SOVIET ATOMIC ENERGY VOL. 41, NO. 2

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000700080002-8
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 113
• Document Creation Date: January 4, 2017
• Document Release Date: September 23, 2013
• Sequence Number: 2
• Publication Date: February 1, 1977
• Content Type: REPORT

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I-
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Russian Original Vol. 41, No. 2, August, 1976
February, 1977
e
SAfEAZ 41(2) 687-792 (1976)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEP1101
(ATOMNAYA iNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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Declassified and Approved For Release 2013/09/23: CIA-RDP10-02196R000700080002-8
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC?
Physics Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: M. D. Millionshchikov
Deputy Director
I. V. Kurchatov Institute of Atomic Energy
Academy of Sciences of the USSR
Moscow, USSR
Associate Editor: N. A. Vlasov
A. A. Bochvar
N. A. Dollezhal'
V. S. Fursov
I. N. Golovin
V. F. Kalinin
'A. K. Krasin
V. V. Matveev
M. G. Meshcheryakov
V. B. Shevchenko
V. I. Smirnov
A. P. Zefirov
Copyright C) 1971 Plenum Publishing Corporation, 227 West 17th Street, New York,
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permission of the publisher.
Consultants Bureau journals appear about six months after the publication of the
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CONSULTANTS BUREAU, NEW YORK AND LONDON
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New York, New-York 10011
Published monthly. Second-class postage paid at Jamaica, New York 11431.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
February, 1977
Volume 41, Number 2 August, 1976
CONTENTS
Engl./Russ.
ARTICLES
Experience in the Operation of Channels with Single-Pass Steam Generation in the Reactor
at the First Nuclear Power Station ? V. V. Dolgov, V. Ya. Kozlov,
M. E. Minashin, V. D. Petrov, V. B. Tregubov, and V. N. Sharapov
687
75
Zone Regulation of the Power of a Power Reactor ? I. Ya. Emel'yanov, E. V. Filipchuk,
A. G. Filippov, V. V. Shevchenko, P. T. Potapenko, and V. T. Neboyan.
693
81
Redistribution and Mobility of Uranium during the Metamorphism of Volcanogenic
Formations ? V. P. Kovalev, A. D. Nozhkin, A. G. Mironov, and Z. V. Malyasova
697
85
Mathematical Simulation of Processes in the Extractive Reprocessing of Nuclear Fuel.
4. Separation of Uranium and Plutonium by the Method of Displacement
Re-Extraction ? A. M. Rozen and M. Ya. Zel'venskii
703
91
Mathematical Simulation of Processes in the Extractive Reprocessing of Nuclear Fuel.
5. Separation of Uranium and Plutonium by the Method of Re-Extraction with a Weak
Acid ? A. M. Rozen and M. Ya. Zel'venskii
708
95
Liquid ?Vapor Equilibrium in Systems with Dilute Solutions of Metal Fluorides in
Uranium Hexafluoride ? V. N. Prusakov, V. K. Ezhov, and E. A. Efremov
711
98
Distribution of the Losses during the Accumulation of Isotopes of the Transuranium
Elements ? Yu. P. Kormushkin, A. V. Klinov, and Yu. G. Toporov ? ?
715
102
Slowing Down of Particles in Highly Anisotropic Scattering. Statistical Fluctuations of
Energy Losses in Collisions ? Yu. A. Medvedev and E. V. Metelkin
718
105
Total Backscattering Coefficients for Obliquely Incident 15-25-MeV Electrons
? V. V. Gordeev, V. P. Kovalev, and V. I. Isaev
725
110
50-MeV Electron Synchrotron with Cyclotron Preacceleration ? S. P. Velikanov,
V. I. Kvochka, V. S. Panasyuk, V. V. Sanochkin, Ya. M. Spektor, B. M. Stepanov,
Yu. M. Tereshkin, and V. B. Khromchenko
727
113
Prospects for the Use of Nuclear-Physics Analytic Methods in Biology as Illustrated by
the Wilt Problem ? V. Ya. Vyropaev, I. F. Kharisov, 0. D. Maslov,
E. L. Zhuravleva, and L. P. Kul'kina
732
118
DEPOSITED ARTICLES
Problem of the Intensity of an Electron Synchrotron with Cyclotron Preacceleration ?
M. Yu. Novikov, Yu. M. Tereshkin, and V. B. Khromchenko
737
125
Effect of Hard Ore-Enclosing Rock on the Efficiency of Underground Leaching
?I. K. Lutsenko, A. A. Burykin, and V. K. Bubnov
738
126
Interpretation of Autoionic Images of the Dislocation Structure of Uranium by Means of a
Computer ?A. L. Suvorov and T. L. Razinkova
739
127
Determination of the Degree of Sensitivity of Mass-Spectrometers to Microimpurities
?M. L. Aleksandrov, N. A. Konovalova and N. S. Pliss
740
128
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CONTENTS
(continued)
EngL/Russ.
y Field Initiated by a Monodirectional Neutron Source in Air ? A. V. Zhemerev,
Yu. A. Medvedev, and B. M. Stepanov
741
129
Basic Laws for the Formation of Tissue Doses from Collimated Beams of Monoenergetic
Neutrons ? V. N. Ivanov
742
129
Total Cross Section for the Interaction of Cold Neutrons with Water ? S. B. Stepanov
and V. E. Zhitarev
743
130
LETTERS TO THE EDITOR
Effect of the Composition of Friable Ore-Bearing Rocks on the Effectiveness of the
Process of Underground Leaching ? A. A. Burykin, I. K. Lutsenko,
B. V. Vorob'ev, and S. I. Korotkov
744
132
Determination of Specific Energy Losses by Charged Particles in Matter
? G. N. Potetyunko
746
134
Use of "Beam Unfolding" for Calculation of j3-Flux Absorption in the Segment Model
? V. A. Kuz'minykh and S. A. Vorob'ev
749
136
Measurement of Spectral Characteristics of Slow-Neutron Fields Using Cadmium Ratios
of Activation Detectors ? I. A. Yaritsyna, E. P. Kucheryavenko, I. A. Kharitonov,
and T. M. Kuteeva
752
138
Investigation of the Removal of T and 85Kr during Processing of Irradiated UO2 in an
Oxygen Medium ? A. T. Ageenkov and E. M. Valuev
755'
140
Pulsed Air-Cored Betatron Powered from a Magnetocumulative Generator
? A. I. Pavlovskii, G. D. Kuleshov, R. Z. Lyudaev, L. N. Robkin,
and A. S. Fedotkin
757
142
Increase in Beam Radius and Size of Image Ellipsoid because of Errors in a Linear
Proton Accelerator ? A. D. Vlasov
760
144
Flowmeter with Radiation Detector for Wells ? I. G. Skovorodnikov . ......... .
762
146
Radioactivity of the Water lin the Ground Shield of Accelerators ? V. D. Balukova,
V. S. Lukanins B. S. Sychev, and S. I. Ushakov
765
148
Effect of y Radiation of Presown Seeds on the Crop Yield and Productivity of Open-Ground
Tomatoes under the Conditions of the Mongolian Peoples Republic ? D. Voloozh
and D. Zhamyansuren
767
149
INFORMATION
Jubilee Celebrations at Dubna ? A. I. Artemov
770
153
Standards of the International Electrotechnical Commission in Nuclear Instrument
Manufacture ? V. V. Matveev and L. G. Kiselev
774
156
CONFERENCES AND MEETINGS
New Materials and Progressive Technology in the Production of Plants for Nuclear
Power Stations ? Z. G. Usubov
776
157
Seminar on Water-Cooled/Water-Moderated Reactors in France ? A. D. Amaev
and V. N. Filippov
778
158
International Congress on Reactors ? V. I. Mikhan
780
160
American ?Japanese Seminar on the Planning, Operation, and Use of Pulsed Fast
Reactors ? E . P. Shabalin
781
161
Symposium on the Treatment of Radioactive Waste from the Nuclear Fuel Cycle
? N. V. Krylova and Yu. P. Martynov
783?
161
The Seventh Spring Seminar on High-Energy Physics ? S. G. Matinyan
785
163
INSTRUMENTS
The GUPS-1 Immersion Follower 7-Level Gauge ? I. I. Kreindlin, Yu. I. Pakhunkov,
and I. R. Rubashevskii
786
163
REVIEWS
S. V. Mamikonyan. Equipment and Methods of Fluorescent X-Ray Radiometric Analysis
? Reviewed by E. M. Filippov
788
165
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CONTENTS
(continued)
A..'n. Engl./Russ.
I. K. Morozova, A. I. Gromova, V. V. Gerasimov, V. A. Kucheryaev,
and V. V. Demidova. The Loss and Deposition of Corrosion Products of Reactor
Materials ?Reviewed by N. V. Potekhin 789 166
N. D. Tyufyakov and A. S. Shtan'. Principles of Neutron Radiography ? Reviewed by
Yu. V. Sivintsev 790 166
The Russian press date (podpisano k pechati) of this issue was 7/26/1976.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
EXPERIENCE IN THE OPERATION OF CHANNELS
WITH SINGLE-PASS STEAM GENERATION IN THE
REACTOR AT THE FIRST NUCLEAR POWER STATION
V. V. Dolgov, V. Ya. Yozlov,
M. E. Minashin, V. D. Petrov,
V. B. Tregubov, and V. N. Sharapov
UDC 621,039.524.2.034.44
By employing various methods of intensifying heat exchange [1-3], we are able to advance the limit of
crisis boiling in the channels almost to the point where the water is completely evaporated in flow. A transi-
tion to a lower level of heat exchange under these conditions does not lead to catastrophic results. The so-
called temperature "jumps" at the cooling surface during such transitions assume a smooth character and ex-
tend the full length of the channel. The maximum temperature rise does not exceed the design value for dry
saturated steam with a flow Gx (where G is the two-phase flow and x is the critical steam content). Intensifying
elements in the transition zone, and their location in regions of reduced thermal load coupled with overall de-
sign modifications can ensure long-term ,fault-free operation of the cooling surface.
Tubular fuel elements type BAES (Beloyarsk Nuclear Power Station) at the world's first nuclear power
station (Beloyarsk) have intensifying elements in the form of circumferential Corrugations projecting within
the tube itself [4, 5]. These intensifiers allow even the first stage to achieve reliable heat absorption
from the fuel elements with a heat content by weight of 60-7070 at the output (under analogous conditions, but
with a smooth tube, the crisis point was readhed at a steam content of 25-3a). Tests were then carried out
with full evaporation and reheat, without an intermediate separator, i.e., on the single-pass steam generator
principle. Reassuring results were obtained.
The present article describes the experimental fuel channels with fuel elements and heat-exchange inten-
sifiers, the channel connection scheme in the reactor loop, and the test conditions, together with some of the
test results.
Scheme of Experimental Loop and Measurement. Tests carried out on fuel elements with heat-exchange
intensifiers were carried out on a loop of the PV-2 reactor [6] at the Beloyarsk Nuclear Power Station in the
same loop that had been used for the boiling crisis experiments [7]. Two experimental fuel channels were con-
nected in series in the loop (Fig. 1). The new element in the loop is a mixing-type condenser built in the form
TABLE 1. Average Parameters of Test
Conditions
P arameters
Number of experimental
reactor channels
2 3
Total power of four fuel
elements, kW
140+7
145+7
172+9
Flow rate of water, kg/h
305+10
300+10
312+10
Heat flow in center of
output fuelelemen2t
calculated, kW/ m
700+70
650+60
1120+100
Steam content by wt. in
the input flow to the
channel, 0/0
30-40
35-45
30-40
Temperature at the out-
put, *C
342+4
350+5
400+10
Steam pressure at the
output, atm
123+3
123+3
123+3
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 75-81, August, 1976. Original article sub-
mitted April 5, 1976.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
687
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Fig. 1
Fig. 1. Connection scheme of experimen-
tal channels in loop: 1) pump reservoir;
2) regulating valve; 3) flowmeter dia-
phragm; 4) boiling channel; 5) full eva-
poration channel; 6) manometer channel;
7) mixing-type condenser; 8) manifold;
9) circulating pump.
Fig. 2. Experimental channel: 1) elonga-
tion compensator; 2) fuel element; 3) ther-
mocouple housing; 4) herrhetically sealed
case; 5) output thermodOuple.
Fig. 2
of a jet pump. ?The operating medium in this condenser is cooling water, and the injected medium is steam
(a mixture of steam and water). The coolant is circulated round the loop by the circulating pump. The broken
line in Fig. 1 represents the remaining coolant equipment of the loop with its pipes and metering equi'pment,
feed pump, and gas compensator reservoir. This equipment provide e the regulation and maintains the pre-
determined water parameters in the pump reservoir. During the tests, particular attention was directed to
maintaining a stable flow of coolant in the experimental loop. For this reason, boiling was not permitted in
the other channels between the pump reservoir and manifold. The cooling water was carried to the condenser
through a reserve system. The water flows in the main and reserve systems were regulated by valves. Regu-
lation of relatively small flow rates at high pressure drops across the valve was carried out by valves taking
the form of pairs of plungers with two counteracting plates, having a depth of undercut along the forming
plunger that varies in a linear manner.
The flow rate of the coolant was varied by means of a unit comprising a metering diaphragm, differen-
tial manometer type DM-6, and a secondary instrument type DSR-1 of accuracy class 2.5 with a 10CP/0 scale.
The coolant temperature was measured by means of a calibration thermocouple type KhA, made from cable
type KTMS with an outside diameter of 1.5 mm. The thermocouple was mounted in a housing made of tube
with an outside diameter of 4 mm and a wall thickness of 0.5 mm. Contact between the thermocouple and the
housing past which the coolant flows was created by hard solder. These thermocouples were installed at the
output of each of the four fuel elements (see Fig. 1) and also at the output TCo, 4 m from the output section
of the fuel elements in the coolant flow.
The secondary instrument for these thermocouples was an automatic potentiometer type KSP-4, of ac-
curacy class 0.25 at 20 mV, equipped with a switch. The coolant, pressure was measured at the output of the
channel with the aid of a unit consisting of a type MED transducer with a type DSR secondary instrument of
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Fig. 3. Location of thermocouples at the output fuel elements
in channels 1, 2, and 3.
accuracy class 2.5 on range 160 kgf/cm2. A standard Manometer was connected in parallel. To measure
the temperature of the outer case of the fuel element, surface thermocouples were used with two secondary
instruments typeEPP-0.9 equipped with switches. The scales of these instruments were 200-400 and 300-
500?C. A portable potentiometer was connected to the first of these instruments to compensate the excess emf
when measuring temperatures above 400?C.
Construction of Channel and Fuel Element. The design of the experimental channel is illustrated in Fig.
2. Each of the experimental channels had a pair of fuel elements mounted one after the other within the flow
of coolant. Both fuel elements of the channel had heat-exchange intensifiers in the form of annular corrugations
projecting into the flow of coolant. To compensate for the difference in temperature of the lower part of the
extended branches, a condenser coil was installed. Pockets for the thermocouples were welded in the tube
above and below the thermocouples. The fuel elements in the experimental channels were separated from the
reactor medium by cores, which also reduced the flow of heat between fuel elements and heat exchange with
the graphite lining. The leads to the thermocouples were led out through a hermetically sealed union. Other-
wise, the channel resembled a standard reactor fuel channel.
The radial dimensions of the experimental fuel elements were identical with those of the Beloyarsk ?
Nuclear Power Station (Fig. 3). The steam was superheated in the second channel in a quarter of the coolant
flow to the fuel element. The superheating regime was tested in three channels altogether.
To reduce the transient zone, and via this, the temperature of the fuel element in which superheated
steam is first obtained (channel 1), the heat generator was profiled, ensuring that the heat flow in the output
parts was reduced and the corrugation pitch needed to intensify the heat transfer to the steam was reduced ac-
cordingly. The annular corrugations projected 0.5 to 1 mm into the flow, 0.5 mm in the fuel elements of
channels 2 and 3, while the fuel and corrugation pitch were distributed uniformly.
The maximum permissible operating temperatures of the outer covers of all fuel elements in channels
1 and 2 was 480?C. Therefore, the greatest steam superheat above the saturation temperature ts did not ex-
ceed 30-40?C. All the preconnected channels had similar fuel elements (see Fig. 1).
A fuel element with an operating temperature of up to 600?C was installed in the output arm of channel 3,
enabling the steam superheat to be increased to 90-100?C above ts at greater thermal loads.
The surface thermocouples for measuring the fuel element temperatures were manufactured using type
KTMS cable of 1.5-mm outside diameter, taking the form of calibrated type KhA thermocouples. The hot
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340 350 380 400 *C 3I40 350 380 400 ?C
1
Fig. 4
z
380 400?C
400 420 4140 460 480 ?
Fig. 5
Fig. 4. Steam temperatures at distances of 1) 150 m and 2) 4.5 m from the output of the
fuel element.
Fig. 5. Temperature of fuel element and steam in channel 3: 1) fuel element at point 9,
motion of transition zone; 2) steam at output from fuel element.
junctions of these thermocouples were formed by welding the cable sheath with thermoelectrodes, the welding
quality being reliably controlled by x-ray examination. The contact between the thermocouple and the casing
of the fuel element was created by means of spring clips made out of type R-18 alloy. To improve this .ther-.
mal contact, the thermocouple was first soldered to the clip with hard solder and a local contact formed under
the cylindrical surface with the outer case of the fuel element. The thermocouples were marked with numbers
(see Fig. 3).
Stages of Testing the Channels. The tests on the channels to obtain superheated steam by means of a
single-pass scheme were started on a reactor at the Beloyarsk Nuclear Power Station in N?xember 1973 (see
Table 1). Channel 1 was intended for checking the method of carrying out tests of this nature. The system
used for monitoring and maintaining the heat engineering parameters and the nature of their variation under
transient conditions were verified. At this stage, the feed water for the loop (steam power station condensate)
was subjected to further purification in ion exchange filters. The first channel operated under conditions with
steam superheated by 10 to 30?C above its saturation temperature for about 1150 h and for about 2050 h with an
80 to 9a steam content at the output. In June 1974, channel 1 was withdrawn without damage from the reactor
in accordance with the program. The temperature of the fuel element did not vary significantly during the course
of these tests.
When the tests were carried out on channel 2, instead of being withdrawn, the channel remained installed
over a longer period of time, the condensate being employed directly as feedwater for the loop, without any
additional purification. The hardness of the feedwater was 2 to 3 ?g . equiv./kg, pH =6.5 to 3.2, dry residue
1.1 to 1.3 mg/kg. Exchange of water in the loop occured as a consequence of making up for natural leakage.
The hardness of the water in the loop circuit was 3 to 14 pig ? equiv./kg, pH =5.7 to 6.9, dry residue 1.2 to 2.8
mg/kg. Channel 2 was tested in the reactor for about 15 months, of which about 125 days were under super-
heated steam conditions. Up to this time, the thermocouples on the casing of the output fuel element showed
virtually no change of reading. Channel 2 was withdrawn from the reactor without damage. It was then re-
placed by channel 3.
The main purpose of the experiments with channel 3 was to study the nature of the temperature regime
in a fuel element with relatively large heat flows, especially in the transition zone, while achieving a, signifi-
cant steam superheat.
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Some Features of the Variations in Heat Engineering Parameters. Before the start of the experiments,
the power of each pair of channels was calibrated with respect to the power of the reactor. This calibration
was carried out at an increased flow rate of water through the channels to prevent boiling.
Before each series of experiments, it was also necessary to regulate the flow rates during the first
rise in power of the experimental channels. With the power of the channels standing at approximately 5CPR)
of maximum, preliminary regulation of the flow rate and temperature of the water in the loop was carried
out. As the power rose, these parameters were readjusted. The parameters was stabilized under conditions
with a steam content of 80 to 90% (by calculation) at the output. The reactor power was then raised in small
steps until superheated steam appeared at the output of the last fuel element in sequence (thermocouple 12,
Fig. 1). The need for such regulation during the first approach to superheat arises out of specific features of
the experimental loop circuit. It was carried out so that successive approaches to superheat could be accom-
plished simply by increasing the power of the channels (reactor) without regulating the flow rate and tempera-
ture of the water.
Two forms of regime instability were brought to light during the experiments. The first instability was
due to fluctuations of flow in the experimental channels. Steam or a steam?water mixture was released from
the channel into the receiver manifold (see Fig. 1) where water underheated to ts was fed in parallel with the
channel. The process of compensation in the collector was accompanied by pressure pulses, which gave rise
to fluctuations of flow rate in the channel from 10 to 15 sec. The flow rate of the water in the experimental
channel was stabilized by a condenser of the mixing type in the form of a water injector (see Fig. 1).
The second regime instability in the experimental channels was due to fluctuations of reactor power,
basically within the dead zone of the reactor power regulator (-1% rated). It was observed that the cause of
these fluctuations was a periodic variation in the temperature of the water in the primary loop of the reactor
following the steam generator, with a period of ?75 sec and an amplitude of ?0.5?C. A reduction in the dead
zone of the power regulator leadstoareductionin the amplitude of these temperature fluctuations, as would
be expected.
The thermocouple equipment for measuring the steam temperature near the output from the fuel element
drew attention to the correspondence of the reading of this thermocouple to the mean temperature of the steam.
In particular, it is presumed that this thermocouple is able to indicate the temperature of the superheated
steam at steam contents x >KPU(117)), for low
acidities ([NO3-1 Y--HNO3) the coefficient of separation j3will be relatively high. The scheme proposed in [4]
is based on the use of 0.3 M HNO3 as the re-extracting agent (Fig. 1).
In the present article we used the method of mathematical simulation for investigating separation re-
extraction; we compare the calculation results with the experimental results, and we compare the two proces-
ses of separating uranium and plutonium without using reducing agents.
To do this, we performed calculations for the scheme of [4] and found the characteristics of the process,
Yex and XV, which define, respectively, the degree of removal of plutonium from the uranium extract and
Pu
the degree of removal of uranium from the plutonium re-extract.
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We varied the following parameters of the process: the acidity of the re-extracting agent (X
NO3), the
flow rates of the extracting agent (V') and the re-extracting agent (L), the ratio of the flow rates (nre = (Vo+
V')/L and ne =V'/L), and the number of stages in each section of the apparatus (Nre and Ne). As the nominal
regime we took the regime of [4] (its parameters are shown in Fig. 1); for this regime we compare the experi-
mental distribution [4] and the calculated distribution of the uranium and plutonium concentration in the aqueous
and organic phases for each stage of the apparatus. As can be seen from Fig. 2, the agreement is good.
In the calculations only one parameter in each regime was different from its nominal value.
The results of the calculations, in the form Of curves showing the variation of Yept and Xtx as functions
of the indicated parameters, are given in Fig. 3, from which it can be seen that, as in the process of displace-
ment re-extraction [3], variation of the acidity of the re-extracting agent and of the flow-rate values produce
opposite effects on the indicators of the separation of uranium and plutonium (as the plutonium content in the
uranium extract decreases, there is an increase in the uranium content of the plutonium re-extract).
It should be noted that the regime of [4] is sufficiently close to the optimal regime* for an apparatus
with eight stages in the re-extraction section and five in the uranium pre-extraction section.
The calculations also showed that the addition of one stage to the uranium pre-extraction section de-
creases XUex b p a factor of 3.18 [vex
u remains practically unchanged); the addition of one stage to the re-ex-
traction section reduces YMby a factor of 2.68 (without changing Xfix).
pe_xu -
Thus, acceptable separation of uranium and plutonium ci =106 g/liter, Xtx =10 mg/liter) would have
been feasible in an apparatus with 16 re-extraction stages and eight extraction stages in the regime proposed
in [4].
The maximum accumulation of plutonium in the aqueous phase in the nominal regime amounts to 190 mg/
liter (a factor of 6); an increase in the re-extraction section does not change the accumulation; for Ne =8 we
find that XI:n,uax =325 mg/liter (a factor of 11).
The accumulation of plutonium in this process is much less than in the .displacement re-extraction pro-
cess; the highest accumulation value obtained for calculations of separation re-extraction is 80 times the ori-
ginal plutonium concentration (30 mg/liter), while in the displacement re-extraction process even in the no-
minal regime the accumulation is 70 times the initial value [3]. The relatively low internal ,accumulation of
plutonium is an unquestionable advantage of the process.
The values for the accumulation of microquantities of plutonium are obtained more accurately in the cal- .
culation of separation re-extraction than in the calculation of displacement re-extraction, when the plutonium,
accumulating in the aqueous phase up to tens of grams, becomes a macrocomponent capable of competing with
uranium for the extracting agent. Consequently, weak-acid re-extraction can be used for separating uranium
and plutonium. The sensitivity of this process to variation of the parameters is less than in the displacement
re-extraction process, and the internal accumulation of plutonium, as indicated above, is considerably lower.
In order to obtain the specified separation (10 mg of uranium per liter in the plutonium re-extract and 10,:tg
of plutonium per kg of uranium) in the nominal regime of operation of [4] we require an apparatus with 24 stages.
Thus, weak-acid re-extractionhas advantages over displacement re-extraction. However, we also can-
not afford to disregard reductive re-extraction; although it involves a loss of reagents, it does require a far
smaller number of stages [1], i.e., has an advantage in the apparatus layout.
? A properly justified choice of one or another of the separation schemes (or a combination of several ele-
ments from different schemes) requires engineering?economic calculations that take account of the proper-
ties of the fuel being reprocessed and the possibilities of automatic control.
LITERATURE CITED
1. V. B. Sheychenko et al., Fourth Geneva Conference, Report No. 435 [in Russian] (1971).
2. US Patent No. 3,714,324, January 30, 1973.
3. A. M. Rozen and M. Ya. ZePvenskii, At. Energ., 41, No. 2, 91 (1976).
4. J. Ortega and A. Rusheed, Anales de Quimice, 69, No. 1, 117 (1973).
*This regime corresponds to the point of intersection of the characteristics for YI,xu and Xtx, when high separa-
tion is achieved.
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LIQUID ?VAPOR EQUILIBRIUM IN SYSTEMS WITH DILUTE
SOLUTIONS OF METAL FLUORIDES IN URANIUM HEXAFLUORIDE
V. N. Prusakov, V. K. Ezhov, UDC 541.12.035.4
and E. A. Efremov
Investigations of the distribution of a substance between the vapor and liquid phases of a solution have
shown that at greatdilutions the solute obeys Henry's law [1, 2]. However, Devyatyk and Vlasov [3], and
Stepanov et al. [4], postulated the existence of a nonequilibrium state of a dilute solution; they proposed
methods for calculating the thermodynamic activity coefficients.
We have therefore made an experimental investigation of liquid ?vapor equilibrium in systems with dilute
solutions of tellurium, molybdenum, and tungsten hexafluorides and of vanadium, antimony, and tantalum pen-
tafluorides in uranium hexafluoride. The results were compared with the theoretical data.
The uranium hexafluoride used in the experiments was purified by fractional distillation. The purity of
the end product was monitored by mass-spectrometric analysis. Radioactive fluorides 123+128TeF6, 88MoF6,
124SbF5, 185WF6, and 182TaF5 were obtained by fluorination of the corresponding very pure metals, preactivated
with thermal neutrons. Vanadium pentafluoride, labeled with the radioactive isotope 48V, was obtained by
fluorination of vanadium metal, obtained after evaporation of a radioactive nitric acid solution of vanadium
followed by roasting and reduction of the precipitate with hydrogen.
Before use the fluoride was freed from hydrogen fluoride by sorption of the latter on sodium fluoride
granules at ?195?C.
Fragments of the radioactive metal (0.01-0.02 g) were fluorinated directly in the still in a boat (Fig. 1).
The entire apparatus was prepassivated with fluorine and thermostated at 75?C. The boat was heated to 400?C.
After the weighed portion of the metal was fluorinated, the still was cooled with liquid nitrogen, and the ura-
nium fluoride from the capsule was condensed in it. The initial composition of the mixture was calculated
from the change in weight of the metal and the capsule.
The fluoride solution obtained was subjected to differential distillation at a pressure of 1520 ? 10 mm and
74.0?0.4?C. For this purpose the magnetic stirrer of the still was switched on. The solution vapor passed
Fluorine
Vacuum
Fig. 1. Schematic diagram of apparatus: 1) jacket; 2) boat; 3)
stirrer; 4) manometer; 5) magnet; 6) throttle valve; 7) still; 8)
electric furnace; 9) lead housing; 10) FEU-13;11) crystal; 12)
flow cell; 13) airthermostat; 14) capsule; 15) trap.
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 98-101, August, 1976. Original article sub-
mitted August 16, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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2,7
2,3
1,9
1,5
ii
47
0 -0,05 -410 -0,15 -420 tg
Fig. 2. Logarithmic graph of pulse count rate vs degree of dis-
tillation for the systems UF6--MF6 and UF6?MF5.
through a flow cell and throttle valve to a trap at 5?C. The radioactive vapor was registered by a photoelec-
tric multiplier with continuous recording of the signal on a KSP-4 pen recorder. The solution was thermo-
stated by means of a water thermostat. The precalibrated throttle valve ensured a constant distillation rate
at a constant pressure drop.
The maximum degree of compression of the solution in the cell was 30. After distillation the solution
was redistilled into the still and the experiment was repeated.
A preliminary investigation was made of the equilibrium conditions for distillation of a solution of TeF6
in UF6. This showed that the equilibrium of the process was retained at a stirrer speed of 100-200 rpm and
a vapor phase offtake rate of 1-3 g/(cm2 ? min).
The experimental data on distillation of binary solutions were processed by means of the equation
Go ?Gi
Go
where 10 and IL are, respectively, the counting rates of pulses from the radioactive label in the vapor being
distilled at the beginning of the experiment and during it, Go is the initial amount of the solution (in grams),
G. is the amount of distillate obtained (in grams), and a is the separation factor.
The equation is a modification of Rayleigh's integral equation for simple distillation [5] applied to the
radiometric method of monitoring the change in the content of a component in vapor being distilled (Fig. 2).
Table 1 lists the values of the separation factors obtained. It also gives the activity coefficients of the
solute 112, calculated from the equations
for a highly volatile impurity
and
712
TABLE 1. Separation Factors of UF6-Based Binary Systems
at 74?C
?
Separation factor
Activity
coeffi-
Investigated concentra-
Dilute solution
experi-
mental
ideal
cient of
solute
don range, wt
.
TeF6 in UF6
10,66+0,05
11,73
0,91
1.10-2-6.10-5
WF6 in UF6
1,39+0,01
2,86
0,49
2.10--2-1?10-2
MoFein UF6
1,22+0,01
1,73
0,70
1,8?10-i-9.10-2
VF6 in UF6
1,28+0,01
1,86
0,69
7.10-3-1.10-3
SbF6 inUFe
6,53?0,05
26,5
4,06
1,5?10-2-8-10-4
,
TaF5 in UF6
217+1
661
3,04
3,3.10-2-9.10-4
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TABLE 2. Separation Factors of Metal Fluo-
rides in the Multicomponent System UF6-
M0F6-SbF5- TaFG at 74?C
System
ISepara
Solute 'tionfac-
tor
anda ?
Concentration
range investi-
gated, wt. crio
? UF,-Mae
UF6 SbF5
UF6 - TaF5
MoFs
SbF5
TaF5
1,25
6,40
215
10-i-10-2
10-2-10-4
10-2-10-4
-4 -0,4-4 -0,8 -, -112
Zg?
Fig. 3. Logarithmic graph of area
under y spectrum vs degree of distil-
lation.
P?
for a high-boiling impurity,
Pa 72
where pi) and 11 are, respectively, the saturated vapor pressures of the solvent and solute.
When a multicomponent solution of M0F6-SbF5- TaFG in UFG was distilled, the signal was sent from the
FEU-13 to a AI-256 pulse-analyzerto register the y spectra of the vapor being distilled. It is known [6] that in
the y-spectral method of radioisotope analysis the overall pulse count rate through all the analyzer channels
from one isotope Eh is proportional to the overall area under all the energy peaks Si; the experimental data
(Fig. 3) were processed by means of the equation
lg Si = (cc -1) lg G0-G, lg So.
Table 2 lists the values of the separation factors obtained.
A linear relation is observed between the logarithm of the counting rate and the logarithm of the degree
of distillation (Fig. 2), i.e., the separation factor remains constant at different solution concentrations.
Thus Henry's law holds for these dilute solutions throughout the concentration range investigated.
Using the Hildebrand van Laar [7], Hildebrand -Scatchard [7], Stepanov -Devyatykh [4], and Vla soy -
Devyatykh [3] methods we made a theoretical estimate of the activity coefficients of TeF6, WF6, MoF6, VFG,
SbFG, and TaFG in binary dilute solutions of uranium hexafluoride; the results are given in Table 3. In view
of the fact that, unlike the metal hexafluor ides, vanadium, antimony, andtantalum pentafluorides may exist
in polymerized form [8, 9], their activity coefficients were calculated on the assumption that the degree of
association is 1 or 4.
TABLE 3. Activity Coefficients of Fluorides of Certain Metals in Dilute Solutions of
Uranium Hexafluoride at 74?C
Solute
Degree of
association
of solute
Activity coefficient calculated
in
lExperimental
coef-
ficient of
solute
[71
[71
[4]
(cell-solute
[4]
(cell-
solvent)
[3] with a rid without allow-activity
ance for mutual influence
of solvent and solute)
TeFs
VVF6
Alas
VF5
SbFs
TaFs
1
1
1
3?
4
1
4
1,408
1,016
1,000
1,821
1,821
1,868
1,868
3,976
3,976
1,021
1,013
1,015
7,193
291,70
4,388
9,931 -
17,508
2,517
1,441
0,986
0,986
1,097
0,114
4,514
0,046
3,129
0,095
0,979
0,811
0,910
0,703
0,293
1,271
0,139
3,516
0,269
3,441
1,337
1,448
15,13
15,13
11,89
11,89
2195
2195
0,121
0,231
0,405
9367
9367
11133
11133
4,47.100
4,47.108
0,91
0,49
0,70
0,69
4,06
3,04
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TABLE 4. Activity Coefficients of Components
of Dilute Solutions at 74?C
Dilute solution
vcalc
expl.
Discre -
pancy, ok
MoF6 in UF6
0,740
0,70
5,7
WF6 in UF6
0,494
0,49
0,8
VF5 in UF6
0,757
0,69
8,8
SbF5 in UF6
5,740
4,06
41,4
TaF5 in UFB
3,120
3,04
2,6
From Table 3 it follows that it is only in the case of a solution of vanadium pentafluoride in uranium
hexafluoride that the experimental activity coefficient [4] is close to its theoretical value (degree of associa-
tion 1).
In the other cases the theoretical activity coefficients do not coincide with the experimental values.
Note that the behavior of dilute solutions of metal pentafluorides in uranium hexafluoride is best represented
by assuming that they exist as monomeric molecules. Dissociation of the compounds at high dilution is not
unexpected, but further experimental data are required to confirm that in dilute solutions the predominant
form of existence of metal pentafluoride molecules is the monomer.
A dilute solution of antimony pentafluoride in uranium hexafluoride is best described (as in the case of
medium concentrations) by the Hildebrand ?Scatchard [10] theory of regular solutions.
The coincidence of the experimental separation factors of binary dilute systems UF6?M0F6, UF6?
SbF5, and UF6?TaF5 with their values in the multicomponent system UF6?MoF6?SbF5? TaF5 is apparently
due to the absence of a mutual influence of the impurity molecules of different species (cf. Tables 1 and 2).
It is known that compounds are not formed in binary systems of metal fluorides [10, 12-14].
The experimental data on liquid ?vapor equilibrium in systems with binary mixtures of the hexafluorides
of uranium, tungsten [12], and molybdenum [14] and pentafluorides of vanadium [15], tantalum [10], and an-
timony [10] for the region of medium concentrations were approximated in the form of a polynomial of degree
lgTi=a0+aisd-a2x2+ . tine,
where x is the concentration of the solute in mole fractions.
The use of this equation to determine the activity coefficients of the components of dilute solutions from
the data for medium concentrations enabled us to obtain the activity coefficients of the solute (Table 4).
For the systems UF6?WF6, UF6?MoF6, UF6?UF5, and UF6?TaF5 the theoretical activity coefficient
of the solute is close to the experimental value.
LITERATURE CITED
1. Ya. D. Zel'venskii et al., Teor. Osnovy Khim. Tekh., 1, No. 2, 229 (1967).
2. Ya. D. Zel'venskii, A. A. Efremov, and V. A. Shalygin, Izotopy v SSSR, No. 5, 25 (1966).
3. G. G. Devyatykh and S. M. Vlasov; Zh. Fiz. Khim., 39, 1171 (1965).
4. V. M. Stepanov et al., Zh. Fiz. Khim., 44, 445 (1970).
5. Ya. D. Zelrvenskii, J. Feitek, and V. A. Shalygin, Zh. Fiz. Khim., 35, 2602 (1961).
6. V. 0. Vyazemskii et al., The Scintillation Method in Radiometry [in Russian], Gosatomizdat, Moscow
(1961), p. 299.
7. E. A. Moelwyn-Hughes, Physical Chemistry, Pergamon, Elmsford (1969).
8. C. Hoffman et al., J. Phys. Chem., 62, 364 (1953).
9. E Lesley, J. Beattie, and P. Jones, J. Chem. Soc., No. 2, 210 (1972).
10. V. K. Ezhov, Zh. Neorgan. Khim., 17, No. 7, 2043 (1972)?
11. V. B. Kagan, Azeotropy and Extractive Rectification [in Russian], Goskhimizdat, Leningrad (1961).
12. V. N. Prusakov and V. K. Ezhov, At. Energ., 25, No. 1, 64 (1968).
13. V. N. Prusakov and V. K. Ezhov, At. Energ., 28, No. 6, 496 (1970).
14. V. N. Prusakov et al., in: Proc. Symp. SEA (Soviet Economic Aid) "Investigations in the field of irra-
diated fuel processing," Karlovy Vary, Feb. 26-March 2, 1968 [in Russian], p. 331.
15. R. Shrewsbarry and B. Musulin, Science, 145, 1452 (1964).
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DISTRIBUTION OF THE LOSSES DURING THE ACCUMULATION
OF ISOTOPES OF THE TRANSURANIUM ELEMENTS
Yu. P. Kormushkin, A. V. Klinov, UDC 621.039.8.002:621.039.554
and Yu. G. Toporov
The authors of [1] investigated for the first time the selection of the costwise optimal accumulation con-
ditions of isotopes of transuranium elements used in radioisotope power generation. We derived in our work
an analytic expression for the cost of the unit mass of an isotope to be accumulated; we assumed that the cost
of a single absorbed neutron is constant in the simplest accumulation chain with a single end-product.
The simultaneous formation of several products is characteristic of the general isotope-accumulation
process. Nevertheless, the selection of economically advantageous accumulation conditions requires know-
ledge of the production cost of each isotope to be accumulated.
In the reactor irradiation stage, one must consider two loss components whose combination, referred to
a single nucleus of the new isotope produced, decides the cost of the isotope. The first component is related
to the cost of the raw material consumed and, more specifically, results from the nuclei of the forerunner
nuclide which are lost in the accumulation process. The second component results from the losses during
the irradiation, i.e., from the production of excess neutrons in the reactor, whose absorption by the fore-
runner nuclei leads to the formation of the subsequent isotope in the accumulation chain.
In a specialized isotope-producing reactor, the latter component depends upon the total reactor losses.
In a multipurpose reactor, the component depends upon the fraction of general reactor losses in a program
for isotope accumulation. The determination of this fraction is an independent problem; methods for solving
this problem can be found in 12, 31. When this fraction is known and the losses for winning the initial material
are known, the proposed method allows the calculation of the cost of a nucleus of each isotope of any accumula-
tion chain in the stage of the reactor irradiation.
It is generally accepted that the accumulation of isotopes in an open chain without branching can be de-
scribed by a system of nonlinear differential equations:
dNot ? (0-1- X0] N (t);
dt
d. (t)
? lb (t) Xi] N (t) +a 0 (t) N0 (t);
dt
(t)(1)
? (t) N (I)
dt
-3- a_1 (I) N (I),
where Ni(t) denotes the number of nuclei of the i-th isotope of the accumulation chain at the time t; b(t) +
denotes the rate at which nuclei of the i-th isotope disappear via all possible channels; a(t) denotes the rate at
which the (i + 1)-th isotope is formed; and Xi denotes the decay constant of the i-th isotope. We have
csia (E) 41)(E , dE;
a i (t) = a,p(E) 'To (E , dE ,
provided that the nuclei of the (i+ 1)-th isotope are formed by the capture of neutrons by the forerunner nuclei;
a? =X'
. provided that the nuclei of the (i + 1)-th isotope are formed in the decay of forerunner nuclei; cri (F)
L L a
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 102-104, August, 1976. Original article sub-
mitted June 17, 1975; revision submitted December 18, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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denotes the cross section of the absorption of neutrons with the energy E by nuclei of the i-th isotope; and
a4(E) denotes the cross section of the radiative capture of neutrons with the energy E by nuclei of the i-th
isotope. The condition Ni (t) It =.0= Ni (0) holds.
The equations of system (1) are the equations of the balance and relate the rate of change in the number
of nuclei of each isotope of the chain to both the rate at which the nuclei are formed from the preceding iso-
topes and the rate at which these nuclei disappear over all possible channels.
In analogy to the equations of system (1) one can state differential equations which describe the redistri-
bution of the losses among the isotopes of the accumulation chain during the irradiation process. The approach
to the description of the process establishes a relation between the redistribution of the losses and the redis-
tribution of the isotope nuclei and reflects the physics of the phenomenon, because in the case of neutron cap-
ture, both a transfer of the losses associated with the cost of the forerunner nucleus and an increase in the
cost of the nuclei owing to irradiation losses occur in addition to the transition of the nucleus of one isotope of
the chain into a nucleus of the next isotope. In this case the integration of the system of differential equations
describing the balance of the losses and the integration of system (1) allow the calculation of the cost of the
isotope nuclei of the chain and make it possible to bring into account the physical and thermal characteristics
of the irradiating apparatus, the charge of the initial material, etc.
The system of differential equations of the balance of losses, which corresponds to the equation system
(1), can be written in the following form*:
duo (t) 00(t) +41uo (t);
at
dui (t) = (b1(t) Ai] u, (t)
dt
[bo (t) xoluo (0+ bo(t) No (t) v (t);
dui (t) _ (0+241 ui (0+ I
(2)
dt
+ (t) 4- u,_, (1)
+b_1 (t) N t_i (t) v (t),
where ui(t) lt_o =14(0). In addition to the previously introduced notation, the following notation is used: u1(t)
denotes the total cost of all nuclei of the 1-th isotope; ui(t)=CE(t)Ni(t) (where Ci(t) denotes the cost of anucleus of
the 1-th isotope at the time t).
C irr (t)
I bi (t) N1 (t)
i=4:1
(3)
where Cirr(t) denotes the target irradiation losses per unit time; and n denotes the number of isotopes of the
accumulation chain.
Since the quantity b(t)N1(t) represents the total number of neutrons absorbed per unit time by the
nuclei of the isotopes of the accumulation chain, the function v(t) is equal to the cost of an absorbed neutron at
the time t. Furthermore, obviously .L u? (0) denotes the losses incurred in acquiring the initial material.t
L=o
In analogy to the equations of system (1), the left side of the i-th equation of system (2) indicates the
rate at which the cost of all nuclei of the i-th isotope changes. One can in this way easily determine the mean-
ing of each term of the right sides of equation system (2). The first term of the right side of the i-th equation
represents the rate at which the total cost resulting from the disappearance of the nuclei of the i-th isotope
decreases. The second term denotes the rate at which the cost is increased by the forerunner nuclei. The
rate of nuclei formation in equation system (1) is characterized either by the decay rate of the forerunner nu-
clei when radioactive decay is the isotope-producing process, or by the rate of neutron capture by the fore-
runner in the case of radiative capture. In differential-equation system (2), the rate at which the cost increases
is characterized (in contrast to the rate at which nuclei arrive) by the rate at which the nuclei of the forerunner
*Naturally, in each real case the form of equation system (1) and of the corresponding system of the balance of
the losses depends upon the form of the accumulation chain.
f Usually the material purchased is a mixture of isotopes. In this case one must know the "history" of winning
the initial material for obtaining the initial conditions of equation system (2), i.e., for separating the losses
incurred in the acquisition of the initial isotopes.
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disappear via all possible channels, because the total cost of all expended forerunner nuclei must be ascribed
to the nuclei which are formed of each isotope of the chain; one must include the cost of the fission nuclei and
the nuclei which decayed outside the chain under consideration.
' The third term on the right sides of equation system (2) has no analog in equation system (1) and denotes
the rate at which the cost increases owing to irradiation losses. Thus, when the isotope nuclei are formed by
the decay of a forerunner, this term of the equation must disappear, because in this case losses related to
the absorption of neutrons do not arise. When the isotope nuclei are formed by radiative capture of neutrons
by the forerunner, this term of the equation is the product of the rate at which neutrons are absorbed by the
forerunner nuclei times the cost of a single absorbed neutron.
We can conclude from Eq. (3) that the neutrons absorbed by fission fragments in the materials of the
building and the leakage neutrons are assumed to be neutrons lost for the accumulation process; the cost of
these neutrons is distributed among the isotopes of the chain in proportion to the absorption rates (equation
system (2)). Thus, the lower the ratio of the number of neutrons absorbed by the isotopes of the chain to the
total number of neutrons, the higher the cost of the resulting nuclei. The missing third term in the first equa-
tion of system (2) corresponds to the assumption that the cost of the nuclei of the first initial isotope in the
open chain is independent of the time of irradiation.
Obviously, at any time the total cost of all accumulated nuclei (including the cost of the nuclei converted
after the last isotope of the chain under consideration) must be equal to the sum of the losses incurred in the
acquisition of the initial material and the losses incurred in target irradiation. Let us show that the system
of differential equations (2) satisfies this condition. To do this, we switch from system (2) to the following
system of integral equations:
We obtain the formula
uo (t) = _ [bo (e) + &duo (t') ?
0
u (t) = ? [b (e) 4- I tit (e ) de
[bo ) kol ui; (e ) de
bo (e) No (e)v (e ) de +
u1 (t)= (b (t') u (e) de
0
[bi_j (e) + u1_1 (e ) de
b (e ) N (t') v (e ) de ?
2 ui (0+ [b. (e) +In](e) de= 2 + cirr (e) de,
0 0
(4)
(5)
by summation over the equations of system (4), where X ui(t) denotes the total cost of the nuclei of all iso-
tl=?
topes in the accumulation chain under consideration; f[bn(V)+ xn]uri(V)dt' denotes the total cost of the nuclei
n 0
converted after the last isotope in the chain under consideration; X u? denotes the losses incurred in the ac-
i= o
quisition of the initial isotopes; and t Cirr
(t')dt' denotes the losses incurred in the target irradiation.
0
Equation (5) indicates that system (2) satisfies the above condition. The number of nonvanishing terms
in the expression X LIP is equal to the number of the initial isotopes.
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Thus, the method which we developed for calculating the distribution of the losses in the accumulation of
isotopes of the transuranium elements makes it possible to calculate the cost of the nuclei of each isotope of
any accumulation chain in dependence on the irradiation time; the method makes it possible to take into con-
sideration the influence of the characteristics of both the irradiating apparatus and the target, i.e., it is pos-
sible to calculate a .quantity which can be the criterion for the economic optimization of those characteristics.
LITERATURE CITED
1. V. P. Terent'ev et al., At. Energ., 29, No. 4, 260 (1970).
2. V. A. Tsykanov, At. Energ., 31, No. 15 (1971).
3. V. I. Zelenov, S. G. Karpechko, and A. D. Nikiforov, At. Energ., 39, No. 1, 9 (1975).
SLOWING DOWN OF PARTICLES IN HIGHLY ANISOTROPIC
SCATTERING. STATISTICAL FLUCTUATIONS OF ENERGY
LOSSES IN COLLISIONS
Yu. A. Medvedev and E. V. Metelkin UDC 539.124.17
The theory of the steady-state slowing down of particles in matter is of considerable interest and has a
wide range of applications. Information on the spatial and energy spectra of particles is needed to solve a num-
ber of problems of reactor physics, shielding physics, nuclear physics, etc. [1-4].
Since an exact solution of the steady-state integrodifferential Boltzmann equation describing the slowing-
down process presents formidable mathematical difficulties, a number of approximate methods have been de-
veloped which enable the particle spectra to be calculated with sufficient accuracy [1-4]. In most of these
methods the distribution function is expanded in a series of spherical harmonics as functions of the direction
of the velocity of the particles. This procedure decreases the number of independent variables but increases
the number of equations to be solved.
'A relatively simple solution was obtained for the elastic slowing down of neutrons for spherically sym-
metric scattering in the center of mass system. In this case it is sufficient to retain only the first two terms
in the expansion of the distribution function in spherical harmonics for neutrons slowing down at "intermediate"
distances. This leads to the well-known 131- or "diffusion" approximation.
As noted in [1] the assumption of spherical symmetry of the angular distribution of elastically scattered
neutrons ceases to be valid for energies > 100 keV. At such energies the angular distribution of neutrons is
peaked in the forward direction even in the center of mass system [1, 5].
For highly anisotropic scattering a fairly large number of terms must be retained in the expansion of the
distribution function in spherical harmonics (see [6] for more details) and a computational technique must be
used to obtain the final result.
This difficulty can be circumvented by assuming that in highly anisotropic scattering a particle loses a
certain fraction of its energy in each interaction without changing its direction. The first equation describing
such a process was derived and solved by Landau [7] in determining the fluctuations of ionization losses of
charged particles in thin layers of material when the change in direction of a particle in slowing down can be
neglected. The fluctuations (or energy spectrum of the particles) in layers of material whose thickness is com-
parable with the total ionization range were investigated in [8] using the equation derived in [7]. If a charged
particle experiences a negligible change in direction in penetrating a certain layer of material (highly anisotro-
pic scattering) the distribution function obtained in [8] will describe the energy spectrum of the particles (or
the fluctuations of ionization losses) at a given distance from the source. Otherwise the result in [8] describes
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 105-110, August, 1976. Original article sub-
mitted November 10, 1975; revision submitted March 15, 1976.
7.18
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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the change in the energy spectrum along the actual path of the particle, which is appreciably different from
rectilinear because of multiple scattering. The latter result is of interest in determining the energy and mass
of particles from the nature of their tracks in photoemulsions, or in the measurement of filters which absorb
particles, since it follows from the condition that the particle spectrum at a given distance has a finite width
that particlres-Of the same energy can traverse various paths in coming to rest.
The solution obtained in [8] for thin absorbers is rigorous for layers of material of such a thickness that
the average energy lost by charged particles in penetrating them is small in comparison with the energy itself.
The results of [8] taking account of the change in energy of the particles in slowing down were obtained from
qualitative arguments and are not completely rigorous as will be shown later.
In the present paper we calculate analytically the steady-state spatial and energy spectra of particles,
slowing down in matter when the energy loss per collision is a small fraction of the energy itself. The results
can be used to investigate the propagation of gamma rays, neutrons, and charged particles in matter. For
highly anisotropic scattering these results describe the particle spectrum at a distance from the source, or
after the particles have penetrated a thickness of material, which is small enough so that the direction of a
particle has not changed much. Otherwise the results obtaineddescribetheenergy spectrum of particles along
the actual path, or the energy fluctuations along the trajectory.
The following fact should be noted. For energies high enough so that the effect of anisotropy in the elas-
tic scattering of neutrons cannot be neglected, inelastic scattering processes in which there is an appreciable
change in the initial energy can affect the slowing down of neutrons. Therefore the results obtained can be
used for neutrons in the energy range [E+, E+ ? El] (here E+ is the source energy and El is the energy of the
first excited state of the moderator nuclei) where the neutron slowing down occurs only as a result of elastic
scattering processes, and the effect of inelastic scattering can be taken into account by the method described
in [9]. For the same reason these results can be applied for soft gamma rays with energies E ? mec2, where
me is the Mass of an electron and c is the speed of light [2]. Charged particles, particularly heavy particles,
lose only a small fraction of their energy in inelastic collisions [3, 4].
The steady-state slowing down in matter of particles from a plane monodirectional monoenergetic source
is described by the Boltzmann equation [1]:
aiD(E; r;
tu, +(Es+ I)C) (E; r;
= dE' E; 11)
o -1
x (I)(E'; r;
(I)
where r is the coordinate of a point in space measured along the normal to the source plane, 'a is the cosine of
the angle between the direction of motion of the particle and the normal to the source plane, 44, r,&) is the
neutron flux per unit ranges of E, r, and A; E s E, pi) is the probability per unit path that a particle
with energy E' moving in the direction IA' is scattered in the direction ? in an element dm and acquires an energy
E in the range a ; E s is the total scattering cross section and Ea is the total absorption cross section.
We seek the solution of Eq. (1) in the form
(1)(r, E, [)= ?(? 1) 0(r, E).
Substituting (2) into (1) and integrating over cl?from?lto + lweobtain
where
OCI) (aEr , r)
?.(Es+ Ea) (r , E)= d E' (E')
X P (E' E)(1)(r, E) (r) (E.? E),
P (E' E) Es (E' E)1Z.(E');
Is (E' E)= 42,(E' E;
(2)
(3)
If we understand by r the path traversed by the particle, Eq. (3), which agrees with the equation derived
in [7], describes the slowing down of particles along the actual path r. For highly anisotropic scattering its
solution gives the distribution function at short distances from the source (cf. [2]).
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If in Eq. (3) we replace Es by v =vEs, ; by y =vEa, and r by t, it agrees exactly with the equation de-
scribing the slowing down of particles in an infinite medium for a pulsed monoenergetic source uniformly dis-
tributed in space, and can be solved by the method developed in [10] for functions v, y, and P(E'--E) of ar-
bitrary form. The result obtained in [10] is valid for A(E) ? E and Ea ?Es(A(E) is the average energy lost by
a particle in a collision).
If Ea ?Es, absorption, which determines the decrease in the total number of particles, has little effect
on the character of the energy spectrum (see [10] with respect to the ratio Ea/Es). Therefore from now on
we assume that Ea ?E s and neglect the effect of absorption on the shape of the neutron energy-spectrum. This
effect is taken into account directly in using results (22) and (43) of [10]. From results obtained earlier [10]
it follows that for Ea =const absorption does not affect the shape of the energy spectrum. This conclusion is
rather obvious since in this case absorption is eliminated from Eq. (3) by the substitution CE; r) =431(E; r)exp
(? rEa).
?
Using the results from:[10]and making appropriate changes (cf. above) the solution of (3) can be written
in the form
where e is given by
8mE!r) ic2.(r) exp (r)
41;) (r; E)
K2(r) femE(r) 2 }
(r)= ?(6.-E ;
E+
r dE AZ s;
E+
I 8m 12 c dEb ) -1
L A (8 ) Zs (em) J j AZ2 /X2
A (E') (E' E) P (E' E) dE;
b2 (E') [E' (E')? P (E' E)dE
(4)
(5)
(6)
(7)
It follows from (4) that for slowing down along a trajectory the particles are grouped in energy close to
a certain average value ?m (r) characteristic for each point of the trajectory. This method of focusing can be
understood from the following considerations. The rate of displacement of particles down the energy scale as
they move along a trajectory (? dem/dr -AEs) depends on their energy. Therefore if the quantity AEs de-
creases with decreasing energy, particles whose energy at a given point of the trajectory is smaller- (larger)
than the average are slowed down less (more) effectively in further motion along the trajectory and fall into
the region of average energy. These notions are in a certain sense analogous to concepts of the energy focus-
ing of neutrons from a pulsed monoenergetic-source uniformly distributed in space as they slow down in an in-
finite medium as described in detail in [11].
It follows from the results of [10] that if
E8= 0)E; A = AmE00;
El? = const; do) = const?
the energy focusing of particles will occur for
n+q1; n1( for n q 0).
Mathematically this means that under conditions (9) and (10) the function K(r), which decreases with
distance, cannot take on values smaller than ?E/A(E) ?1. Otherwise the width of the distribution function
could increase without bound.
Let us investigate the nature of the change of the energy spectrum of neutrons as they move along a tra-
jectory. It is known [1] that for elastic scattering of neutrons
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P (E' E) = t? (p[1.--k(1--)] X 0 (E' ? E)0 [E ? (1? )E'1,p
where cp0.4) =1 + E(0070) P/(?) is a function characterizing the angular distribution of elastically scattered
neutrons in the enter of mass system, 0(z) is aunitary function, 0 =4M/(M+ 1)2, and M is the mass number of
the moderator nuclei.
Substituting (11) into (8) we obtain
b2 (E) = ViE22
Since
ri
(E) = 4114)(0 =
21
(13)
-1
2a2 1
Sao 3
(E)
3ao
000)
1 2]
(12)
(where': is the average value of the cosine of the scattering angle and A2 is the mean square value), the results
(12) can be rewritten in a more physically descriptive form:
10
AE = TfIE [1? (E)1; b2 (E) 4 2E2 [K2 (E)? (E)21. (14)
It follows from (14) that b2(E) a- 0 and A(E) a0. For ? =1,A(E)=b2(E) =O.
Let us investigate the nature of the neutron spectrum under the conditions
p.(E)=const; pz (E) = const; Zs = ZT)Eq,
which make for easy calculations in (5) and (7) and at the same time are sufficiently general.
Using (5), (7), (14), and (15) we obtain:
for q=0
for q*0
sm(r)= E exp ??Fo as ;
4 1
K (r) =
02_Th2 8 rZs '
2 1-t I .
r=
of3 (1 ?To zos LE& (E)0.
K(r)= K (r) ? 4q F en, \24-1-1
13 (I ?TO 6 L
(15)
(16)
(17)
(18)
(19)
where 6 =1
These results show that for a constant elastic scattering cross section (q =0) the average energy around
which the neutrons are grouped in their motion along a trajectory depends on the source energy and decreases
exponentially with distance (16). In this case the -width of the energy spectrum increases monotonically [K
1/r, cf. 117]]. Since our results are valid for K(r) ?1[10], Eqs. (16) and (17) can be used at distances
4
132 (1_ To2o 29 (20)
which for heavy moderators (6 ?1) and highly anisotropic scattering (1 ? ?1) are appreciably larger than the
neutron mean free path /s =1/E5?
When the elastic scattering cross section increases with energy (q>0), the average neutron energy de-
creases monotonically with distance [Ern ? (1/r), cf. (18)]. The width of the energy spectrum in this case in-
creases monotonically, approaching the constant value Ko =4q/6 (1 ?11)6 '..1E/A(E) ? 1 (19). For (Em/E.F)cl ?1
the nature of the neutron energy spectrum is independent of the source energy and is determined by the pro-
perties of the moderating medium.
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If the elastic scattering cross section decreases with increasing energy (q v(06 (I ?T1) -17 A (E)
>1 we can write Eq. (4) in the form
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1:1) (r, E)dE= dE exp f [8,1(j)2-(--0E12
'[/23I2 (r)
where
and em(r) is determined from
E+
(r)
52 (r) =4 (en') , r dEp2 (E)
K (r) =17 Ica (E) '
St
E+
dE
r=
k (E) ?
En,
(28)
(29)
(30)
We assume as in [8] that the particles penetrate a thin enough layer of material so that the average
change in energy is small in comparison with the energy itself. In this case assuming that p2(E) and kst(E)
are constants we obtain
522(r)= rp2; Ern (r)= E+ st ?
Substituting (31) into (28) gives a result which agrees with [3, 8].
The change in energy of particles during slowing down was taken into account qualitatively in [8]. To
do this it was proposed to replace the multiplication by r on the right-hand side of the first of Eqs. (31) by
integration over dr and thento transform this integral into an integral over energy by using (30). Thus the re-
sult obtained in [8] agrees in form with (28) where a(r) has the following form:
(31)
E+
Qo (r) ? dkEP2 (E) ?
st(E)
ern.
(32)
We illustrate the difference between (32) and (29) by considering the propagation of nonrelativistic fast
heavy charged particles in matter. In this case [3, 4]
p2 (E) = 4C m:c4z2 = const;
(33)
(
E)= 2Cmernch2 1 r 4E me
st E 111 m (34)
2e
where m and ze are the mass and charge of the moving particle, and C=7Pelr? The final result can be ob-
tained in a simple and descriptive form.
By substituting (33) and (34) into Eq. (32) of [8] it follows that
where r is the path length traversed by a particle.
Substituting (33) and (34) into (29) and (30) and treating the logarithm as a slowly varying function we
obtain
(E12 ft ? (1? r Kg]
'C22 (r) m2reni[-4 [t?r/ R1
E+ m
n e
I mJ
(35)
(36)
(37)
where R =E 172kst (E ?)
It is obvious that II is only of the same order of magnitude as the total range of a charged particle in
matter since it has already been noted that Eq. (34) is valid only in the high-energy region (for energies > 1.5
MeV for protons and> 5 MeV for alpha particles [3]). For fast particles this agreement may be close (when
E? is large).
Using (35) and (37) we obtain
ONO 2x (1? x)
Q2(r) [1? (1? x)21 kx R (38)
It follows from (38) that our results agree with those of [8] for thin layers of material, i.e., ?for small
x, since as x-0
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212((rr)
0 (1 2?
(39)
Equation (35) was well confirmed experimentally [12]. It should be noted that in this case samples of
rather thin foils (x ?1) were used. For a foil thickness even of the order 0.2 R we find from (39) that the
difference betwee (35) and (37) is ic1, which is within the limits of experimental error. The difference be-
tween (35) and (37) begins to be important for penetration through sufficiently thick layers of material (x=0.5,
S220/02=0.67).
It follows from (38) that in the penetration of sufficiently thick layers of material the width of the energy
spectrum of the particles must increase more rapidly than predicted by the results in [8], approaching infinity
as r --R. However our results are valid so long as the width of the energy spectrum is small, i.e., for K ?1,
and also as long as Eq. (34) is valid. Using (29), (36), and (37) we obtain
(1-71R)2
K (r) =2 ln [ 4E* me ]
In this case we find from the condition K ?1 that our results are valid at distances
R?r me 1
2m
n { 41E+ mme
(40)
(41)
i.e., along most of the path traversed by a particle before coming to rest if Eq. (34) holds. This shows that
energy fluctuations are negligible along most of the path.
LITERATURE CITED
1. A. Weinberg and E. Wigner, The Physical Theory of Neutron Chain Reactors, Univ. Chicago (1958).
2. 0. I. Leipunskii, B. V. Novozhilov, and V. N. Sakharov, Propagation of Gamma Rays inMatter [in
Russian], Fizmatgiz, Moscow (1960).
3. B. Rossi, High Energy Particles, Prentice-Hall, New York (1952).
4. S. V. Starodubtsev and A. M. Romanov, Penetration of Charged Particles Through Matter [in Russian],
Akad. Nauk UzbekSSR, Tashkent (1962).
5. M. N. Nikolaev. and N. 0. Bazazyants, Anisotropy of Elastic Scattering of Neutrons [in Russian],
Atomizdat, Moscow (1972).
6. E. Oblow, K. Kin, and H. Goldstein, Nucl. Sci. and Engng., 54, 72 (1974).
7. L. D. Landau, On the Ionization Loss of Fast Particles. Collected Works, Vol. 1 [in Russian] Nauka,
Moscow (1969), p. 482,
8. I. Ya. Pomeranchuk, Zh. Eksperim. Teor. Fiz., 18, No. 8, 759 (1948).
9. Yu. A. Medvedev, E. V. Metelkin, and G. Ya. Trukhanov, At. nerg., 36, 277 (1974).
10. Yu. A. Medvedev et al., At. itnerg., 38, 156 (1975).
11. M. V. Kazarnovskii, Trudy FIAN, 11, 176 (1959).
12. C. Madsen and P. Venkateswarlu, Phys. Rev., 74, 1782 (1948).
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TOTALL,ERACKSCATTERING COEFFICIENTS FOR
OBLIQUELY INCIDENT 15-25-MeV ELECTRONS
V. V. Gordeev, V. P. Kovalev, UDC 539.171.2
and V. I. Isaev
Total coefficients, angular distributions, and other characteristics of backscattered electrons are needed
for shielding calculations, the shaping of radiation fields, etc.
It is rather difficult to describe differential and total characteristics theoretically. Satisfactory results
have been obtained under a number of restrictions [1, 2]. At the same time total election backscattering coef-
ficents have been measured in only a few cases [3, 4].
Total backscattering coefficients for 4.7-14-MeV electrons incident obliquely on aluminum and lead tar-
gets of semi infinite thickness were measured in [3]. Similar measurements for aluminum, iron, copper, and
lead using 12.8-25-MeV electrons were reported in [4]. We have performed relative measurements of total
electron backscattering coefficients as a function of target thickness and the angle of incidence of the electron
beam for aluminum, copper, and lead targets.
The measurements were performed at the LUE-25 electron linear accelerator [5]. A beam of electrons
1 cm in diameter from the accelerator was incident on a target in air at a distance of 7 cm from the exit window
of the accelerator. The targets were 10 cm in diameter and varied in thickness from 0.81 to 10.5 g/cm2. In
order to record the electrons which penetrated a target of thickness less than the electron range in the target
material a copper hemispherical shell 2 cm thick and 10 cm in outside diameter was connected to the target.
The hemisphere was placed so that the electrons which penetrated the target were incident nearly normally
on the hemisphere, since the total electron backscattering coefficient is minimum for normal incidence. The
target and hemisphere were rotated by remote control. The charge deposited on the target and hemisphere
was collected on a 100-mF energy-storage capacitorwhose potential was measured by an electrometer ampli-
fier. The discharge time of the whole circuit was approximately three orders of magnitude longer than the
irradiation time. The charge incident on the target was monitored by a secondary emission detector. Follow-
ing [4] we can write
1 ? (0, x) qt (0, x)-1- q (0, x)
1 ?710 (x) qto (x)-F qs, 0 (x) ' (1)
where n , x) is the backscattering coefficient for electrons incident on the target surface, 0 is the angle be-
tween the normal to the target and the direction of the incident beam, x is the target thickness, q(0, x) is the
Fig. 1. Total electron backscatter-
ing coefficients for copper and lead
targets at 0) 15, x) 20, and A) 25
MeV.
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 110-112, August, 1976. Original article sub-
mitted August 6, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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%
30
20
10
JO
20
10
_ a
70?C
Fig. 2. Dependence of electron backscattering coefficients on target thickness and the angle
of incidence for a) aluminum and b) copper at 0) 15, x) 20, and A) 25 MeV.
Fig. 3, Dependence of total electron backscattering coefficients on target thickness and the
angle of incidence for lead at 0) 15, x) 20, and A) 25 MeV.
charge deposited on the target and hemisphere, q5(0, x) is the charge of secondary electrons, n0(x), qto(x),
and q80(x) are, respectively, the backscattering coefficient, the charge taken from the target and hemisphere,
and the charge of secondary electrons for normal incidence of the electron beam on the target. The values of
qt(9, x) and q0(x) were obtained during the course of the experiment, and the values of '0() were taken from
[6, 7]. Following 18] the values of qs(O, x) were calculated from the expression
48 (0, x)=48o (x) 60 (1 +PI(O, x)], (2)
where 60 is the secondary emission coefficient for the incident beam, and 13 is the efficiency of scattered elec-
trons in forming secondary electrons. For the range of electron energies investigated =1. The values of
60 given in [6] are 2.1, 2.8, and 4% for aluminum, copper, and lead, respectively. 60 varies slowly with
energy and was assumed constant in the calculations.
Using Eqs. (1) and (2) it is easy to Obtain the relation
, 1-60 ri qt (0, x) ? gt (0,
10(X)
(0, 3;) 1+ 60 L (x) q10 (x) ?
(3)
The results were processed in the following way. Using Eq. (3) the value of t0(x) was calculated as a
function of the target thickness for normal fncidence of the ele'ctrOn beam-. Then i 6, x) was calculated by
using these values.
Figure 1 shows the measured values of the total electron backscattering coefficients for various angles
of incidence of the electron beam on targets of senii-infinite thickness.
The experimental data are adequately described by the empirical fon/Ulla
(0, 00) = exp [a+ b (1 ?cos0)1,
where a and b are coefficients depending on energy and the target material. For lead a =3 ? 0
0.05 E; for copper a =1.15 ?0.03 E, b =3.8 + 0.02 E (here E is the electron energy in MeV).
a and b are equal to 0.35 and 4.71 respectively at E =15 MeV. The values of i p, co) in Eq. (4)
percent.
Figures 2 and 3 show the measured values of the total electron backscattering coefficients as functions
of the target thickness for various angles of incidence of the initial beam. The values of n , x) increase with
increasing target thickness and reach a maximum for a thickness approximately equal to x=cos0/(1+ cos0),
where x is in units of the extrapolated electron range in the target material. This is true for the whole energy
range studied. The error of the relative measurements is determined mainly by the error of the electrometer
(4)
.06 E , b=2 +
For aluminum
are given in
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amplifier, and is ?10 for the ratio q(6, x)/q0 (x). The maximum error of the measurements in [7] is no
more than ?12.5%. Because of its small absolute value the error in the determination of 60 does not appreci-
ably affect the error in the measured value of ri (0, x) .
LITERATURE CITED
1. R. Dashen, Phys. Rev., 134A, A1025 (1964).
2. N. P. Kalashnikov and V. A. Mashinin, in: Proc. Second All-Union Symp. on the Interaction of Atomic
Particles with a Solid [in Russian] (1972), p. 362.
3. S. Okabe, T. Tabata, and R. Ito, Ann. Rep. Rad. Center Osaka Pref., 4, 50 (1963).
4. V. P. Kovalev et al., At. itnerg., 32, 342 (1972).
5. V.1. Ermakov et at., At. nerg., 29, 206 (1970).
6. T. Tabata, Phys. Rev., 162, 336 (1967).
7. D. Harder and L. Metger, Z. Naturforsch., 23a, 1675 (1968).
8. L. N. Dobretsov and T. L. Matskevich, Zh. Tekh. Fiz., 27, 734 (1957).
50-MeV ELECTRON SYNCHROTRON WITH CYCLOTRON
PREACCELERATION
S. P. Velikanov, V. I. Kvochka
V. S. Panasyuk, V. V. Sanochkin,
Ya. M. Spektor, B. M. Stepanov,
Yu. M. Tereshkin, and V. B. Khromchenko
UDC 621.3.038.61
The operating principles and design of pulsed accelerators with an extremely strong magnetic field have
been described [1]; in [2], there is a model of an electron cyclic accelerator with a pulsed magnetic field with
which experiments were performed on the acceleration of electrons to 2 MeV in the field of an H111 standing
wave. Elements of the theory of cyclic acceleration of particles in a cylindrical cavity containing an H111 wave
have been presented [3]. One of the characteristics of the acceleration principle is the preacceleration of
particles to relativistic energy along a spiralling orbit by the electric field of a standing wave at a fixed fre-
quency. Further acceleration is carried out in the field of this same wave and also in a rotational electric
field to maximum energy along an orbit of constant radius.
This paper discusses a cyclic electron accelerator constructed for use as a source of synchrotron radia-
tion in the vacuum ultraviolet region and also discusses the results of preliminary experiments intended to check
the theory given in [3]. The operating principles of the accelerator have been described [1-3].
Accelerator Design
The main design feature of the accelerator is that the electromagnet for the guide magnetic field is at
the same time an accelerating uhf resonant cavity and a vacuum chamber [1-3]. Because of this, the frequency
of the uhf oscillator is selected on the basis of minimal energy capacity in the excitation system for the elec-
tromagnet. Optimization of the normal mode of the resonant cavity with respect to this parameter leads to an
oscillator frequency value wo 1.8 ? 10" sec-I, which corresponds to a relativistic orbit radius rr =1.6 cm.
It is necessary to accelerate electrons to an energy E =50 MeV in order to obtain particle radiation in the re-
quired wavelength region (Xs S. 600 A).
The following basic units in the design of the accelerator can be identified: electromagnet, resonant
cavity, acceleration chamber, excitation system for the electromagnet, oscillator for the accelerating field,
and particle injector.
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 113-117, August, 1976. Original article sub-
mitted July 14, 1975.
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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To uhf oscillator
To pulsed-current
generator
pichrotron
ow
auon
a
n 10
25
20
15
10
10
15 I 20 215 P, mm
rr =15
Fig. 1. a) Diagram of electromagnet with acceleration chamber: 1) accelera-
tion chamber; 2) injector; 3) unit for excitation of resonant cavity; 4) electro-
magnet; 5) guard cylinders. b) External view of electromagnet assembled
with acceleration chamber: 1) electromagnet; 2) guard cylinders; 3) injector;
4) tightening clamps; 5) acceleration chamber; 6) vacuum channel. c) Depen-
dence of magnetic field decay index in median plane of electromagnet on dis-
tance from the axis.
Electromagnet, Resonant Cavity, and Acceleration Chamber. To obtain the specified accelerator para-
meters, it is necessary to excite a guiding magnetic field with an induction B 10 T on the orbit. This ex-
plains the choice of an iron-free design for the electromagnet. The electromagnet (Fig. la, b) is a massive
single-turn loop, the internal surface of which must create the required falloff of the magnetic field and act
as a cavity resonator with a normal frequency equal to the frequency of the accelerating field. Figure lc shows
the dependence of the decay index on distance from the electromagnet axis in the median plane. The shape of
the internal profile of the electromagnet is selected so that the decay index at the relativistic orbit is suffi-
ciently removed from the condition for parametric resonance. As shown by calculations, resonance coupling
and nonlinear resonances represent no hazard for the accelerated electrons.
728
Fig. 2.. Current trace for excitation system
for magnetic field.
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Fig. 3
7.70
2 3 4 5 5 8 70 20 30 40 50 80 100 r
Fig. 4
Fig. 3. Oscilloscope traces of basic processes in the accelerator: a) light,
b) y-ray, c) magnetic field, and d) accelerating-field pulses.
Fig. 4. Dependence of minimum uhf-oscillatorpower on accelerator energy:
0) experiment.
The magnetic fields near the ends of the electromagnet reach 30 T. Therefore measures must be taken
to insure mechanical stability of the system. In our case, where the actual length of the current pulse (T <
10-5 sec) is small in comparison with the period of the natural oscillations of the system, mechanical stability
is provided by the choice of a sufficiently thick wall for the copper loop and by tightening of the loop with
clamps at the point of current feed.
The resonance properties of the resonant cavity (frequency and Q) are mainly determined by the shape
and size of the internal surface of the loop and by the degree of screening of the cavity. The dimensions of
the internal cavity were selected so that the resonance frequency corresponded to the optimal oscillator fre-
quency f 3000 MHz. Reduction in the diameter of the opening of the loop near its ends (see Fig. la) makes
it possible to obtain not only the required configuration of the magnetic field in the electromagnet but also con-
siderable screening of the internal cavity with respect to high frequencies. To increase the screening of the
resonant cavity at the ends of the loop, guard cylinders transparent to the guide magnetic field are installed
at the ends of the loop. This makes it possible to obtain a resonant cavity with Q 103.
An acceleration chamber can be either the internal cavity of an electromagnet in which the required
vaccum is produced or a glass vacuum envelope installed in an electromagnet that is not vacuum-tight. As
shown by experiment, the use of the internal cavity of the electromagnet as a vacuum chamber limits the maxi-
mum energy of the accelerator to =15 MeV because of breakdown of the vacuum gap at the point where the
electromagnet is connected to the excitation system. The cause of the breakdown is plasma from the uhf dis-
charge and from the particle injector. A glass vacuum chamber (see Fig. la, b) increases the electrical
stability of the electromagnet and simplifies its design. It should be noted that the plasma from the uhf dis-
charge within the vacuum chamber screens the quasistatic electric field of the electromagnet, which has a
perturbing effect on the accelerated electron bunch, and also removes from the walls of the acceleration cham-
ber the charge of accelerated particles striking them.
For an acceleration cycle about 2.5 ? 10-6 sec long, the electron range does not exceed 1000 m, which
offers an opportunity to decrease the demands on the vacuum system of the accelerator. Calculations using
the technique in [4] show that the relative particle losses through scattering by residual gas are no more than
1% for a vacuum of ?10-4 mm Hg and an initial electron energy of 5 eV. A vacuum of 10-4-10-5 mm Hg is
maintained in the acceleration chamber.
Excitation System for Electromagnet. If one assumes a sinusoidal variation of the magnetic field (using
the first quarter-cycle for acceleration) in the system for excitation of the guiding magnetic field then de-
generates into the simplest pulsed current generator (PCG) in which the current in the load is produced by
discharge of a condenser bank into an inductive load (electromagnet). The energy stored in the condensers
of the PCG must exceed the energy in the magnetic field of the electromagnet; in addition, one should strive
to reduce the parasitic inductance of the PCG, including the inductance of condensers, spark gaps, and leads,
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Fig. 5 Fig. 6
Fig. 5. Dependence of accelerator intensity on level of initial magnetic field for 1)P=
10 kW and 2) 2.5 kW.
Fig. 6. Dependence of accelerator intensity on intensity of accelerating field.
,
in comparison with the inductance of the electromagnet. In our case, the PCG is a bank of 24 low-inductance,
high-voltage IK-50-3 condensers which are switched into the total load by three low-inductance, vacuum spark
gaps. The parasitic inductance of the PCG is 10-8 H; the inductance of the electromagnetic is 2 ? 10-8 The
total energy capacity of the bank is 90 kJ; the maximum current in the electromagnet is 2.5 MA; the frequency
of the natural oscillations of the LC circuit is 105Hz.
The excitation system also includes a preliminary field bank (PFB) which produces a field of low ampli-
tude (-0.1 T) in the electromagnet but one of sufficient duration to produce the required condition of cyclotron
resonance at the center of the acceleration chamber. The bank consists of four IMU-5-140 condensers which
are connected to the electromagnet by a vacuum spark gap through a Bitter solenoid with an inductance Lc=
2 ? 10-6H. The maximum current of the bank is 4 ? 104 A; the frequency of the circuit is 5 ? iO3 Hz.
An oscilloscope trace of the magnetic field of the electromagnet at small values of the main magnetic
field (for convenience of illustration) is shown in Fig. 2.
The repetition rate of current pulses in the electromagnet, and consequently of cycles of acceleration,
is determined by the time for restoration of the electrical stability of the vacuum spark gaps and by the charg-
ing rate of the PCG device. The time between two successive firings of the spark gaps is ?5 min.
Oscillator for Accelerating Field. An acceleration mode with the initial rate of rise of the magnetic field
different from zero is possible with sufficiently high intensity of the accelerating field, as has been shown [3].
Using the parameters for the excitation system for the magnetic field, and setting wo = 1 . 8 ? 1010 sec-1 and e =
50 MeV, we obtain a minimum intensity of the accelerating field E =5 ? 105 V/m, which corresponds to an ac-
celerating-field oscillator power P=2.7 ? 103 W when the accelerating resonant cavity has a Qc.:600. Such os-
cillator power corresponds to zero intensity of the accelerator. The working power of the oscillator should
be selected so that the intensity of the accelerating field is greater than the intensity of the space-charge field
of a bunch. A magnetron is used in the accelerator which has a power of 200 kW in a pulse of 2.5 ? 10-6 sec;
this permits acceleration of up to 1011 particles [5].
Electron Injector. According to the operating principles of the accelerator, the source of particles
should be located at the center of the acceleration chamber. There are several methods for realizing such
an injector; it is most convenient to use as a source of electrons an erosion plasma which is injected along
the magnetic lines of force into the central region of the acceleration chamber by means of a coaxial plasma
accelerator (Marshall gun) [16]. ?The density of the plasma injected by the gun into the center of the accelera-
tion chamber is ?10H cm-3. The diameter of the plasma beam at the center of the accelerator is no more
than 10 mm (for an axial field with an induction of 0.1 T). The axial velocity of the plasma is no more than
5 ? 106 cm/sec which is acceptable for the capture of electrons into the acceleration mode. Reproducibility
of plasma flux parameters is not worse than 2 a .
EXPERIMENTAL RESULTS
Particle acceleration can occur only with a rate of rise of the magnetic field in the electromagnet that
is not too high and with a fixed intensity of the accelerating field in the resonant cavity [3]. The relation
730
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determining the maximum permissible rate of rise of the magnetic field as the initial time through the intensity
of the accelerating hf field was found by detection with a scintillation counter of the 'y-ray pulses produced by
the accelerated particles during their deceleration in a target (Fig. 3). This dependence is shown in Fig. 4
after conversion to the coordinates "oscillator power ?accelerator energy" with allowance for the parameters
of the device. The curve in Fig. 4 makes it possible to determine the minimum uhf oscillater power required
for acceleration to an energy E =ym0c2 for constant length of acceleration cycle and sinusoidal rise in the mag-
netic field. Good agreement is observed between theory and experiment.
The dependence of accelerator intensity (in relative units) on the level of the initial magnetic field set
by the PFB (see Fig. 2) is shown in Fig. 5. Here the accelerator intensity is assumed proportional to the
bremsstrahlung intensity. A certain increase in intensity with increase in Bi at small values of Bi is explained
by an improvement in the operating mode of the injector. The steepness of the drop in the curve at Bi =Bo de-
pends on the amplitude of the accelerating electric field. The width of the region of the drop increases as the
amplitude increases, which indicates an increase in the area bounded by the phase-stability curve. This re-
sult is in accord with theory [3].
The energy spread of the accelerated electrons also depends on the intensity of the accelerating field.
Writing the equation for the separatrix in the coordinates u=p ? pc, co, where pc is the momentum of the
equilibrium particle and co is the particle phase with respect to the wave of the accelerating field [3), we ob-
tain at the time of completion of acceleration (aB/atiT/4=0) with pc ?moc,
eE (sin ?1) = ? (2--? u2.
Pe
Then it is easy to determine the maximum energy spread of the accelerated particles:
(1)
As =17 2eE
E V MOCTWO (2)
The relative amplitude of radial phase oscillations Ar/r is also determined by Eq. (2). Substituting E =2 ? 108
W/m and y =30 in it, we obtain Ar/rerzs0.07 or the diameter of the electron bunch d =2ir2 mm. The diame-
ter of the electron bunch is determined experimentally from the width of the y pulse emitted when the beam of
accelerated electrons impinges on a target with allowance for the variation of the magnetic field in the system.
The resultant value of the diameter (d--=:2.5 mm) is in agreement with the theoretically determined value.
Visual observations and photography of the synchrotron radiation from an accelerated electron bunch confirm
this value.
As is well known, synchrotron radiation from electrons accelerated to relativistic energies is a source
of information about accelerator intensity. Keeping in mind the features of the injector used in this accelera-
tor and taking into account the results of [3], we obtain the expression
Bp
N = No {--,- ?1 arcsin r1 2 ( )1} ,
2 '
Bp max (3)
for accelerator intensity, where No =n0V (V is the volume of the region in which particle capture into the ac-
celeration mode occurs; no is the density of the plasma electrons from the source at the center of the accelera-
tion chamber).
The resultant dependence is shown in Fig. 6 (curve 1) in the coordinates (N/No, E). Also shown is an
experimental curve obtained by measurement of the intensity of synchrotron radiation from electrons accelera-
ted to 20 MeV and normalized at the maximum intensity (curve 2). The discrepancy between experimental
and theoretical relations can be explained by the influence of space charge at the time of electron bunch forma-
tion [5].
The absolute value of the numbers of accelerated particles can be found by comparing the intensity of a
narrow spectral range of synchrotron radiation with the radiation from a lamp calibrated against an absolute
black body in the same spectral range. The intensity of synchrotron radiation is converted into accelerator
intensity by means of the formulas given in [7]. Measurements showed that the intensity of the accelerator was
better than 5 ? 108 particles per pulse for an amplitude of the high-frequency field E =2 - 108 V/m.
In conclusion, the authors are grateful to A. A. Sokolov for valuable advice furnished during the period
of accelerator startup and testing and to the staff of the Department of High-Voltage Engineering at the Lenin-
grad Polytechnic Institute for help in the development of the PCG.
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LITERATURE CITED
1. V. ,S. Panasyuk, A. A. Sokolov, and B. M. Stepanov, At. Energ., 33, No. 5, 907 (1972).
2. A. V. Gryzlov et al., in: Proc. II All-Union Conference on Charged-Particle Accelerators [in Russian],
Vol. 1, Nauka, Moscow (1972), p. 170.
3. A. V. Gryzlov et al., Zh. Tekh. Fiz:, 42, No. 1, 13 (1972).
4. A. G. Vlasov, Izv. VUZ, Ser. Fiz., No. 1, 20 (1961).
5. M. Yu. Novikov, Yu. M. Tereshkin, and V. B. Khromchenko, At. Energ., 41, No. 2, 125 (1976).
6. P. N. Dashuk et al., Technology of High Pulsed Currents and Magnetic Fields [in Russian], Atomizdat,
Moscow (1970).
7. Synchrotron Radiation in Solid-State Studies [in Russian], A. A. Sokolov (editor), Mir, Moscow (1970).
PROSPECTS FOR THE USE OF NUCLEAR-PHYSICS ANALYTIC
METHODS IN BIOLOGY AS ILLUSTRATED BY THE WILT PROBLEM
V. Ya. Vyropaev, I. F. Kharisov,
O. D. Maslov, E. L. Zhuravleva,
and L. P. Kul'kina
UDC 543.53:633.51
The investigation of.the role of microelements in various biological processes is undoubtedly not only of
purely scientific interest but also of great national economic significance.
It is well known that such elements (macroelements) as C, H, 0, N, S, P, K, Na, and Ca form vitally
necessary components of parts of plant cells and the microelements Cu, Fe, Co, Mn, Zn, Mo., Se, Sb, I, and
tens of others play an important role in the biological processes occurring in living things.
According to Vinogradov [1, 2], one can assume the presence of all chemical elements in living matter,
and it is natural to expect that they perform a definite biological task. However, the question of exactly what
biological task is performed by a given microelement has not been resolved thus far [3]. Obviously, one
of the reasons is the absence of reliable analytical methods which would make it possible to perform analysis
over the entire spectrum of elements on the test samples of small mass (0.1-0.01 g) that are typical of biology
[4].
Biological objects (plants or living organisms) have a remarkable property from the viewpoint of activa-
tion analysis ? their matrix is described by the mean conventional "formula of life" H
?2 960?148 OC 14801318 Ni6Si.e.,
those elements which yield short-lived radioisotopes under neutron activation. This circumstance makes it
possible to perform neutron activation analysis of a series of elements with high instrumental sensitivity and
places the method of neutron activation in prime position for the analysis of biological objects for elemental
composition from the viewpoint of discovering the biological task of microelements. The combination of neu-
tron activation analysis with such nuclear-physics methods as autoradiography, tracer atoms, etc., is even
now proving to be of significant help to the biological sciences in the solution of scientific and practical prob-
lems.
In this regard, we discuss a very important specific example ? the problem of cotton-plant wilt. Wilt
is a fungous disease which leads to withering and death of the cotton plant. The disease is a typical one for
many agricultural crops. At the present time, the causes of this phenomenon have not been completely ex-
plained, but there are two basic hypotheses: Withering of the cotton plant occurs because of failure in feeding
through the action of the parasite fungus resulting in blockage of transport vessels in the plant; withering and
death of the plant occur through the action of toxins developed by the parasite fungus which enter the organs
of the plant.
Translated from Atomnaya Energiya, Vol. 41, No. 2, pp. 118-122, August, 1976. Original article sub-
mitted October 18, 1974.
732
This material is protected by copyright registered in the name of Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. Nd part
of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $7.50.
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Declassified and Approved For Release 2013/09/23: CIA-RDP10-02196R000700080002-8
Fig. 1.
Channel number .
Gamma spectra from samples of cotton-plant roots: 1) diseased, 2) healthy.
Wilt causes tremendous economic loss and hinders further increase in cotton productivity. The disease
is so widespread that it reduces the cotton harvest significantly. Losses because of wilt amount to 10-30%
and more in all the cotton-growing areas of the world.
At the present time, no one disputes the fact that it is possible the infection of the cotton plant by wilt
is connected in some degree with definite anomalies in the content of certain microelements in soil and plants
which affect both the wilt-resistance of cotton plants and the vital activity of the parasite fungus [5-7].
Because of this, healthy and wilt-infected cotton plants were examined for the content of various micro-
elements by means of neutron activation. The main purpose of these studies was to determine the quantitative
content of microelements in various plant organs and to attempt to establish on the basis of the experimental
data some regularity in the behavior of the relative content of these elements.
Cotton-plant samples were selected from plants of a single crop cultivated under identical soil conditions
and were prepared from five to 10 plants, i.e., they were averaged for a given field. The selected samples
were separated into parts for irradiation: roots, stems, leaves, bolls, and fibers.
Since neutron activation analysis makes it possible to perform studies of microelement content with a
sensitivity as high as 10-9 g/g, it is necessary to maintain particular sterility in the preparation of samples
for irradiation. In addition, one ought not subject the samplestoany physicalor chemical effects since it has
been established that up to 75% of certain elements is lost in thermal and chemical incineration [8].
The samples were prepared in the following manner: The cotton-plant samples, after being thoroughly
cleansed of dust, were dried in a drying cabinet without ashing at a gradual rise in temperature from 50 to
120?C over a period of 10-15 h. The air-dried samples were ground into a powder in an agate mortar. Sam-
ples in the form of pellets 20 mm in diameter, 2-4 mm thick, and weighing ?1000 mg were prepared from
this powder by compression at pressures up to 250 atm. Such samples proved to be very convenient and prac-
tical to work with. They were compact, had sufficiently high mechanical strength, small volume, high density
and mass (which is very important in the preparation of samples from plants and other biological objects),
and also fixed sized and shape. In addition, accuracy of calibration is considerably increased for them, and
an optimal geometry for spectral measurement is easily selected.
The samples were packaged (each pellet separately) in polyethylene and placed in a stack along with stan-
dards in a special container of pure aluminum. The irradiation was carried out with a thermal neutron fluence
of 101-6 n/cm2 (f =2.3 ? 1012 n/cm2-sec, rirr =70 min). The neutron fluence was determined from the induced
activity of standards with known activation cross sections.
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0
(D
0
(D
Es)
(D
-n
(D
(T)
(D
n.)
o.)
(r)
R3
o)
. .
0
0
-0
0
n.)
co
Co
TABLE 1. Microelement Content in Healthy (H) and Wilt-Infected (W) Parts of Plants, %
V
g
0
r...)
Root
Stem
Leaf
Ball
Fiber
w
W/H
It
W 1W/H
H
W
H
W
W/li
H
W IWAI
Na
0,1
0,12
1,2
0,03
0,011
0,37
0,049
0,055
1,1
0,019
- 0,022
1,16
3-1Cr3
- 8.10-3
2,7
K
0,6
1,18
1,9
1,65
2,32
1,4
4,1
2,1
0,5
4,46
6,0
1,35
0,6
0,97
1,6
Ca
1,2
2,
1,5
3,7
1,76
0,5
1,5
1,43
0,96
3,5
3,0
0,85
0,6
0,5
0,86
Sc
7,4..10-6
2,1-10-5
2,8
6,4.10-6
8,4.10-5
1,32
2,5.10-5
4,2.10-5
1,7
1,5-10-5
3,7.10-5
2,5
2,4.10-6
3,1.10-6
1,3
Cr
1,5-10-4
1,5.10-4
1,0
3,2.10-3
3,8.10-3
1,2
0,004
0,007
1,7
--