--
00 Cl
(Z7 0...
8
40
,,,,,, ??,1
C0 I I
II
U
E,
milliwatt-
days/ ton
-.. t.....
if)
CD I.0
C) N.
....,14
Cf)
I-0
If)
..,?-? --?
N.
If")
Cr) --?
8 .0
o.
n a)
In c?D
...../I .5.
0; C;
00
-a
If)
0-
c\I a)
oo If)
Ca' CC
C; C;
.
0 C)
-, CV
.C)
Cr)
0 0
..../. II)
olQh
W5hQ5CrI5 WohQoaf9
ofs
+ W11Q1 Qh0 (I
(i)a shcr h '
where wik is the yield of the k-th fission fragment on
fission of the i-th isotope; Xk is the disintegration con-
stant of the k-thfission fragment; Sk (in analogy to the
case of uranium breeding) designates the operating time
during which the equilibrium quantity of the k-th fission
fragment is produced in the reactor. The losses due to
individual fission fragments in the stationary state are
equal to
where
and
W5 + 1475
Zs
I + a piritg)D
at,
wsh
(7 5
W5 =
h
(Doh Shah
(18)
f c
, GP
Woh ?aq -1- h ---
w9 L A,1
la O'n
(19)
Ho 1 + +
11(71?
Utilization of Uranium
In.its'initial state the system has a neutron excess
expressed by Equations (9), (11a), and (11b). If the
breeding of uranium in the reactor occurs in such a way
.that the quantity of U238 nuclei per cm3 remains con-
stant (N8c? = N80), then it can be shown that the relative
volume change of the moderator is
VA/
This means that the moderation and diffusion character-
istics of the system are practically invariant, and there-
fore one can write
(N man+ DB2)? = (IV mum + DB2); (29)
T?8=-- (PT ?Ps'
(..B2T)?= (B2x).
(21)
In such an equilibrium system the neutron excess
is determined by the expression
67 = v;e-B2I ?1 ? R [1 + e-n2I (17'5? vi,u)+
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If we substitute psc? and R50" into expression (26), we
shall obtain the corresponding energy yield. It can be
seen from this formula that in general E increases with
decreasing p6c13 and with increasing 116, but the values
of these quantities are related to each other by the
limiting criticality conditions, which by expression (22)
demand that 6c? = 0.
The table shows several values of U295 equilibrium
concentrations (p6a3) and the corresponding energy re-
lease (E) pr ton of introduced natural uranium in re-
lation tothe over-all operating time S since beginning
of reactor operation, using several critical assembly
dimensions [2]. The table wes compiled using the
following parameter values:.
?
0,02s ,
"9 "I ?"Til
1+ cfpuRT
(Z? s
Or' 5 rit, 1 +-NS) (22)
1 a6
W '
If the neutron excess in the system is initially equal to
we can convert expression (22) into the expression
? z' (1+ ap,i1C)
?*86.-B2' vpu
1
1 ? (5? ?
Q5 \ a5
0? us
K (55
1? 1),e
where we define
, 6rg
W5 = W5 -F1 + a6S ;
= 0,712; IV =- 0,4086; T=500? K ; ,v'5= 2,08;
(23) vpu = 2,64; vi,u= 1,97; ay. = 1,34; i?:r 1=--0,106;
cr,f, af
Wpu 0,0210; W5 = 0,0216;
17, = 1,91, v, = 2,14.
(24a)
K (s) apt, (2 ? + 0,02s -I -1 W,, (24b)
ao
?W8 (24c)
and have used expressions (6), (7), and (11b).
If the reactor was initially critical (6? = 0), and
remained critical after a given operating time in an
equilibrium state (6?3 = 0), then under these conditions
Equation (23) was satisfied, and consequently, it was
possible to utilize the introduced uranium pfic?. We have
employed in our computations the fact that W5 can be con-
sidered independent of s because of the small value ot
C6.
The operating period S (which we define to be
that operating period in which we have total renewal
of the uranium in the reactor) is linked to the concen-
trations of the introduced uranium p5d = N5d/N5? and
of the utilized uranium, in accord with expression (4a),
by the relation
e,
? ? 1) .
05 c.?5?
(25)
In the course of an equilibrium-state operation with one
ton of introduced natural uranium, we obtain the
energy
E=t1 ? v._ -1-
Q, (T5
(cq' -c-rf f-i-.14)] 6450 millwatt-daysiton. (26)
9 69 a9
The figure shows the attainable utiliza-
don E per ton of introduced natural uranium, with re -
spect to S. It can be seen from the figure that for
identical reactor dimensions and short operating periods
it is possible to attain higher utilization with high
uranium concentrations, while for long operating periods
a higher utilization is attained with low uranium con-
centrations. One can therefore expect that for given
co ^ 7000
-o
10000
9000
99
0,766
Rcrit, cm
182
8000 0,788 172 \ \
\ \
\
0,813 166 \ \
0,827 166 \ \
\ %
\\
0,855 173 ?\\
5000 --- \\
0,869 181
......... ---.,
--*----. ---"- ---..
- ? ? -........**-.. .......
--,......, ...........
? ??,-,_... -...
\s'
nou
(11 6000
;4
g 4000
? 3000
1000
I.
10 10 30 40 50
Operating period, S
Utilization of natural uranium in a homogeneous
reactor
985
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reactor dimensions and corresponding to each operating
period S there exists a certain optimum uranium con-
centration (optimum io8) which permits attaining a
minimum p5c? and consequently, maximum utilization.
Optimum Cycle in an Equilibrium State
For a reactor of fixed dimensions the conditions
? 1 ? [ 1 + N N 4lam (1 + LifB2 = 0
is os
determine the reciprocal relation between 8.? and 08,
The requirement = 0 (23) specifies the attainable
equilibrium concentration pe as a function of the
values of 00 and 08. It can be seen from expression
(23) that for 6 = 0, the quantity p5c? decreases mono-
tonically with increasing 8-? ; on the other hand, it can
increase or decrease as a function of tp 8, and for OF/
/8 = 0 it can assume a locally extreme value, lead-
ing to the result
Or
(1?'(1)8(3- /32Vpu)2 = K (Q. + 211v (It 00)
6 V '5 05
(27a)
1
= [1 ? K (QT -cr? 0?) .
e v V5 05
Pu r,271))
A more detailed analysis shows that a local minimum
of pe corresponds to the negative sign in Equation
(27b), and that this value appears to be physically
realizable in contrast to the value which corresponds
to the positive sign in Equation (27b).
It is possible to eliminate pe from Equations (27)
and (23) and to find a relation between tp Band efor
which p5a) appears as a minimum:
trcr8=
0.5
V
K ?? ?W.
0 11?-1?Wr n2
11 K (1 11)8e?, Vpu)2?Vire-
986
11(28)
In order to have the reactor initially critical, we
must satisfy
= 710 (I ? 11)8)
0.5 + NAI (1L1
111
_2 B2)
I '
AT5
in such a way that Equations (28) and (29) determine
the parameters for which the reactor is initially critical
and at the same time has a value of 08 (optimum
uranium concentrations) such that for S it has a mini
mum attainable concentration pep as determined by
Equation (27). By calculating the values of tpg Opt cor-
responding to various values of s in the interval s = 10
to 50, we shall obtain the function tp 8 opt (s) and the
corresponding concentration of uranium in heavy water
for which one can always attain the maximum uranium
utilization.
Smaller s means we get smaller values of sog opt
(i.e., the concentration of uranium in the moderator
will be large), while for increased s the values of S?8 opt
will also grow (i.e., the uranium concentration will
decrease). This means that the optimum cycle in the
equilibrium state occurs not for a constant uranium con-
centration, but rather for a gradually decreasing con-
centration; this reminds one of the dilution cycle
proposed in [1] as a means of extending the period of
use of an equilibrium-state reactor which had stopped
being critical.
It is necessary to note once more that the analysis
we have conducted concerning an optimum cycle is
based on the assumptions that17V5 and IN9 do not ,depend
on the utilization and appear to be constant; i.e.,
removal of fission fragments from the reactor is carried
out at a constant rate and is independent of the operating
cycle, , and neutron capture in U236 is small. However,
even in the case where fission fragment removal from
the reactor is carried out simultaneously with uranium
renewal (Sk = S), the above analysis remains qualita-
tively valid.
(29)
LITERATURE CITED
1. V. M. Byakov and B. L. Ioffe, Transactions of the
Second International Conference on Peaceful Uses
of Atomic Energy [Russian translation], (Geneva,
1958) 2; Nuclear Reactors and Nuclear Power
[in Russian] (Atomizdat, Moscow, 1959), p. 398.
2. I. Rochek, Calculations on the Critical Dimensions
of Homogeneous Reactors [Russian translation],
Trudy In-ta yadernoi fiz. (Prague, 1958), No. 325.
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DETERMINATION OF THE SOLUBILITY OF METALS
IN LITHIUM
Yu. F. Bychkov, A. N. Rozanov, and V. B. Yakovleva
Translated from Atomnaya Energiya, Vol. 7, No. 6, pp. 531-536
December, 1959
Original article submitted March 9, 1959
The solubility of uranium, zirconium, iron, nickel, titanium, molybdenum, niobium and beryllium in lithium at
temperatures of 700-1000?C was determined to assess the stability of metals in lithium and establish the mechanism
of corrosion. It was found that nickel and beryllium have a high solubility (of the order of 1%), iron, zirconium,
titanium and uranium are slightly soluble (from hundredths to thousands of one percent) and niobium and molyb-
denum have a very low solubility (less than 10-41o). Crucibles of the lithium to be tested were filled in a special
still with distilled lithium and hermetically sealed in a container in a medium of argon. The solubility of the
metal to be tested was determined by chemical analysis of rapidly cooled lithium fusions after they had been
kept for 50-100 hours in the container at a predetermined temperature. The presence of isothermal transfer of
aluminum, beryllium, zirconium and silicon via lithium to steel and iron was discovered. Under these conditions
maximum solubility of the metal in lithium was reached far more slowly than in the absence of transfer. Lithium
can be purified by getters? uranium and zirconium? slightly soluble in lithium.
The thermophysical properties of lithium are
superior to the properties of other metallic heat carriers
and it is, therefore, of great interest to find materials
which are stable in lithium at high temperatures.
To assess the stability of metals in lithium and
determine the mechanism of corrosion.it is necessary to
know the solubility of various metals in it at different
temperatures, i.e., the lines of the liquidus of the phase
diagrams of the metals with lithium. There is little
data in literature on the solubility of high melting point
metals in lithium which could provide a basis for select-
ing alloys stable in lithium. It is known that after a
residence time of 100 hours at 480? C in vibrating zir-
conium crucibles,the lithium contained 0.01% zircon-
ium, and after tests at 760?C ? about 1% zirconium [1].
It is also known that chrome steels, iron, niobium,
molybdenum and tantalum have a high stability in
lithium at temperatures up to 800?C, whereas chrome-
nickel steels are stable only up to 500?C [2].
Lithium forms alloys with magnesium, aluminum,
silicon, silver, platinum, copper and gold at comparat-
ively low temperatures [3]. Leaching of nickel to a
depth of 0.02 mm was detected metallographically in
type Ya0 chrome-nickel stainless steel after a residence
time of 40 hours in lithium at 1000?C; this converted
the y phase in the surface layers of the crucible to the
a phase [4].
The change in the mechanical properties, structure
and composition of carbon, chrome and chrome-nickel
steels after 230 hours corrosion testing in lithium at
800?C was investigated in [5]. The tests were carried
out in Armco iron crucibles. Under these conditions
chrome-nickel steels and also chrome steels with 2%
nickel were intensely corroded while chrome steels
were more stable. 1Kh12MV4B steel was the most
stable. The resistance of stainless steels, iron, beryl-
lium and thorium to corrosion in lithium at 300 and
600?C under static conditions was investigated in [6]
by the metallographic method and the change in weight.
According to the data of this work, thorium and low-
carbon high-chrome steel containing 14-10 chromium
had the maximum resistance. The resistance of pure
Iron and chrome-nickel steel of type 18-8 alloyed with
niobium was almost as high; ordinary 18-8 steel and
high-chrome steel with 0.6-0.7% carbon underwent
severe corrosion; nickel and Inconel were still more
markedly corroded.
Investigation Procedure and Apparatus. Crucibles
of the metals to be tested were used to determine the
solubility in lithium. The inner surface of the cru-
cible was ground, after which it was electrolytically
polished or etched. These crucibles were filled in a
special still with freshly distilled lithium (Fig. 1). Elec-
trolytic lithium 10 was placed in a stainless-steel evapo-
rator 8, welded to the lower flange of a vacuum cham-
ber 1. The crucible was heated by furnace 9 to a tem-
perature of about 800?C. The vaporizing lithium
heated the stainless-steel condenser 2 (of thickness
1 mm) to 250?C; this condenser was in the form of a
trihedral pyramid with guides welded to the sides. The
lithium deposited on the condenser flowed down the
three guides into three crucibles 6, installed on the sole
987
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and filled them, while the elements more volatile than
lithium condensed in the cold parts of the chamber.
Difficultly volatile elements remained in the evaporator.
During the distillation the pressure in the chamber was
kept at 10-4-10-3 mm Hg. After the process had been
completed the still was filled with pure argon; the con-
tent of impurities in the lithium after distillation was
reduced: sodium to 0.02-0.00/0, potassium to 0.015%,
iron to 1-4 ? 10-4%, magnesium to 0.00/0 and less;
silicon, nickel and chromium were not detected.
The crucibles filled with lithium were placed in
Yal-T stainless steel containers, to which the covers
were slowly welded in an arc furnace in an atmosphere
of argon. The containers were then placed in the
furnace for isothermal treatment. Crucibles of metals
which react at the temperature of the test with stainless
steel were isolated from the steel by sheet molybdenum,
with which they were fixed in the containers.
Since the content of lithium-dissolved metal
depended markedly on the rate of cooling from the
temperature of isothermal treatment, after the treat-
ment was finished the containers were cooled in water.
988
As was shown by direct measurements, this ensured cool-
ing of the lithium fusions to the solidification point in
less than 50 sec.
The content of the elements dissolved in lithium
was determined calorimetrically. The initial materials
for the investigation were zirconium iodide of 99.9%
purity, titanium of grade TG -0 smelted into rods of
diameter 30-40 mm in a MIFI SM-3 arc furnace, baked
briquets of molybdenum and niobium powder, Armco
iron smelted and cast under vacuum, distilled beryllium,
uranium and nickel crucibles cast or obtained from sheet
by pressing.
The mechanical properties of molybdenum, niobium
and zirconium before and after reaction with lithium
were determined on a micromachine for specimens of
diameter 1.2 mm. The properties of the other metals
were investigated on specimens of diameter 3 mm with
a working length of 20 mm.
Isothermal Transfer of Metals via Lithium. Cru-
cibles of Armco iron,Yal? chrome-nickel steel and Zhl
chrome steel, in which lithium and the samples of the
metal to be tested were placed, were used in the mi-
Fig. 1. Diagram of the apparatus for filling crucibles with distilled
lithium: 3) screen on which sodium and potassium condense;
4) funnel; 5) screen; 7) backing; 11) support; 12) thermocouple;
13) brace; 14) diffusion pump; 15) thermocouple; 16) cover
(remainder of the legend given in the text).
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a b
Fig. 2. Macrostructure (x 2) of the crucible walls after isothermal transfer via lithium at 1000?C: a) silicon
on iron after 40 hours; b) aluminum on iron after 50 hours; c) beryllium on Yal-T after 400 hours.
tial experiments. After they had been kept at the tem-
perature of the test ,the welded sealed containers con-
taining the crucibles with lithium and the samples were
cooled in water.
It was found that if the material of the crucible
differs from the material of the sample, precipitation
of the metals from the lithium fusion may occur on the
walls of the crucible. The precipitation of large
crystals of silicon on iron (Fig. 2a), aluminum on iron
(Fig. 2b) and beryllium on steel (Fig. 2c) can be de-
tected very clearly by visual means. The transfer and
precipitation of metals from the fused system can also
be judged by the variation in the microhardness of the
surface of these crucibles (Fig. 3).
The transfer and precipitation of metals during
isothermal treatment is only possible if the chemical
affinity of the dissolved metal for the material of the
crucible is greater than the affinity for lithium. Where-
as silicon and aluminum, which have a high affinity
.900
800
700
600
500
400
300
700
100
Si
41
03 0,5 0,7 0,9
1,1
1,3 1.5
?
1,7 2,0
MID
Fig. 3. Microhardness of the surface of the crucibles:
0) stainless steel crucible ; ?) iron crucible.
for iron, were precipitated from lithium, lithium-dis-
solved magnesium was not precipitated on iron.
The transfer and precipitation of zirconium were
investigated by means of the radioactive isotope Zr.
After Zr95 powder wrapped in tantalum foil and placed
in a Yal-T stainless-steel crucible had been kept in
lithium for 100 hours at 900?C it was found that the
tantalum foil had not become active, whereas the
crucible, with which the zirconium was not in direct
contact, had a y activity corresponding to 4 ? 10-3 g
of zirconium. At 800?C about 10-4 g of zirconium was
transferred in 10 hours from a plate of radioactive zir-
conium to a Yal steel crucible. This shows that at
temperatures of 800-900?C the chemical affinity of
zirconium for tantalum is slight, whereas that of iron
for nickel, included in the composition of stainless
steel, is high. By reacting with zirconium dissolved
in lithium, stainless steel disturbs the equilibrium,
which leads to further dissolution of zirconium and its
transfer on to the crucible walls. Naturally, in the
presence of transfer the rate of dissolution of the metals
increases.
Weight %
Ni oo
0,1
Be
2 50 100 200 400
Hours
Fig. 4. Kinetics of the dissolution of nickel in
lithium at 750?C and beryllium at 1000?C.
989
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The concentration of zirconium in lithium under
conditions of transfer was determined by comparing the
y activity of Zr s6 in a given sample of lithium and the
radioactivity of a known sample of the initial Zr".
The uniformity of the distribution of zirconium was
checked by measuring the radioactivity of different
lithium samples. After 100 hours in stainless-steel
crucibles the zirconium content in lithium determined
by means of Zr" at 900?C was 1-1.4 ? 10-210. This
value was of the same order as the solubility of zircon-
ium in lithium determined chemically. From these
experiments it follows that, in particular, tantalum
crucibles can be used for the determination of the
solubility of zirconium in lithium. In [5] carburiza-
tion of chrome-nickel steel to 0.6-0.710 carbon and
chrome steel to 1% carbon as a result of isothermal
transfer at 800?C of carbon from an iron crucible via
lithium was observed.
Solubility of Metals in Lithium. The attainment
of the limiting (equilibrium) solubility of metals in
lithium is a fairly long process. The limiting solubility
is reached only after several hours. For example, at
750?C after 2 hours the nickel content in lithium was
0.33-0.4%; after 50 and 200 hours the nickel content
was 0.5-0.55%, i.e., the maximum solubility, equal to
was reached after several hours. Similar behavior
was also shown by other metals. The beryllium con-
tent in lithium at 1000?C increased when the residence
time was more than 50 hours.
The values of the maximum solubility from the
exit of the curves on the plateau were taken as the
limiting solubility (Fig. 4). The limiting solubility of
beryllium is reached far more slowly than that of nickel
as a result of which isothermal transfer of beryllium on-
to steel, reducing the beryllium content in lithium,
takes place in the first case. Moreover, the rate of dis-
solution of beryllium was probably somewhat less be-
990
700 800
?
OSO
900 1000 1100 1700
T, 'C
Fig. 5. Solubility of zirconium in lithium at
700-1000?C.
TABLE 1
Solubility of High-Melting Point Metals in Lithium
Metal
Temp.,
?C
Solubility,
weight %
?
Iron
900
0 .0 I
1000
0.02-0,1
It
:I 200
0,15
Nickel
700
0,15
750
0:-)
850
1,313
II
950
,,..
Titanium
900
0.014
Molybdenum
IWO
< 1 0 -4
1700
0,03-0,1
Niobium
1000
21-1 41.Llld 9811d '1.08/1 ' L LT M 4 6003 '6910H `903H `ToloH
, ,
iS `,,EO
'991011 ?681q1 VZII . 001 I 'el 'LUC'S ' 14411,1I.'1,,LISPD 'OA `,,,esJS togs N
0,7,;311 'ErotuIS 'c,1131
'moi, T, 'ay ??,qg
' eztuS ' ,5y2-1)1.
0
I
'2 ,.sy ?
1. 814)1
, PI?11.1
'osituo 69,1?
479131 '901A1 '8111
Mill ?t9IgA.
'1391 na '6EIeg
0101 'gull
'9LIM 4091Tud_
'90Ild 6610a ?iei I .
,
401101 /9 1Z 99fNI
111 9-I
rappird-g
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f13 umouNun ippt
sadmosy anpoe- g
0r?L'C
L'C'-'C
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.
A9W 93
(sArp oc T tuoi; aPI-Jteffisado)osi anTlov-uan
(Pa nui itio0) g 'I V
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TABLE 3
Beta-Aative Isotopes (Half-lives more than 30 days)
Mev
T ,
2
o?o , I
0 , i?o ,3
0,3-0,5
0,5-0,7 0 ,7-0 ,9
0 , 9-1,1
1,1-1,3
30-50 days
Fen, Nb95, Rum,
lig203
Fe's, cout Hpsi
Ce", pmus Rbs 4
50-100 days
S66, Sb124
SC46, C068, Y21,
Zr95, Tessm,
Tb", W185
Te95,74, Sb124, Tb162
Tb16s, Ir122
Sb"
100-200 days
Ca45, Relis
Tals2
Lull , Tal82, Yss
Tun?
Tull?
200-365 days
Aguom
Ce144, 131049
Zn65, Ce"
Ag115771
Rh"
Rh", Rh"
1-3 years
Rum, Tu171
sb125 p/047,
Eu"
511,21m, csis4
Na22, Sb', Cs"
Pm"
3-5 years
Tr"
5-10 years
Ra228
Co6?
Cd"
Re
10-'30 years
113A02 1:1)21?,
Pon'
Euiss, Eui54
5r90, Eu152
Kr85, Cs127, Eu152,
Eu154
Eu"
Eu152
Cs"
30-100 years
smi51
Ho"
Holas
>100 years
Niss, Zr23,
pdm,
Re187
C", 5i32, Se",
Rb', Tess, 029,
Cs", L03E1
Tess, Lulls
Be's, Ms, Nbs4,
In", Am"
Cl"
A126
/O/ eseeiej -101 panaiddv pue Pe!PsseloeCI
CIA-RDP10-02196R000100040004-6
T A BLE 3 (Continued)
Beta-Active Isotopes (Half -lives more than 30 days)
T,
2
Ea' Mev.
5-active iso-
topes with un-
known E8
Isotopes whose decay is not accom.-
panied by the emission of a- and
8 -particles
1,3-1,5
1,5-1,7
1,7-1,9
1,9-2,3
2,3-2,7
30-50 days
Rb84' Cd115'1,
Te122171
prams
A97, Awes, Tell", xe3.29, ybo39
50-100 days
S188
Co58, y91,
slain
Sb124
win
Bel, As", Rb83, Sr85, Zrr, Nb",
Te81m, In11411 Te12501' 1125, Eu148'
Gd, Tuna, 1.075, Re183, Re", Os"
100-200 days
SO123
Tel""
Se" Y88, Sum, Tel", Tei23,n, cei39,
E,;149, Gd", Dy199, Wu', Au185,
Hg184
200-365 days
V", Ma", CO" Ge88, Sulu", pra143,
PM144, SM145, G?1.153
1-3 years
Os,"
Fess, 114o", Cd'", Lum, Lulls, Tel"
3-5 years
A49
Hf"
5-10 yearsBi2?7
RV", Be",
10-30 years
0
Eut92
Eu""
Nb", pram
30-100 years
>100 years
K4?
Fe8?
Ca", Ti", Mn", Ni", Kr", Tc97,
Lam, Pb202, Pb205, Bi208
M
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on!?1 'mud
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9CS ri
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en a 'Can 'esztli,
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`41,1111S , vtTPNI zotoD
weal( sOI <
anID
Lroill ',,JD `TeauTV
itztulf 'etenD
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etzuW 'mud
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mud 'ocaL
spin
siezA ,ot -pi
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sluaA 00 I-i
mulD 'intuD
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?DOR
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tzETIL ?stOM
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of 'cp1111 '8913d
`za. nzzyll oszil
Tull
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'OH 'Int% 0131V
1000d 'VESTS .00V
SOZOd 'TOZ HI 'LlOd
coz!fl
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upi 09-03
NIzoci ?goz1 \' `sood
%MI ?II . S III !II `ooz.:0,1
io,-.0.1 't ix !ft
ptz!ti trn-strOV
L?H '091>IH
tillu 03-T
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SM....2H
MU] I >
lity
A ysi .
sadolosi annov-utidjV
V 3'1E171,
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Declassified and Approved For Release 2013/02/21
cleft
Liwid
L umotniun
imm sadol
Os! annou- 70
...tzula 'ttz"d
siraK 0I<
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evz,la
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ogzukg `vi,..r) `str,J3
onr.,1
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`cseld `tezdN `zizull
mull
nozulj `nzei.T. 'He'll
liTui 0903
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szzO.
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ozzfl `7.W.4
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tigod `0i00,1
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1,1011 '61gUil 'TOY
stz?ki
'91z,?1V `trzull `tit,od
'nal. `ozOlj `Tizod
g Izod `ctrid umzod
'81zul1 `tzzILL 'LOY
zzz,W
?lizod 'mull 'ingod
tz0),I `oz0.4
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UT al 1 >
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SadOlOST 0/1110E- X>
6<
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To determine Ea one. can use, for example, ioni-
zation or magnetic a spectrometers. It should be noted
that when several groups of a particles with different
energies belong to the same isotope, all of the Ea are
taken into account, and the given isotope is appropriately
indicated in the various columns of the table.
If Ti or Ea of any isotope is exactly at the end
of the interval corresponding to a particular row Or
column, that isotope is placed in the following row or
column.
Tables 1-4 herein presented enable one to indicate
a group of appropriate isotopes for an indicated inter-
1002
val of Ti and E8 (or Ea). To make the latter more
precise, it is convenient to use the detailed table of
isotopes [1], and the use of a radioactive decay chain
scheme may be of additional assistance in a number of
cases in identifying the activities.
We consider it our duty to express our gratitude to
Yu. A. Zysin for a discussion and his advice.
LITERATURE CITED
1. D. Strominger, J. Hollander, and G. S.Seaborg,Rev.
Mod. Phys. 30, 585 (1958).
2. N. Hallden, Nucleonics 13,78 (1955).
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MORPHOLOGICAL TYPES OF INDUSTRIAL URANIUM
DEPOSITS AND METHODS FOR THEIR PROSPECTING
D. Ya. Surazhskii
Translated from Atomnaya fnergiya, Vol. '7, No 6, pp. 539-543
December, 1959
Original article submitted May 30, 1959
The grouping of uranium deposits according to the comhination of their morphological features is proposed. Five
groups of deposits are distinguished, for each of which the following are examined: the prospecting system, the
most efficient ratio between mining and drilling operations, the density of the prospecting network and the
conditions for the classification of reserves.
General Remarks
As with other mineral ore deposits, the prospecting:
of uranium deposits is carried out either by drilling or
mining operations or a combination of both. The choice
of the prospecting system, the most effective ratio be-
tween mining and drilling operations, the density of the
prospecting network and the conditions for the classi-
fication of the reserves are determined mainly by the
shape of the ore bodies, their dimensions, the degree
61 variability with respect to the metal content (gener-
ally expressed by the coefficient of variation) and the
degree of discontinuity of the mineralization (expressed
by the coefficient of ore bearing, i.e., the ratio between
the area occupied by the conditioning ores and the totall
area of the ore-bearing bed or ore-containing fissure).
From the combination of these morphological features, I
known uranium deposits can be divided into five groups:
1) mineralized beds; 2) large bed-like deposits; 3) ;
bed-like, pillar-like and vein-like deposits; 4) lend-
cular and pocket-like deposits; 5) systems of thin veins.'
Prospecting of Mineralized Beds
(First Group of Deposits)
This group includes continuous beds of uranium-
bearing sedimentary rocks developed in areas measuring
tens of square kilometers. They are characterized byuni1
formly poor mineralization distributed without inter-
ruption along the strike, to the dip and with respect to
the thickness of the productive levels. The boundaries
of the mineralization coincide with the lithological
boundaries and can be determined visually. The coef-
ficient of ore bearing is close to unity and the coeffi-
cient of variation with respect to the metal content in
the ore does not exceed 20-30/0.
The most characteristic deposits of this type are
uranium-bearing marine shales, uranium-containing
phosphorites and analogous sedimentary syngenetic de-
posits in which appreciable distribution of the metal
deposited simultaneously with the adjoining rocks is
not found.
The prospecting of such deposits consists mainly in
the drilling of the ore bed according to an isometric
network. Mining opera dons (small shafts, prospecting
pits and crosscuts driven from them) are carried out on
a small scale, solely to check the data of borehole
samples. Reserves of all industrial categories (A, B, and
C) may be revealed during prospecting. In this connec-
tion the network of boreholes must not be less than
100 x 100, 200 x 100 and 400 x 200 m,respectively.
In deposits which are prepared for exploitation,the re-
serves between mine workings at a distance of up to
200 m from each other can be included in group A2, and
reserves between workings at a distance of 400 m from
each other in group B.
Prospecting of Large Bed-Like Deposits
(Second Group of Deposits)
Deposits of this group consist of large bed-like
bodies with nonuniform distribution of the metal, cor-
related with specific stratigraphic levels. In contrast
to deposits of the first group, not allof the bed thickness,
but only part of it, is industrially valuable; the con-
tinuity of the mineralization may be interrupted by
instances of narrowing. Instead of a single ore body,
in practice it is, therefore, necessary to deal with
several more or less isolated ore bodies, each of which
occupies an area sometimes measuring several square
kilometers.
The contours of the ore bodies are determined
solely from test data on samples. The coefficient of
ore bearing varies from 1.0 to 0.8, and the coefficient
of variation with respect to metal content reaches 100%.
This group includes the largest of the known epi-
genetic uranium deposits in sandstones, conglomerates
and other sedimentary rocks of primarily continental
facies. A combined mining-drilling system with a
1003
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marked predominance of core drilling is usually em-
ployed for the prospecting of these deposits. The main
task of drilling operations is the mapping of the ore
bodies in contour, while that of the mining operations
is to record the boundaries of the industrial minerali-
zation wth respect to the thickness of the ore-contain-
ing formations, and also obtain data for the complete
characteristics of the chemical and mineralogical com-
position of the ores, their physicotechnical properties,
etc.
In the case of isometric forms of the ore bodies
drilling is carried out according to a square network,
in all other cases by lines perpendicular to the plane of
maximum variability of mineralization.
If there is sufficient evidence to assume that the
ore lenses are located in several layers and pass beyond
the limits of the main ore bed, part of the boreholes (up
to 10-10 of the total) is sunk to a depth ensuring the
intersection of all the ore-bearing measures and the re-
cording of ore bodies below the main ore-bearing level.
As usual, mining operations consist in driving road-
ways and rises at intervals of 80-120 m in one of the
ore districts, principally to check drilling data and ob-
tain material for technological samples. If prospecting
is carried out by roadways and the thickness of the ore
body exceeds the width of the roadway, crosscuts are
also driven, generally at intervals of 40-60 m.
In contrast to deposits of the first group, reserves
exposed by boreholes of the 200 x 100 m network are
not placed higher than category CI. Reserves of cate-
gory B are considered to be those within the limits of
enclosures found by drilling on the 100 x 100 m network;
mine workings which confirm the drilling data being
present in one of the districts where the deposit is
located.
Prospecting of Bed-Like, Pillar-Like and
Vein-Like Deposits
(Third Group of Deposits)
The difference between these deposits and those
described above is that the form of their ore bodies and
their location in the area are determined not only by
the lithological composition of the adjoining rocks but
also (in some cases, chiefly) by folded and ruptural de-
formations. Many of the ore bodies are characterized
by a relatively high thickness (reaching several tens of
meters in places) and also by marked variations in the
shape, dimensions, conditions of occurrence and the
area of the transverse section at comparatively small
intervals along the strike and to the dip. The mineral-
ization is generally uninterrupted but the shape of the
ore bodies is complicated by the presence of isolated
blocks of waste rock. The boundaries of the industrial
mineralization are determined solely from test data
The coefficient of ore bearing varies between 0.8-0.5;
the coefficient of variation sometimes reaches 15C1%.
1004
The area of such deposits (in the dip plane) does not
exceed several hundreds of thousands of square meters.
Such deposits generally consist of one or more (two-
four) ore bodies.
This group includes many bed-like bodies in se-
dimentary rocks of continental facies, metasomatic
deposits on the flanks of steep folds, vein-like deposits
within major faults, stockworks in crushing zones as-
sociated with the faults, pillar-like bodies at the inter-
sections of two tectonic zones, etc. The main role in
the prospecting system is played by mine workings, a
series of crosscuts intersecting the ore body along the
short axis at distances depending on the configuration
and cross-sectional area of the deposit at the given
level. In some cases the crosscuts may be partially re-
placed by chamber-diamond drilling boreholes. The
alternation of crosscuts and chamber-diamond boreholes
is fairly common in practice. Staples and rises, which
serve to confirm the continuity of the mineralization
along the vertical, between the levels of the roadways,
are also important.
Deep drilling on a very close network (generally
50 x 50 m) makes it possible to assess the reserves not
higher than category C. As a result of the complexity
of the shape and the markedly nonuniform distribution
of the metal in the ore, reserves of category B are con-
sidered only within the limits of sublevels completely
prepared for extraction operations. Reserves of category
A2 are generally not revealed at the normal density
employed for the prospecting network.
Prospecting of Lenticular and Pocket-Like
Like Deposits
(Fourth Group of Deposits)
The ore bodies are sometimes localized in specific
stratigraphic levels or are associated with ruptural de-
formations (for example, in the contact zone of granites
and sedimentary-metamorphic rocks),but in general the
lithologic and structural control of the mineralization
is less clearly expressed here than in deposits of the other
groups. The outlines of the industrial mineralization
are determined solely from the data of tests. In many
cases the zones of distribution of the lenses are in the
form of narrovf(up to 300-500 m) bands of considerable
extent. The dimensions of the ore bodies in the dip
plane do not exceed several tens of square meters. The
coefficient of ore bearing within the individual lenses
does not exceed 0.50-0.25; the coefficient of variation
of the metal content within the individual lenses often
reaches 2000.
The group described above includes small lenses
of hydrothermal ores in zones of tectonic contacts,
bedded and anticlinal veins,and domal structures of
higher orders,and also a number of deposits, the pre-
dominant role in which is occupied either by purely in-
filtration processes or processes of the metamorphism
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Grounine of Uranium Deposits According to the Main Morphological Features
Group
. _
Characteristics
Maximum areas of
the ore bodies
Coefficient
of variation
(maximum),
10
Coefficient
of ore
bearing
1
Continuous seams of uranium-bearing
sedimentary rocks with uniform minerali-
zation, recorded uninterruptedly over large
areas. In general,the boundaries of the
mineralization coincide with the lithologic
boundaries and are established visually.
Tens of square
kilometers
30
1
2
Large bed-like deposits with. nonuniform
distribution of the metal, correlated with
specific stratigraphic levels. The boundaries
of the mineralization are established only
by the results of tests or y measurements.
Square kilorheters
100
1.0-0.8
3
Bed-like, pillar-like and vein-like
deposits controlled by folded and ruptural
deformations. The boundaries of the
mineralization are established only by
the results of tests or y measurements.
Hundreds of
thousands of square
meters
150
0.8-0.5
4
Lenticular and pocketlike deposits with
markedly nonuniform distribution of the
metal. In general, lithologic and struc-
tural control is not clearly expressed. The
boundaries of the mineralization are
established only from the results of tests
or y measurements.
Tens of thousands
of square meters
200
0.5-0.25
5
_._
Thin veins in rupture and shear fractures.
The mineralization is very nonuniform, in
the form of small lenses, the combination
of which forms ore pillars. The boundaries
of the mineralization are established
visually.
Tens of thousands
of square meters
200
0.25-0.02
of rocks having an increased content of radioactive
elements in comparison with the clarke.
A combined mining-drilling system is used for
prospecting these deposits.
Core drilling on a network of 50-70 x 30-40 m by
lines at right angles to the general direction of the ore
bands makes it possible to determine the width and ex-
tent of the mineralized zones, assess approximately the
value of the area coefficient of ore bearing and map the
individual largest lenses roughly. The mine workings,
a system of adits, roadways and are plotted to de-
termine the outlines of the individual ore lenses.
With the normal density of the prospecting network,,
the reserves of these deposits cannot be included in
categories A2 and B. Reserves of category C1 are re-
vealed mainly by mine workings on a 40-60 x 40-60
m network. They are sometimes also considered by
interpolation between the mine workings and boreholes.
Prospecting of Thin Veins
(Fifth Group of Deposits)
This group includes hydrothermal deposits formed
by the filling of fissures. In general. they are character-
ized by extremely nonuniform distribution of the metal.
The ore accumulations are generally in the form of flat
lenses localized in thin rupture and shear fractures rest-
ing on larger dislocations. A combination of such
lenses sometimes forms ore pillars inclined at different
angles to the level; such pillars alternate with oreless
or poorly productive districts of vein fissures, the ratio
of the total area of the ore lenses to the area of the whole
ore-containing fissure being frequently more than 0.10
and generally equal to 0.04-0.03.
The prospecting of these deposits is carried out
almost exclusively by means of mine workings. Since
the deposits in the majority of cases are represented by
tens or even hundreds of parallel veins, not by one vein,
1005
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crosscuts play a very important part in the system of
mining operations. The length of the crosscuts and the
optimum distance between them are determined in
each individual case on the basis of the average extent
of the ore bodies and the established or proposed
boundaries of the distribution of rocks lithologically
favorable for mineralization.
The underground prospecting of individual veins
revealed by crosscuts is carried out by continuous trac-
ing in each prospecting-extraction level or by the com-
plete excision of blocks of size 30 x 40 to 40 x 50
m. According to existing standards of mining develop-
ment work, such distances between the boundary work-
ing are minimal but even they cannot ensure the pro-
vision of reliable data on the reserves and quality of
the ores within the limits of individual extraction
blocks.
A comparison of the calculation of the reserves
with the results of extraction indicates that the actual
reserves of metal in the individual blocks are in a num-
ber of cases several times less or more than the reserves
calculated from prospecting data. But as a result of the
mutual compensation of high and low errors,the error in
the determination of a combination of blocks (10-12
blocks) does not exceed the limits permissible for ca-
tegory C1.
During the prospecting of the above-described de-
posits an important role is played by small crosscuts or
long boreholes in the walls of the workings. The ne-
cessity for such boring operations and drilling is caused
by the generally increased tendency of the productive
fissures to ramification, with the concentration in the
ore apophyses of considerable reserves of metal some-
times exceeding the reserves in the main vein.
The importance of the different types of worRings
depends on the position of the ore pillars. In the case
of steep inclination of the latter the assessment of the
veins is carried out mainly from the data obtained as a
result of roadway drivage. When the ore pillars are
gently inclined ,the data for the assessment of the veins
1006
can be obtained mainly by driving vertical workings,
i.e., raises and staples.
The low coefficient of ore bearing and the slight
thickness of the ore veins, which are often in the form
of thin tectonic joints, exclude the possibility of a re-
liable assessment of the reserves of these deposits by
means of boreholes. Under such conditions drilling is
used only for an approximate solution of the problem of
the possible depth of the industrial mineralization.
It was established, for example, that when the ore
veins lie in a gneiss-shale stratum the lower boundary
of the uranium deposits frequently coincides with the
surface of the granite massifs forming the basement of
the surrounding rocks. The topography of this surface
can be established by drilling so-called structural bore-
holes. Small drillings from the mine workings sometimes
give a considerable effect both during prospecting and
the geological servicing of existing mines; they success-
fully replace small crosscuts during the prospecting of
parallel veins, ore apophyses and displaced parts of the
ore-containing fissures.
SUMMARY
The above-given morphological characteristics of
the present known uranium deposits can be jointly sum-
marized, as shown in the table, as follows.
Deposits of the first group prospected by drilling;
deposits of the second, third and fourth group ? by a
combination of mine workings and boreholes with a
different density of the prospecting network; deposits
of the fifth group ? by mine working only.
The groups of uranium deposits indicated in the
table also differ from each other according to the con-
ditions of classification of the reserves. During the
process of geological-prospecting operations, the reserves
of all three industrial cavItgories (A2, B and CI) can be
revealed only in deposits belonging to the first group.
In deposits of the second and third groups the reserves
do not have a higher classification than B; in deposits
of the fourth and fifth groups the extraction must be
based mainly on reserves of category C1.
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EXTERNAL y-RADIATION DOSAGE DUE TO FALLOUT OF
SEVERAL FISSION PRODUCTS
V. P. Shvedov, G. V. Yakovleva,1 M. I. Zhilkina, and
Letters to the Editor
T. P. Makarova
Translated from Atomnaya gnergiya, Vol. 7, No, 6, pp. 544-545
December, 1959
Original article submitted July 18, 1959
A flask,1 m2 area,was used to make a monthly col-
lection of radioactive fallout during 1958 in the city of
Zelenogorsk. After having been dessicated and incine-1
rated, the contents of the flask were analyzed, using al
single-channel scintillation y spectrometer with a large
CsI crystal.
y -lines whose energies were approximately 150,
500, and 750 key, and whose intensities dropped off in
periods of about 30, 40, and 70 days, were discovered
in the spectra of the fallout samples. These could be I
unambiguously attributed to the y lines of Gem, Ru193,
and (Zr+ Nb). With the aid of a 47r counter, a
calibration of the y spectrometer was made in order
to make the conversion from the area of the photo-
peak to the absolute 13 activity of each isotope. The
isotopes being identified were radiochemically separated
from the series of samples, and a subsequent measure-
ment made of their 8 activity with calibrated end-
window 13 -counters. A comparison of the spectrometer
method and the radiochemical method showed that the
error in the determination of the absolute activity of
the y emitters by the use of the spectrometer tech-
nique was at most 1010. The absolute activity of the
Cs i" cOntained in the fallout samples was determined
by the radiochemical method.
The absolute activity in the monthly fallout per
1 m2 of the earth's surface of an arbitrary isotope (Atot)
can be represented in the form of a geometrical progres-
sion
-'tot =Ao+Ane-?' I Ane-2X+ ? ? ? +Aoe-tX,
where Ao is the average activity of the daily fallout per
1 m2 of the isotope; X is the decay constant of the
isotope (days-1); t is the sampling period in days.
Or
I An (1?e -M)
tot
It is possible to determine from this the average activity
of the isotope (A0), and therefore the number of active 1
atoms of this isotope in the daily fallout. The knowledge
of the number of active atoms (which is equal to the
number of future decays of the isotope) enables one to
calculate the y radiation dosage from this isotope for
the future.
The y -radiation dosage of radioactive fallout was
calculated for a point 100 cm from the earth's surface
neglecting the shielding of the y radiation. The cal-
culation of the dosage was made by integrating the y
radiation over an infinite plane surface [1], using the
Hirschfelder formula [2, 3] to calculate l the secondary
rays.
The results of the dosage calculations are shown in
the Table. The 30-year dosage rate from ?Zr, Ru193,
and Ce141 is equal to the dosage rate for the year.
Thus, for a dosage rate in the year from the y
radiation of Cs137 equal to ?1 mr/year, the dosage rate
from Zr, Rum, and Ce14/ amounts to 7.5 mr; i.e.,
as a result of the continued tests of atomic weapons, the
short-lived isotopes make a considerable contribution to
the dosage from the external radiation. The dosage
rate from radioactive fallout in 1958 already amounts
to ?1/3 of the world-wide average dosage rate due to
cosmic radiation (28 mr). The value calculated pre-
viously [4] by us for the 30-year dosage due to radio-
active fallout for the years 1954-1956,inclusively,was
16 mr, and for the year 1957 a value of 18 mr was ob-
tained. The sharp increase in the dosage attests to the
growing danger from the testing of nuclear weapons.
30-Year Dosage Due to Radioactive Fallout in 1958
Isotope
Dosage,
Mr
(Zr ?1-N.1.)95
6,5
Rum3 , .
? 0,9
(;e141
0,1
Cs137
32,6
_ Total
40,1
1007
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LITERATURE CITED
1. G. V. Gorshkov, Gamma Radiation of Radioactive
Substances [in Russian] (LGU, Leningrad, 1956).
2. J. Hirschfelder and E. Adams, Phys. Rev. 73, 863
(1948).
3. J. Hirschfelder, J. Magee, and M. Hall, Phys. Rev.
73, 853 (1948).
4. L. I. Gedeonov, V. P. Shvedov, and G. V. Yakov-
leva, Atoffinaya fnergiya 7, 545 (1959).?
? Original Russian pagination. See C. B. translation.
* * *
CALCULATION OF THE EXTERNAL y*RADIATION'
DOSAGE DUE TO FALLOUT OF RADIOACTIVE
FISSION PRODUCTS
L. I. Gedeonov, V. P. Shvedov, and G. V. Yakovleva
Translated from Atomnaya Energiya, Vol. 7, No. 6, pp. 545-547,
December, 1959
Original article submitted May 20, 1957
In connection with the performance of atomic
weapons tests and the fallout of radioactive fission pro-
ducts over the whole earth's surface, an estimate based
on continuous observation of radioactive fallout is made
for the external y-radiation dosage. It is not possible
to make a direct measurement of the y-radiation dosage
due to radioactive fallout at great distances from the ex-
plosion site, since the natural y background is much
larger than the y radiation of the fallout of fission pro-
ducts. A calculation appears to be the only possible
method of determining the dosage.
In the present paper, an estimate is made of the
dosage of the y radiation due to fallout of fission pro-
ducts in the territory of the Leningrad region from the
beginning of the atomic weapons tests up until January
1, 1957.
The dosage was calculated for a point located 100
cm above the earth. It was assumed in the calculation
that all of the fallout of active substances remains in an
infinitely wide and thin upper layer of the earth's surface.
Such factors (which would tend to cause a decrease in
the activity) as washing out of the soil, the action of the
wind, the shielding due to surface irregularities, and
others, were not considered; only the natural decay of
the radioactive substances in the fallout was taken into
account. The y -radiation dosage was calculated from
the time of the fallout to the complete decay of the
fragments (till t = co). )Only such a calculation enables
one to tell what the upper limit of the dosage will be.
The calculation was made according to the formula
D-=kQ,
1008
where D is the dose (in roentgens), i.e., the amount of
energy evolved in 1 ems of air by the y radiation; Q
is the total number of future ,6 decays of the fission
fragments which have been deposited on 1 cm2 of soil
during the whole preceding time starting from the
moment of fallout; kis a coefficient which character-
izes the value of the dose at a height of 100 cm above the
the earth due to 1 decay per 1 cm2 on soil. .
The number of future decays of the fragment acti-
vity for an age of this activity greater than 60 days was
calculated according to formula [1]
.Q=3515at, (1)
where a is the activity of the fragments (decays /min)
which have fallen out on 1 cm2 of the soil; tis the age
of the fragments which have fallen out (days).
The number of future decays for an age of the
activity less than 60 days was found according to the
formula
Q= (t), (2)
where (p (t) was found by use of a curve given in [1].
The measurement of the activity of the fallout of fission
products per 1 cm2 of soil was made daily from the 6th
of March, 1954, according to the method described in
[2]. Activity of an unknown age was conditionally re-
lated to the middle of the series of tests just prior to
the fallout of the activity. The results of the calcula-
tion of the numbers of future decays are given in Table
1.
Considering the relatively small amount of testing
which was carried out up to 1954, one can assume that
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TABLE 1
Number of Future Decays on 1 cm2 of Soil
---------
Year of fallout
Number of future decays
on 1 cm2 of soil
1954
8,88.106
1955
14,7.106
1956
10,9.106
1954-1956
34,5.106
the activity of all the fragments which had fallen prior
to 1954 did not exceed the activity of the fragments
during 1954. So the number of future decays per cm21
of soil from all the testing is estimated as Q = 4.3.107
decays/ cm2.
The calculation of the coefficient k was carried out
in three steps; 1) the calculation of the number of y
quanta per one future B decay of the mixture of fissiOn
fragments; 2) the calculation of the flux of y quanta
from an infinite plane which passes through a 1 cm2 area
located at a height of 100 cm above the earth; 3)
calculation of the y radiation dosage in roentgens. 1,
The number of y quanta per future 13 decay dc-
pends on the age of the fragments at the time of fallont,
which for the sake of simplicity in the calculation was
taken as 75 days.
Those beta-active fragments whose proportion of a
75 day-old mixture of fragments was greater than 0.Tiol
of the total are given in Table 2.
It is taken into account in Table 2 that in the
Rufos_Rhios equilibrium chain there is one 13 decay which
is recorded, since the energy of the a particles of Ru106
is so small that in a measurement with a thick source the
they are not recorded. For this reason Pm147 and Sm151
are missing from the table.
TABLE 2
The average number of y quanta per decay is found
according to the formula
v
(3)
The average energy of the y quanta emitted is found
according to the formula
11
abc
Eav
11
aibi
5=1
(4)
At an age of 75 days, the mixture of fragments has
v = 0.45 quanta per 1 future 13 decay; Eav = 0.60 Mev.
The flux of y quanta emitted by an infinite plane
contaminated with fission fragments (passing through a
1 cm2 area 100 cm above the plane) is given by (neg-
lecting secondary radiation) formula (5) of [3].
Qv ,.
N = ? t ( ? WOW,
where N is the y -quantum flux; Q is the number of
8 decays per 1 cm2 of soil; v is the number of y
quanta per 1 8 decay; Ei (-10011) is the function Ei of
the argument (-10011); ? is the attenuation coefficient
of the rays in atmosphere in 1 cm-1 (for Eav = 0.60 Mev),
equal to 10.8 ? 10-5 cm-1.
The y -ray energy loss in air for a small coefficient
of true absorption r + a 5 amounts to.
(5)
I 1011--e?("113)1=10 (.r-1-0R)x, (6)
Relative Number of Future Decays of Fragments in a 75 Day-Old Mixture
Isotope
Period I
1
I
Yield at
time of
formation,
%
Portion of
the total
number of
future de-
cays,_a_
Number of
y quanta
per 1 13 de-
cay, b
Average
y -quantum
energy, c
_
Sr89
Sr"
y91
Zr96?N1)99
Nb"
11W"
B uinfi_m,106
Cs137
Ce"'
Ce144
Pr"'5
54 daysl
27 year
61 days
65 days
35 days I
42 days
1 year ,
33 yeari
33 days .1
290 days .
? 1
5
5
5
6
0
3
5 2,5
6
5
Q058
0,150
0,060
0,160
0,054
0,032
0,066
0,150
0,044
0,113
0,113
0
0
0
.1
1
I
0,2
0,92
0,7
0,5
0,01
0
0
0
0,72
0,75
0,5
0,8
0,66
0,15
0;08
1009
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where I = NEay; x is the path length of the y rays in
air (iri cm); (r+ 8) is the coefficient of true absorp-
tion in the Compton effect and photoeffect; r + o8 =
= 3.8 ? 10-5 cm-1.
The energy yield of the y radiation in penetrating
1 cm of air is
/ (Td-cro)=NE,av(T-1-o) Mev,
while the dose in roentgens [3] is
D=1,45-10-5NEav(t+ad.
(7)
(8)
On substituting expression (5) for N into (8), we obtain
D=--1,45105
2
Qv (r+ Eav Ei (_100 ti) r. (9)
Putting in the numerical values for I/ r + a/3, Eav, and
Ei (-100 ? ), we get
D=3,7.10-11:9 r. (10)
The value 3.7 ? 10-1? is the dose rate at a point
100 cm above the earth corresponding to 1 decay per
cm2 on the earth's surface. Estimation of this quantity
based on data in the literature yields the following
values (r/decay): 8.2 ? 10-1? [4]; 4.6 ? 10710 [5];
16 ? 10-10 [6]; 3.4 ? 10-10 [7].
One should regard the first of the values just given
as too high, since it was assumed in calculating that
for each 13 decay 1 y quantum is radiated. If one used
the value of 0.45 y quanta radiated for each decay, the
value 3.7 ? 10-1? r/decay is obtained instead, in the first
case.
The authors of [6] note that they give only the order
of magnitude of the quantity. Taking these limitations
into account, the various estimates of the value of the
dosage rate per decay agree well with the values found
in this article. On substituting the previously calculated
value Q = 4.3 ? 107 decay/ cm2 into expression (10) for
D, one obtains
D = 0.016 r for a 30-year period.
1010
The dosage value for England is estimated [8] at
0.055 r. For the USA, the value of the dosage calculated
using the assumptions of the present paper fluctuates' in
the range 0.006-0.160 r [9], depending on the distance
from the firing ground. The value of the dosage re-
ceived by humans over a period of 30 years from cos-
mic rays and the natural radioactivity of the soil is
between 4.3 and 5.5 r [10. 11].
By comparing the data adduced,it is clear that the
y -radiation dosages obtained for several countries are
approximately the same in value, and much less than
the natural y -ray dosage. Although, as is shown by
these data, the external y radiation of radioactive
fragments does not present an immediate danger, never-
theless the presence of additional radiation can be-
come a cause of undesirable genetic consequences. In
addition, a considerable part of the fallout activity be-
longs to Sr" whose capture inside an organism is
dangerous.
The authors express their gratitude to Prof. K. K.
Aglintsev for his valuable guidance and advice in the
completion of the present undertaking.
LITERATURE CITED
1. V. A. Blinov and L.' I. Gedeonov, Reactor Physics
and Heat Engineering [in Russian] Atomnaya
fnergiya (1958) Supplement No. 1, p. 96.
2. V. P. Shvedov, V. A. Blimov, L. I. Gedeonov, and
E. P. Ankudinov, Atomnaya inergiya 5, 577 (1958)!
3. G. V. Gorshkov, Gamma Radiation of Radioactive
Substances [in Russian] (LGU, Leningrad, 1956).
4. The Effects of Atomic Weapons (US Gov. Print.
Office, Washington, 1950).
5. R. Lapp, Bull.Atomic Scientists 11, 45 (1955).
6. M. Eisenbud and J. Harley, Science 121, 677 (1955).
7. I. Blifford and H. Rosenstock, Science. 123, 619
(1955).
8. J. Cockroft, Nature 175, 873 (1955).
9. M. Eisenbud and J. Harley, Science 124, 251 (1956).
10. R. Lapp, Bull. Atomic Scientists 11, 216 (1955).
11. Science 123, 1157 (1956).
*Original Russian Pagination, See C. B. translation.
* * *
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THE NEW ISOTOPES Sbn2 AND Sb114 AND THE IDENTIFICA-
TION OF SW' AND Sb115
I. B. Selinov, Ya. A. Grits, Yu. P. Kushakevich,
Yu. A. Bliodze, S. S. VasiPev, and T. N. Mikhaleva
Translated from Atomnaya gnergiya, Vol. 7, No. 6, pp. 547-549
December, 1959
Original article submitted February 7, 1959
In searching for new isotopes of antimony, and with
the aim of identifying the antimony isotopes whose half '
lives are 7 and 31 min [1], a study was undertaken of the
activities formed in sufficiently thick targets enrichedI
with tin isotopes (of mass numbers 112, 114-118) upon
irradiation of the targets in the 120-centimeter phaso-1
tron at the MGU Scientific Research Institute of Nuclear
Physics. In order to isolate the isotopes obtained in thei
(p, ri) and (p,2n)reactions, the irradiation was carried
out at several proton energies of 7 to 30 Mev.
A comparison of the activities formed in various
enriched isotopes of tin as a result of bombardment by
protons of various energies showed that the 7-minute
and 31-minute activities belonged to Sb113 and Sb116
105
104
3-103
3-103
respectively, these having been obtained in the SW"
(p, 2n) SO" and Sn116(p, 2n) SO reactions.
We did not observe in the case of SO an activity
with a half-life Ti = 60 min (which was ascribed to the
latter isotope in [2]); one can assume that the y lines
which were related to Sb116 do not in fact belong to Sb116,
but to Sb116, which has Ti = 60 min. In addition, we
discovered two new isotopes: Sb112, with T = 0.9i 0.1
min, and Sb114, with T = 3.3 ?0.3 min (Figs. 1 and 2).
These isotopes were obtained in the Sn112 (p, n) Sb112
and Sn114 (p, n) Sb114 reactions.
The chemical separation of the antimony was done
just as in [1]. In studying the short-lived isotope Sb112,
it became necessary to use an incomplete separation
1
1
.?
Group
1
Group
2
. .
T =
0.9 min
T2
(S 2
= 3.5
in (Sb
)
.
.
= 16 min
(Sblie
5
10
15
20
25
30 35
40
45
50
t, min
Fig. 1. Half-lives of radioactive isotopes of antimony chemically separated from
tin enriched with Sn112, after irradiation of the tin by protons.
Isotopic composition of the target (in perclent): Sn112 ? 52.3; Sn114? 1.5;
Snl" ? 1.5; Sn116? 11.2; Sn117 ? 4.2; Sn'118 - 11.2; Snl" ? 4; Snl" ? 10.7;
S n122 ? 1.4; S n124 ? 0.2.
Proton energy 15 Mev; exposure 1 min. 1rhe activity with a half-life of T = 3.5 min
is determined for the most part by the isotope 5b118 (T = 3.5 min), and partially by the
isotope Sbl" (T = 3.4 min), since the Sn118 content in the target is 7.5 times as large
as that of Sn114.
101_1
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t, 'TIM
25 30 35
3.105
10 5
3 10'
8
o 10
3402
to'
3.10
10
1012
5
10
15
20
i
i 1
\1.... 1111111111k
T 2 = 16 min(Sb116-)
\
/
:. \
I '? li = 3.4 min(Sbl
\
\
-,....
ij
\
T
z
.... To= 1hr(Sb11
\
i
0
lgT
8
7
6
5
4
3
t, hours
Type of
transformation
14)
Fig. 2. Half-liVes of radioactive isotopes of antimony
chemically separated from tin enriched with Sn114, after
irradiation of the tin by protons.
Isotopic composition of target (in percent): Snm ? 0.6;
Sn114? 57.2; Sn116? 3.3; Sn116? 19.6; Sn111? 10.8;
Snug ? 6.8; Sn116? 0.4; Sn126? 1.3; Sn12? 0.1;
Sn124? 0.1. Proton energy 15 Mev; exposure 1 min.
Sb li
(stable
,11P
Nbf23 istable
I T> 1018
or 20
years)
--active
wit
attc._____,
s
119
r fiv/
Sb122
I
I
1
Sb
sby
,e
18
I
Sb
\
?
b121
\
St"f
118
St"
/
/
\
\
\
' Obi
sb120I
Sb
'\
? se"
(sbyfs.)***
..
..?
.01121
.01b
12
I
1
Sb ?-?
sbt94
.0
?f?(3?
I
58 60 62 64 66 68 70 72 74 76 78 80 82
Fig. 3. Half-lives of radioactive isotopes of antimony. Neutron number N is plotted on
on the abscissa. The left branch of the curve corresponds to ? - and 13+ -active isotopes,
and the right branch corresponds to - -active isotopes. As yet undiscovered isotopes are
indicated in parentheses.
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of the antimony (about fio), in order to start the measure-
ment of the activity within 3 min after terminating the
bombardment. The initial intensity of the antimony
with Ti = 0.9 min which was separated from the target
which had been enriched with Sn112 and bombarded by
15 Mev protons was 15 times as high as the initial in-
tensity from a mixture of other isotopes of antimony.
The analogous ratio for Sb114 was equal to 30.
The maximum energy of the 13,4- emission as de-
termined by the absorption method amounted to 2.7+0.2
Mev in the case of Sb114. The gamma .spectrum, which
was measured with a scintillation spectrometer using a
100-channel pulse-height analyzer, consists of three
lines; the y line of the annihilation radiation, the
1300+30 key line, and the less intense 900+60 key line.
The gamma spectrum of Sb112 has, besides the annihila-
tion line, only one y line, whose energy is 1270+30 key.
As is evident in Fig. 3, the isotopes of antimony with
even neutron numbers (Sb113, Sb115, Sb117) have a greater
T.1 than the isotopes next to them with odd neutron
m..
numbers(Sbm 0114, shi
, ) It is to be anticipated that
the still undiscovered isotope Sb111 has a value Ti ftc
1.1 - 1.5 min; i.e., somewhat larger than the Ti
of Sb112. A more detailed description of work on the new
isotopes of antimony will be given later.
The authors express their gratitude to V. S. Zolotarev
for making enriched isotopes of tin available, to Yu. A.
Vorob'ev and the members of the phasotron staff, and
also to L. Ya. Shavtvalov for his work on the spectro-
meter.
LITERATURE CITED
1. I. P. Selinov, Yu. A. Grits, D. E. Khulelidze,
E. E. Baroni, Yu. A. Bliodze, A. G. Dentin, and
Yu. P.Kushakevich, Atomnaya Energiya 5, 660
(1958).?
2. D. Strominger, J. Hollander, and G. Seaborg, Rev.
Mod. Phys. 30, 585 (1958).
? Original Russian pagination. See C. B. translation.
* * *
STABILITY OF A CHARGED BEAM IN STORAGE SYSTEMS
A. A. Kolomenskii and A. N. Lebedev
Translated from Atomnaya nergiya, Vol. 7, No. 6, pp. 549-550
December, 1959
Original article submitted June 8, 1959
In connection with the proposal on the feasibility of
reactions with intersecting beams of relativistic particles
[1], there has been increased discussion recently con-
cerning methods of storage [2] of high current in annular
magnetic systems. Of particular interest for such systems
is the study of the interaction of the large number of
particles in a storage orbit. Besides the lateral repulsion
of the beam, which mainly affects the betatron oscilla-
tions, there are also interesting effects connected with
the azimuthal inhomogeneities of the density and the
resulting redistribution in energy of the particles.
It follows from quite simple physical consider-
ations that under certain conditions, a distribution of
the beam which is homogeneous with respect to the
azimuthal direction is unstable. For simplicity, let us
consider a monoenergetic beam. The field due to a
positive density fluctuation which is formed accelerates
particles moving in front of the fluctuation and decele-
rates particles moving behind it. If at the same time
the rotation frequency decreases with a rise in energy
dco
? 0, the fluctuation tends to be
dE
die
resolved. The condition dE ? < 0 is obtained in weak-focus-
ing and strong-focusing systems above the critical
energy. In view of the practical importance of the
question, and the physical interest which plasma effects
exhibit in storage systems, it is therefore appropriate
to examine such instability in greater detail.?
The change in energy of a particle in the presence
of an azimuthal electric field is described by the
Hamiltonian [2]
( do.) \ 1472
2 ,
(1)
*After this note was written to the press, another study
[3] was published, in which the beam stability was also
examined in the region above the critical energy.
1013
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In which the canonic momentum W is connected with the
energy E by the relation
(' (11:.
i=.\
P!
(2)
where v is the velocity of the particle. (The index S
indicates quantities evaluated at the average energy of
the stored beam.) The canonical coordinate o) which is
conjugated to W is connected with the azimuthal angle
e by the relation (I) = 0- wst; in the general case of
arbitrary periodic systems, 0 is the so-called generalized
azimuth [4]. The quantity 6(q', t) is the azimuthal com-
ponent of the electric field of the beam.
We will describe the state of the beam by the dis-
tribution function F(W, t), which can be represented
in the form of a sum
F (W, tp,1)--=-Fo (w)-1- (HT, (p,t); f < Fri, (3)
i.e., we shall examine small deviations from an equilib-
rium state which is homogeneous with respect to the
azimuthal direction. It is clear from physical consider-
ations that 6 =0 in the equilibrium state, since the
linearized kinetic equation has the form
Of at ( am-)
at -1- afq) dE )S
(4)
or, if we take the Fourier transform on the azimuthal
angle and a Laplace transform on time;
do)
(5)
In order to connect g(k) with the Fourier component of
the charge density, we make use of the fact that the
electric field of the beam is well shielded by the
horizontal covers of the vacuum chamber and is practi-
cally the same as the field of a rectilinear beam which
is located between two conducting planes. Whence
+03
2
(k, t)= i Ake \ f (14, k, t) dW ; ?y=( 1_!)_h/2(6)
R2y2 r
?CO
where R is the average radius of the orbit.
This same expression can be obtained rigorously, if
we use for the field of the shielded circular current the
expressions given, for example, in [5]. The exact
result of expression (6) will be given in a more detailed
study; we will note here only that the quantity A, which
depends on the ratio of the transverse dimensions of the
beam to the gap width d, has a value in the range 2-3
in cases of practical interest. Expression (6) was ob-
tained by using the assumption that the dimensions of
the inhomogeneity are large in comparison with the
aperture of the chamber; i.e., k