SOVIET ATOMIC ENERGY VOL. 32, NO. 2

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000300100002-9
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 99
• Document Creation Date: December 27, 2016
• Document Release Date: March 1, 2013
• Sequence Number: 2
• Publication Date: February 1, 1972
• Content Type: REPORT

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41i
Russian Original Vol. 32, No. 2, February, 1972
Translation published August, 1972
-?
-
5 .
SOVIET
ATOMIC
ENERGY
ATOMHAR amprma
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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/
(
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An arrangement with Mezhdunarodnaya Kniga, the Soviet book
export age*, makes available both adv7hoevopies.pf the Rus-
sian 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.nd helps to im-
prove the quality of the latter. The translation began with the first
issue of the Russian journal.
Etlitorial 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 Editors: N. A. Kolokollsov
N. A. Vlasov
A. ),k Bochvar
N. A. Dollezhal'
V. S. Fursov
- I. N. Golovin
V. F. Kalinin
? A. K. Krasin
A. I. Leipunkiit
V. V: Matev
M. G. Meshcheiyakov
P. N. Palei
V2B. Shevchenko
D. L. Simonenkoi
V. I. Smirnov
A. P. yinogradov
A. P. Zefirov
Copyright ?1972 Consultints Bureau, New York, a division of Plenum Publishing
Corporation, 227 West 17th Street, New York..-N. Y. 10011. All rights reserved.
No article contained herein may be reproduci.!.1 for any purpose whatsoever
without permission of the publishers.
Consultants Bureau Journals appear about six months after the publication of the
original'Russian Issue. For bibliographic accuracy, the English issue published by
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'CONSULTANTS _BUREAU, NEWYORK AND LONDON
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New York, New York 10011
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Published monthly. Second-class postage paid at Jamaica, New York 11431:
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SOVIET ATOMIC ENERGY
A translation of Atomnaya energiya
Translation published August, 1972
Volume 32, Number 2 February, 1972
Organization of Radiation Monitoring at Nuclear Power Stations ? A. A. ll'khman,
V. M. Dedkov, and A. N. Romanov
Radiation Safety Conditions in Uranium Mine Drifting Operations ? N. I. Chesnokov,
Yu. A. Lebedev, and I. V. Pavlov
Thermodynamic Properties of Uranium?Aluminum Alloys ?V. A. Lebedev,
CONTENTS
Engl./Russ.
121 107
124 111
V. I. Sal' nikov , I. F. Nichkov, and S. P. Raspopin
129
115
Production of AC227 and Th228 Isotopes by Irradiation of Radium in the SM-2 Reactor
? Z. K. Karalova, R. N. Ivanov, B. F. Myasoedov, L. M. Rodionova,
Z. I. Pyzhova, S. M. Kalebin, and V. Ya. Gabeskiriya
133
119
Interaction of High-Energy Radiation with Matter ? V. S. Barashenkov, N. M. Sobolevskii,
and V. D. Toneev
137
123
Plasma Accumulation through Ionization of Residual Gas in an Electromagnetic Trap
?Yu. I. Pankrat'ev, M. G. Nozrachev, 0. A. Lavrent'ev, B. G. Safronov,
V. A. Naboka, and E. F. Ponomarenko
144
131
Nonlinear Theory for the Excitation of Regular Oscillations by a Relativistic
Electron Beam ? V. I. Kurilko, A. P. Tolstoluzhskii, and Ya. B. Fainberg . . .
150
137
Verification of of the Neutron Diffusion for a Mediuniwith Channels (Lattice of Channels
with Large Transverse Dimensions) by Means of the Pulse Method
?I. F. Zhezherun
155
143
ABSTRACTS
Uranium Extraction from Low-Grade Silicate Ore with the Aid of Thiobacteria
?E. G. Kuznetsova and I. P. Kuligina
165
153
Effect of Noise Currents on Measuring Circuits of Reactor Channel Control Systems
?A. G. Ivanov and V. M. Matyukhin
166
153
Heat Exchange Crisis in the Boiling-up of Liquids ? A. N. Vasil'ev
and P. L. Kirillov
167
154
An Approximate Method for Calculating Fast Neutron Shields ? B. S. Sychev
168
155
A Universal Expression for the Characteristics of the Scattered Electron Distribution
as a Function of the Medium and the Initial Electron Parameters
?V. V. Arutyunov, V. F. Baranov, and A. G. Zrazhun
169
156
Calculation of Bremsstrahlung Intensity by the Monte Carlo Method ? V. V. Arutyunov
and V. F. Baranov
170
156
Dosimetric Characteristics of Neutron Threshold Detectors ? T. V. Koroleva,
K. K. Koshaeva and S. N. Kraitor
170
157
LETTERS TO THE EDITOR
Short-Term Reactor Cooling ? S. 0. Slesarevskii, M. N. Korotenko,
M. M. Nazarchuk, D. T. Pilipets, and S. S. Stel'makh
172
159
Fast Neutron Fluxes in Experimental Channels of the MR Reactor ?A. V. Borodin,
V. I. Vikhrov, V. F. Krasnoshtanov, V. N. Perevezentsev, and G. E. Shatalov
175
161
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Heat-Transfer Properties of Cermet Compositions of the System A1203?Mo
? V. A. Osipova and Kh. A. Kyaar
CONTENTS
(continued)
Engl./Russ.
177 162
Carbon Electrotransference in Beryllium ? V. P. Gladkov, V. S. Zotov,
and D. M. Skorov
179
163
Thermodynamics of the Extraction of Plutonium(IV) from Perchloric and Nitric Acid
Solutions in the Presence of Oxalic Acid ?A. S. Solovkin and A. I. Ivantsov. . .
182
164
Simulation Experiment on the Water?Oil Contact in Exploration of Stratal Fresh Water
by Recording Delayed Neutrons ? Ya. E. Kostyu, A. P. Osipenko,
and V. A. Shkoda-UPyanov
184
166
Separation of Liquid Mixtures by Thermodiffusion through an Electric Field
?V. P. Kuchinov, B. I. Nikolaev, and A. A. Tubin
187
167
Separation of Isotopes of Nitrogen and Hydrogen in the Photodissociation of Ammonia
?B. U. Utirov, G. M. Panchenkov, V. K. Korovkin, and Yu. G. Basov
189
169
Operating Characteristics of Dispersive Air-Equivalent Scintillators
? G. P. Volosyuk, S. P. Vershinina, 0. A. Gunder, L. S. Prokoreva,
and L. V. Sigalova
192
171
Electrical Discharge in Radioactive Dielectrics ? V. V. Gromov and V. V. Surikov . . .
194
172
Isotropic Neutron Source Using the LUE-25 Linear Electron Accelerator
?V. P. Kovalev, V. P. Kharin, V. V. Gordeev, and V. I. Isaev
196
173
Calculation of the Yield of D?T Neutrons with Periodic Replenishment of the Target
with Tritium ? V. T. Tustanovskii
198
175
Relative Probability of AM242 Beta Decay ? V. Ya. Gabeskiriya
201
177
Slow Neutron Capture Cross Section of Pa231 ? B. M. Aleksandrov, M. A. Bak,
A. S. Krivokhatskii, and E. A. Shlyamin
203
178
C1249 Fission Cross Section for Fast and Thermal Neutrons ? B. I. Fursov,
Kh. D. Androsenko, V. I. Ivanov, V. G. Nesterov, G. N. Smirenkin,
L. V. Chistyakov, and V. M. Shubko
205
178
An Unidentified Alpha Activity of Thorite ? K. A. Petrzhak, M. I. Yakunin,
and G. M. Ter-Akopiyan
207
179
INFORMATION
Startup of the Third Power Unit of the Novaya Voronezh Nuclear Power Station
209
181 /
CHRONICLES
XXI Session of the Comecon Permanent Commission (PKIAE SEV) ? A. Panasenkov. . . .
210
182
Collaboration Logbook
212
182
The Russian press date (podpisano k pechati) of this issue was 1 /24 /1972.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ORGANIZATION OF RADIATION MONITORING
AT NUCLEAR POWER STATIONS
A. A. Il'khman, V. M. Dedkov, UDC-621.039.766
and A. N. Romanov
The basis for the organizational and functional structure of radiation monitoring at domestic nuclear
power stations was developed under the influence of traditions which grew up during the period the first nu-
clear power stations were built. At the present time, the requirements for radiation monitoring are set
fourth in "Health Rules for Nuclear Power Station Design" (Medgiz, Moscow (1968)). According to these
rules, a radiation monitoring service, which is organizationally an independent subdivision, is provided
at a nuclear power station. The functional structure is characterized by the existence of an independent,
sufficiently many-sided system consisting of subsystems, each of which is provided for the solution of defi-
nite problems in the field of radiation monitoring.
One of the aspects of the accepted functional structure related to the nature of the usage of informa-
tion circulating within the radiation monitoring sphere is discussed below. Obtaining the necessary infor-
mation is accomplished in three basic ways; by remote measurements, by measurements with portable
instruments, and by sample collection. Remote measurements provided continuous data on the radiation
situation in a nuclear power station; portable instruments permit more detailed information about radiation
levels for a specific monitored unit; sample collection enables one to obtain quantitative and qualitative
characteristics for individual radiation parameters.
Of greatest interest is the informationacquiredby remotemonitoring. In domestic nuclear power sta-
tions, remote monitoring is centralized and, as a rule, is done at a separate panel attended by a special
operator from the radiation monitoring service. A diagram of the main information channels for this panel
is shown in Fig. 1. The content of the information reaching the operator and the nature of its use is shown
in Table 1.
Analysis of the data presented in Table 1 indicates that the main responsibility of the operator at the
radiation monitoring panel is essentially the recording of events and the transfer of required information to
duty personnel of the radiation monitoring service and to operating personnel of the technical subsections
of the station. Although obtaining information about various radiation anomalies, the operator does not have
the capability of doing anything about their cause. In such situations, all necessary measures are taken by
the appropriate personnel of the technical departments. Thus one observes a definite break between the
volume and amount of information acquired by the operator and his capabilities, which transforms a basic
element of the system (panel and operator) into an intermediate link intended for the transfer of informa-
tion to a location where it can be used actively, i.e., to the control system of the nuclear power station.
There is a fundamental possibility for simplifying the radiation monitoring system based on the trans-
fer of the appropriate information directly to personnel able to take the necessary measures to bring about
control of a situation. To accomplish this, it is advisable to include an independently functioning radiation
monitoring system within the complex control system of a nuclear power station in the status of a subsystem.
This step makes it possible to furnish the appropriate information circulating in the sphere of the system
under discussion to the operators at the power station panels, i.e., to the personnel directly controlling the
technical processes at the station.
In nuclear power stations at the present time, information and computing systems with organized
display for the operator are used for automation of the basic technical processes. The appropriate infor-
mation from the radiation monitoring subsystem should be introduced into such a system. The results will
Translated from Atomnaya Energiya, Vol. 32, No. 2, pp. 107-109, February, 1972. Original arti-
cle submitted March 26, 1971.
? 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
121
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TABLE 1. Characteristics of Rat:61.16A MiSnitoring Panel at a Nuclear Power Station
Information
Role of operator in ob,-
taming (using) informa-
tion
Remarks
flow num
ber (as in
Fig. 1)
1 content
purpose
1
ialues of 7-ray dose rate
and aerosol concentra-
tions in attended and
semi-attended locations
gas concentrations in
attended,semi-attended,
and unattended loca-
tions of the controlled
area
Charactize radiation sit-
uation
Take instrument read-
ings, control individ-
ual elements of moni-
toring system
?
2
Specific activity values
for the process media in
the main loops
Characterize radiation
status of loops and
equipment
The same
?
3
Concentration of radioac- Prevent discharge of ra-
tive materials in liquid dioactive materials frorr
and gaseous wastes dis- nuclear power station in
charged outside the lim-
its of nuclear power sta-- amounts greater than
tion permissible
Take instrument readings,
calculate daily dis-
h
c arge
_
4
Audible and visible Warn personnel of pres-
alarms for radiation le- ence of radiation
vels above permissible hazard
in attended locations of
controlled area
Inform (by telephone)op-
erating personnel of the
technical departments
about the appearance of
a radiation anomaly;
record the anomalous
event
Area alarms are acti -
vated automatically
5
Radiation levels in un- Inform operating person-
attended locations, spe- nel of technical depart-
cific activity of process ments about the appear-
media and of wastes dis- ance of a radiation
charged outside limits of anomaly
nuclear power station
The same
Warning on the engineer-
ing panels about a
change in basic radia-
tion parameters is given
automatically
6
Radiation levels in at- Inform duty personnel of _
tended, semi-attended, the radiation monitor ing
andunattended locations service about radiation
of the controlled area levels in the areas
Information is telephoned
by the operator on re-
quest from the duty
personnel of the radia-
tion monitoring service
7
Amount of radioactive Warn personnel in the ex-
material discharged Record data
ternal monitoring group
from the nuclear power, about above-permissible
station into the envi-
discharges
ronment
Information transmitted
by telephone
be; an increase in operational control of a nuclear power station, which is very important because the in-
crease in specific power of reactor units imposes increasingly rigorous requirements on safety problems;
a reduction in the number of service personnel at a nuclear power station because of the elimination of
operators for the radiation monitoring panel; economies in the area of panel locations because the secon-
dary equipment for radiation monitoring can, in this case, be placed in the general circuit for technical
control panels and not in a separate arrangement, etc.
The proposed reorganization of functional structure involves changes in other important problems of
radiation monitoring with the principal ones being; the volume of radiation monitoring, the degree of auto-
mation of information collection and analysis, the volume and quality of information displayed to control
panel operators, and construction principles for groups of technical systems. The organizational structure
of the radiation monitoring service may also undergo certain changes.
122
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Operating per-
sonnel of tech-
nical depart-
ments
Duty personnel of
radiation moni-
toring service
External radia-
tion monitor-
ing group
4
Controlled
working
areas
Operator at ra-
diation monitor-
ing panel
Process loops
Waste removal
channels ( liq-
uid and gas-
eous)
Fig. 1. Diagram of main information channels to the
radiation monitoring panel at a nuclear power station.
(Numerals indicate the information flow number.)
In conclusion, it should be said that questions of cost were not a deciding factor in the construction of
the first operating nuclear power stations which served as the basis for the creation of radiation monitoring
systems for subsequent nuclear power stations. Thus the presently accepted organizational and functional
structure was not only acceptable but also useful - it made -it possible to obtain rather complete data on all
aspects of radiation monitoring. Subsequent development of nuclear power in this country, associated with
the construction of a large number of commercial nuclear power stations, moves into the forefront the re-
quirement of reduction in capital expenditures for station construction along with the requirement for in-
crease in operational reliability. From this viewpoint, the proposed solution can have a decided effect.
123
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RADIATION SAFETY CONDITIONS IN URANIUM
MINE DRIFTING OPERATIONS
N. I. Chesnokov, Yu. A. Lebedev, UDC 613.6:621.039
and I. V. Pavlov
Radon is liberated constantly from the walls of the mine faces dnd sidewalls and from broken-up
mine muck, rubble, ore, and gangue, and gets into the air circulating through underground uranium ore
mines at a rate of 2.10-8 to 5 ? 10-8 Ci/sec ?m2 [1].
Artificial ventilation is built into all mines with the purpose of minimizing the radiation effects of the
radon given off, and even more so the radiation effects of the radon daughters: P0218 (RaA), pb214 (RaB), and
B? 214
(RaC), with their short half-lives. The intensive ventilation, while removing the randon present, also
severely upsets the radioactive equilibrium between the radon and the radon daughters. When the distur-
bance of this equilibrium is taken into account, the degree of radiation effects of the mixture of radon daugh-
ters can be estimated from the amount of latent energy of decay.
The energy is determined from the formula [2]:
q)=Kg)(0?1 CRaA 0 ? 5 CRaB + 0 ? 4CRaC) (1)
where (pis the latent energy in MeV/m3; CRA,
-RaB, CRac are the respective concentrations of each of
the radon daughters in Ci/m3; Kg) is a conversion factor equal to 1.3 -1018 MeV /m3 [2].
The yearly average allowable amount of latent energy in the mine atmosphere coyAc is 1.3 .108 MeV
/m3 if the miners have spent not more than 15 to 17 years on the job [2].
Nevertheless, there have been cases when uranium energy reached a level of 2 .1011 to 3 .1011 MeV
/m3 [3] in unventilated mine areas, i.e., a level at which miners working in such an atmosphere would be
subjected to radiation exposure several times in excess of the critical allowable yearly dose.
The latent energy can be kept down to allowable levels, as a rule, through high-intensity ventilation.
But when the galleries driven through the mine are very long and when a considerable amount of radon is
liberated into the mine atmosphere, it is not always possible to maintain the required conditions through-
out the mine working areas. In those cases, the time the miners are permitted to stay at various mine
work sites must be limited, or air-cleaning filters and individual respirators must be put to use.
Experience in driving mine galleries has taught that miners spend most of their time in areas within
30 to 40 meters of the stopped mine face (Fig. 1). This means that radiation protection calculations can be
reliably oriented on the basis of the average latent energy in the mine face area cofaavce. This, in combina-
tion with individual dosimeter badges, will provide adequate radiation safety for the miners.
The pattern of variations in the latent energy in mine drift work is a highly intricate one, and depends
on a host of factors, those of greatest importance being: a) the intensity and position of the sources giving
off the radon; b) the radon concentration and the latent energy at the ventilation air intake point; c) the amount
of air supplied to the mine working site and the aerodynamic characteristics of the ventilation system (vol-
ume swept in ventilation, air leakage distribution in the vents and ducting, distance from end of vent to
mine face breast, etc.).
Most of the determining factors vary with time over fairly broad ranges. Moreover, some of the
factors have received inadequate study (e.g., the degree of precipitation of radon decay products in the
ventilation ductwork and on the walls of the mine working area). This necessitates introduction of certain
Translated from Atomnaya Energiya, Vol. 32, No. 2, pp. 111-114, February, 1972. Original arti-
cle submitted April 28, 1971; final revision submitted July 22, 1971.
0 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
124
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6
8)5
2
Fig. 1
9 02 04 06 0,8 1,0 '
Specific amount of radon
given off, n? 108 Cf./sec ? ni2
Fig. 2
Fig. 1. Arrangement for ventilation of mine drfit area in forced venti-
lation (a) and in combined ventilation (b); 1) fans; 2) ducting; 3) aerosol
filters; 4) boundary of mine face area.
Fig. 2. Dependence of amount of air needed to ventilate mine face area
on specific amount of radon given off; 1) without aerosol filter; 2) with
aerosol filter; Cin = 3.1 0-7 Ci/m 3; in = 9 ? 107 MeV/m3.
assumptions into the calculations, and specifically leaving out of account precipitation of radon decay prod-
ucts, ignoring air coming from pneumatic tools, etc.
The difficulties encountered in calculating the average radon concentrations and the latent energy can
be eliminated by using the following ratios:
Cj ?Gin
ZRn
C av?Cin '
(2)
Z ? 1 (3)
(1) (Pay? Tin
which we shall term the ventilation indices for radon ZRn and for the latent energy Z
The ratios ZRn and Z 49 provide the link with the volume-averaged concentration of radon and the latent
energy in the mine working area Cay, (pay and the corresponding values in the emanating jet stream Ci,
These indices characterize the rate of air exchange between the various mining areas and the arrangement
of radon evolution sources in the mine. They are virtually independent of the air turnover time in the mine
areas.
Consider the equations characterizing the time variation process of the amount of radon and of the
latent energy in the mine areas:
w dcdtav_ D
W dTav WX,p TC av? (pay) Q (Wi (5)
Here W is the volume of the mine area swept out in ventilation in m3; Q is the amount of air supplied to the
mine working areas in ventilation in m3/sec; D is the flow of radon per sec from the mine working areas
in Ci/sec; X (p is an empirical constant characterizing the fall-off in latent energy, and is equal to 3 ?
sec-I [4].
(4)
In Eq. (4), radon decay is ignored, since the radon decay constant is relatively small (ARn = 2 .1 ? 10 -6
sec-1), while the air turnover time in the mine working areas is usually not longer than 104 sec.
The first term in the right-hand member of Eq. (5) characterizes the buildup of latent energy in re-
sponse to the formation of radon daughters, and their subsequent decay, while the second term in the equa-
tion characterizes the process by which the latent energy changes through increment and loss of radon
daughters added or carried off by the ventilation air stream.
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-2 100
-0
eo
60
x
o 20
;
3
2
0 02 0,4 06 0.8 1,0
Specific amount of radon
released to mine air, n? 10?
Ci/sec. m2
Fig. 3. Dependence of additional ex-
posure experienced by miners on spe-
cific amount of radon given off in
continuous ventilation of mine face area:
1) for 1 h; 2) for 2 h; 3) for 3 h.
Substitution of the values ofCJ
? and (p. from Eqs. (2) and (3) into Eqs. (4) and (5) yields, for steady-
state conditions:
, D
Cav = Cin-r- Qznn (6)
yin Kgr av (7)
Way? wx,pI Qz,p ?
1+ wp wx,p
The numerical values of ZRn and Z cp can be determined experimentally either by using laboratory
simulation models or by observing natural conditions.
In mine drifting work, ZRn and Z, depend primarily on the position of the sources of emanation and
air leaks in the ducting. At the mine face the distance from the end of the ductwork to the breast of the
mine face is also of essential importance. The greater this distance, the smaller ZRn and Z (p will be, and
the worse the ventilation conditions will be at the mine face and in the mine generally.
The average level of irradiation of the mine worker during a shift is determined by the amount of
latent energy of the radioactive aerosols:
av
(Pface
Wsh 6 4- Tay (1-6),
(8)
where 6 is the relative residence time of the miner at the mine face. Since 6 >0.8 as a general rule, ef-
forts must be made to increase the quantity of air supplied directly to the mine face Qface in the event that
it becomes impossible to attain the condition coav CoYAC ?
Curve 1 in Fig. 2 illustrates the dependence of the amount of ventilation needed to- keep the amount of
latent energy from rising above 0.8 (pyAc on the specific amount of radon given off at the mine face from a
cross sectional area 8 m2 over a length of 40 m, at Cin = 3 ? 10-7 Ci/m3, (pin = 0.9 ? 108 MeV/m3, ZRn = 1.0.
Z= 1.5.
Since the capacity of the local ventilation fans is not greater than 3 to 5 m3/sec, air leakages in the
ductwork make it difficult to supply more than 2 to 3 cubic meters of air per second to a mine face of con-
siderable extent. It is for that reason that it does not always prove possible, in the case of mine workings
subject to heavy radon emanation, to keep up adequate radiation safety conditions solely by means of ventila-
tion. If the radon concentration and the latent energy are high in the air intake area, recourse to aerosol
filters incorporating FP particle-trapping fabric will be mandatory [5]. The effect achieved through the
use of these filters is illustrated by Fig. 2, curve 2. Calculations of the amount of ventilation required
when the filters are used can be based on Eq. (7), with the substitution in = 0.
To remove radon decay products filters for cleanup of mine air must combine a high degree of cleanup
with a high dust capacity, and must be lightweight, compact, nonhygroscopic, and offer comparatively little
aerodynamic resistance. Experimental prototypes of such filters have been through production tests at
several uranium mines, where results showed over 90% efficiency in cleaning up the mine air, both in terms
of coarse-disperse mine dust and in terms of radon decay products.
The filters consist of separate cylindrical sections extending 2 meters in length. The required dust
capacity (to 0.3 kg/m2) is achieved through the use of Lavsan [Dacron] fibers.
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The most favorable conditions for the effective use of these filters is in the ventilation of mine areas
by the combined method (see Fig. 1b), which offers some distinct advantages over the forced-flow method
(particularly the fact that gaseous products of ignited explosives are removed from the air with much
greater dispatch).
This means that ventilation incorporating the use of aerosol filters, when required, will in principle
meet the needs of radiation safety in terms of the miners' working conditions.
But this inference is valid only for the case of steady-state ventilation conditions. A serious deterio-
ration of the radiation energy situation at the mine face could result from outage of a local ventilation fan.
In order to evaluate the hazard involved in local-ventilation fans failing or being switched off, we con-
sider the differential equations describing the process by which the amount of radon and the latent energy
in the mine change, when there is no flow of air whatever except for the diffusion process:
w dCav D (?
1) "Cavin. (9)
dt
dcp
w fiat v 1,171 r
Yr 'T av Tav)? (10)
A rapid increase in the radon concentration after the shutdown of a fan leads to a fall-off in the radon
flow, by the law [6]
D (t) -= S AnnKd(C0 -- Cay),
where S is the surface area of the exposed mine area in m2; Kd is the radon diffusion coefficient in the
rock with porosity taken into account in m2/sec; Coo is the radon concentration in the pores of the rock at
a depth at which radon diffusion into the mine atmosphere is virtually absent in Ci/m3.
When the fan is operating, we have Cali ?77 (3)
where ne, ye denote the electron density and velocity; ue is the cross section for ionization by electrons;
T denote the ion density and lifetime. The experimental results show that the number of accumulated
ions increases with time (with duration of injection) and is directly proportional to the pressure (density)
of the neutral gas. Increasing the duration of injection to 1-2 msec is accompanied by a rapid rise in the
number of ions in the trap, to ? 1011, a density of ?109 cm-3. Subsequent accumulation of plasma proceeds
much more slowly for the following reasons. Ions will continue to accumulate in the trap for so long as the
rate at which they are being lost is less than the rate at which they are being formed. The rate of forma-
tion of ions is proportional to the neutral gas density and to the density of fast electrons in the trap. On
account of their low energy, the secondary electrons produced during the ionization of the residual gas will
not contribute to any great extent to the rate at which ions are formed. Consequently, it is desirable to
have in the trap as many fast electrons as possible. The injection current from the electron gun is limited,
however, by the negative space charge within the trap. The number of fast electrons in the trap can be in-
creased only by replacing secondary electrons lost from the trap by diffusion by electrons from the cathode
of the electron gun. The rate of this process is small, since it is determined by the difference in the rates
of diffusion of slow and fast electrons. Further, after the neutral gas in the trap has been completely ionized,
further accumulation of ions under our conditions can occur only through ionization of gas entering the trap
from the rest of the vacuum system, through the narrow gaps between the magnet coils.
The circuit for on-off modulation of the beam from the electron gun did not permit the duration of an
injection pulse to be increased without limit. It was possible, however, to vary the repetition frequency of
the injection pulses. Consequently, to permit investigation of the accumulation process, we utilized the
following regime of operation. The injection current is raised to its maximum value, and the pauses be-
tween injection pulses arranged so that the plasma does not have time to collapse before the succeeding in-
jection pulse is applied. The accumulation process is illustrated in Fig. 4, which shows oscillograms of
the injection current and the ion current in the ring gap. The upper pair of oscillograms were taken at the
beginning of the accumulation process, and the lower pair under conditions of saturation. The ion current
is quite small while the injection pulse is being applied. Termination of injection, when the excess negative
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n Cm-3
w
49
48 -
0,7 -
45
45 -
43
0,2 -
0,1 ,7;77vpz(
10
20
Fig. 6
30
z/0
H2, kG2
15
,
1
d
I
%I_
\?\
A
/
400
500
800
1000
Fig. 7
1200
1400 E, eV
Fig. 6. Ion density as function of magnetic field. p = 10-6 mm Hg, E = 500 eV, le = 10
mA. Duration of injection pulses 20 msec; pause between injection pulses 2 msec.
Fig. 7. Electron energy distribution after injection has been switched off. E = 1700 eV,
p = 10- mm Hg; 1) Tdelay = 0 pcsec; 2) rdelay = 1500 ?sec.
7
charge is no longer maintained by the electron current from the electron gun, is followed by a more intense
loss of ions through the ring magnetic gap. The number of ions which leave during the pause between injec-
tion pulses is proportional to the density of accumulated ions. This quantity rises from pulse to pulse and
reaches saturation in a few seconds. The pulse of ion current is almost rectangular. The ion lifetime was
determined from the decay of the ion current when injection was switched off. It was 5-10 msec.
The pressure in the rest of the vacuum system (of volume 200 liters) was observed to fall during the
accumulation process. Density estimates based on the reduction in pressure agree with estimates based
on the number of ions leaving the trap through the ring gap during the pause.
The ion density in the trap under saturation conditions must be determined by the rate at which ions
are being lost. The ions in the potential well can leave it either as a result of collisions, or as a result cif
diminution of potential in the magnetic gaps. The density limitation associated with ion loss through the
magnetic gaps was discussed at the beginning of the article. It can be seen from Fig. 5 that the ion density
increases with increasing energy of the injected-electrons. Increasing the energy of the injected electrons
creates a deeper potential well and so shifts the density limit associated with the potential "sag" towards
higher values. This also means that a greater current can be injected into the trap.
The loss of plasma through diffusion across the magnetic field must get less as the magnetic field is
increased. Increasing the magnetic field will also counteract the diminution of potential in the magnetic
gaps, which is proportional to the thickness of the sheet of electrons leaving the trap through the magnetic
gaps. Figure 6 shows the square-law dependence of density on magnetic field. The maximum density esti-
mated in our experiments is ? 1012 cm-3 (magnetic field in gaps ?5500 Oe, energy of injected electrons 1.5
keV, residual gas pressure 10-7 mm Hg). This value is almost 100 times greater than the density of the
neutral gas. The low residual gas pressure implies a long accumulation time. This regime is justified,
however, as the lifetime of the plasma particles increases as the neutral gas pressure is reduced.
The lifetime of electrons in the trap must depend on their energy. The slow, secondary electrons
formed by ionization of the neutral gas and captured by the magnetic field must pass more rapidly to the
walls of the trap than fast electrons. Figure 7 shows the energy distribution of electrons leaving the axial
magnetic gap in the pause between injection pulses. One of these curves was measured immediately after
the injection current was switched off. The other was measured 1.5 msec later. There are effectively no
low-energy electrons. The mean energy of the electrons is ?I key; the energy of the electrons injected
into the trap is 1700 eV. The energy distribution does not change much over 1.5 msec. This implies that
fast electrons have a longer lifetime than cold electrons and that energy losses are small. This conclusion
is further supported by measurements of the temporal dependence of the electron current in the axial mag-
netic gap for various retarding potentials.
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The energy losses are characterized by the injection current under steady-state conditions. In the
ideal case of zero losses, the injection current must "cut off" completely. In reality, the injection current
goes to make up the losses. If the current is multiplied by the injection energy, we obtain the power P con-
sumed in making good the losses in the trap. For E = 1700 eV and an injection current of 10 mA, P = 17 W.
The total energy of the electrons in the trap is approximately equal to W = EN, where E and N denote the
mean energy and the number of electrons in the trap. For E = 1 keV we have W = 0.12J. The energy life-
time canbe estimated as Tenergy = W/P r=-17.5 msec. The loss of ions from the negative potential well must be
accompanied by an increase in the depth of the well, and the loss of ions must occur simultaneously with
the loss of electrons across the magnetic field. The main energy losses are, evidently, those due to the
passage of electrons across the magnetic field.
The long lifetimes of the plasma particles testify to the stability of the plasma within the trap. Low-
frequency oscillations of diochotron type [12] are observed to develop under saturation conditions (see Fig. 4)
in the magnetic gaps of the trap. These oscillations further increase the rate at which cold electrons pass
to the walls of the magnetic gaps.
LITERATURE CITED
1. Berkovich et al., Second Geneva Conference (1958) [Russian translation], Vol. 1, Atomizdat, Mos-
cow (1959), p. 146.
2. H. Grad, Phys. Rev. Letters, 4, 222 (1960).
3. T. Allen and R. Bickerton, Nature, 191, 794 (1961).
4. M. G. Koval'skii, S. Yu. Luktyanov, and I. M. Podgornyi, Yaderni Sintez, 1, 81 (1962).
5. D. Hagerman, Nuc. Fus. Suppl., 1., 75 (1962).
6. 0. A. Lavrent'ev, Ukr. Fiz. Zh., 8, 440 (1963).
7. 0. A. Lavrent'ev, Ukr. Fiz. Zh., 8, 446 (1963).
8. 0. A. Lavrent'ev et al., Ukr. Fiz. Zh., 8, 452 (1963).
9. 0. A. Lavrent'ev, in: Magnetic Traps [in Russian], izd.
10. A. Ware and J. Faulkner, Nucl. Fus., 9, 353 (1969).
11. K. D. Sinernikov et al., in: Plasma Physics and the Problems
AN USSR, Kiev (1965), Third Edition, p. 77.
of Controlled Thermonuclear Synthesis
[in Russian], Izd. AN USSR, Kiev (1965), Fourth Edition, p. 388.
12. Yu. I. Pankrat'ev et al., At. flerg., 31, 274 (1971).
149
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NONLINEAR THEORY FOR THE EXCITATION OF
REGULAR OSCILLATIONS BY A RELATIVISTIC
ELECTRON BEAM
V. I. Kurilko, A. P. Tolstoluzhskii, UDC 621.384.6:621.3.038.624
and Ya. B. Fainberg
1. The collective interaction of charged-particle beams with plasmas is an effective mechanism for
exciting high-frequency fields and may be used, in particular, to accelerate charged particles [1, 2]. Non-
linear theory for this interaction has shown that the maximum amplitudes of the fields excited, governed by
the opposition of these fields to the beam motion, increase with increasing electron energy. It is interest-
ing in this connection to extend the study to relativistic electron beams. Nonlinear theory for the collective
interaction of a relativistic electron beam with a plasma was first worked out in [3]. It was shown in [3-5]
that the energy of a relativistic beam can be used efficiently to excite collective plasma oscillations. The
primary interest in these studies, however, was in the instability of an unbounded homogeneous beam in an
unbounded plasma, while under actual experimental conditions the beam is frequently injected into a bounded
plasma. In this case new beam particles continuously enter the interaction region. The energy of the os-
cillations which they excite may accumulate in the plasma* and lead to an increase in the field amplitude.
The dynamics of the excitation of regular oscillations in an interaction between a modulated pulsed
beam and a slow-wave cavity (Vp c) was analyzed in [9, 10] with an account of accumulation. f
In this paper we will examine theoretically the dynamics of the development of the two-stream instabi-
lity in the interaction of an unmodulated relativistic beam with such a cavity. Our goal is to determine the
maximum amplitude of the excited field, with an account of the opposition of-this field to the motion of the
beam particles, and to determine the energy distribution of the beam at the cavity exit. This distribution
is interesting, in particular, for the development of the self-acceleration of an electron beam proposed in
[13].
2. We thus assume that an unmodulated pulsed electron beam is injected into a slow-wave cavity (Vp
= Vo; where V0.E c is the velocity of the beam particles at the entrance to the cavity), in which a regular
oscillation at frequency and having a wave number k11 is excited. The condition of field regularity reduces
to the requirement that the growth increment (51 for the instability be small in comparison with the distance
Au) AkilVo = 7rV0/L (where L is the cavity length) between individual frequencies in the spectrum of driving
forces exerted on the cavity by the beam [9, 10]. In this case we can neglect the excitation of spatial har-
monics of the cavity field not in synchronism with the beam. Then the self-consistent system of equations
for this problem can be written
a2E?
at2 ? Q2E11? ?43T-1J;
j = g dpu (p) f (t, z, p); F11 = E (t) cos klizcb (r); 23-t g (r)r dr =1; W(0)=.
(la)
(lb)
*Accumulation of the energy of irregular oscillations excited by an electron beam in a plasma half-space
was studied in the quasilinear approximation in [6-8].
fThe efficiency of the interaction of a relativistic beam with a retarding structure was studied in the approx-
imation of a specified field in [11, 12] on the basis of the energy spectrum of the electrons leaving the system.
Translated from Atomnaya Energiya, Vol. 32, No. 2, pp. 137-142, February, 1972. Original arti-
cle submitted March 29, 1971.
150
C 1972 Consultants Bureau, a? division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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0,5
0 0,2 0,3 44If the zi and pi integrals in system (2) are known,
eE,7c
moc2 the solution of kinetic equation (la) is
Fig. 1. Dependence of the growth increment = (1116 - zi 4016 iP -Pi (To 40)1, (3)
on the field amplitude and injection energy for where dn aI(q0)dq0 is the number of beam particles in
L = 4 (a) and L = 6 (b). 1) yo = 3; 2) yo = 5; 3) the trajectory whose parameters qo lie in the interval
yo = 7; 4) yo = 10. (q0, qo + dqo). The function 1(q0) is determined unam-
biguously by the injection conditions; in our case of a
monoenergetic beam, dn = I (to)dto is the number of beam particles which enter the cavity during the time
interval (to, to + dto), and 1(t0) is the current of beam particles at the cavity entrance. We thus find the
final expression for the beam current density in the cavity:
j (r, z, t)= eg (r) dt0I (to) z1 (t1, to) [z ? zi (T1, to)]; (4)
0 D11. A theoretical discussion of the diffusion
cooling coefficients in porous media is given in [16]. This paper substantiates relationship (3), demon-
strates the validity of expression (4) for an anisotropic medium, and establishes that
( Do 2
C D1) ?
if A(v) is independent of the velocity. These theoretical results simplify the use of expression (3) in ex-
perimental investigations. They also confirm the admissibility of comparing most of the data given in Table
1 with theoretical calculations and with each other, since relationship (4) was satisfied within the limits of
the error in Ci in experiments where this relationship was not used beforehand.
In using relationships (4) and (5), there remains an arbitrary coefficient (CI_ or CD), which should be
expressed in terms of known quantities. The point is that the aim of experiments with pulsed neutron sources
in porous media is different from the aim of similar experiments with solid blocks. Actually, while the ma-
terial characteristics that can be used in calculations are measured in experiments of the latter type, the
diffusion coefficients DII and DI are far from being such universal quantities. Besides the characteristics
of the material, they also include the characteristics of the channels (porosity and channel dimensions and
shape). Therefore, the purpose of experiments in porous media is the verification of theoretical expres-
sions for D11 and 131. Consequently, it would be desirable to have theoretical expressions also for the other
coefficients in expression (3) (C1, CII and Cx)?
(5)
*Expressions similar to Behrens' equations were derived in 1948 by S. L. Sobolev and V. S. Furs (cited
in [11, 12]).
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1200-
1000-
42
42
0,3
44 102 8 ,cm-2
z
, I 71,/
`.5 I / 0,321
/7/
44i I i'7F 0,40
IA'
0,5 /91 4421
e ?o,
Fig. 3. Results obtained in measuring the decay constants
a for beryllium-oxide blocks in a B12, B11, a coordinate
system. The points and crosses represent the a values
when only B1 or B12 varies. Curves 1-5 represent the in-
tersections of the surface a = vZ, + Di.132? + D11B1 ? CB41
4
IIBII (CI. + Cl) B2_03211?G1311 by the planesB, equal to
0.226.10-2, 0.273 .10-2, 0.321 ?10-2, 0.406 ?10-2, 0.491
? 10-2 cm-2; curves 6 and 7 represent the intersections of
the surface by the planes B211, equal to 0.122 ?10-2 and
0.141 ? 10-2 cm-2.
0,226
42n
A simple derivation of expressions for the diffusion cooling coefficients in a porous medium is given
in [17]. It has been shown that
= co (140_D ) 2 ; cii = co ( DDoll )2 ;
(6)
C = 2C, D- " .
Relationship (5) and the approximate relationship (4) are obtained from these expressions.
The second remark concerns the results pertaining to channels with large cross sections. It is evi-
dent from Table 1 that the experimental values of DI almost always (except the results of [2]) coincide with
the values calculated by means of the Carter and Benoist equations within the limits of measurement accu-
racy *
For channels with a large cross section [(VA) > 1.5; R = 2V/S is the hydraulic radius of the channel,
and V and S are its volume and surface area, respectively], the theoretical values of DII somewhat exceed
the experimental values, the more so, the larger the channel radius. This is clearly shown in Fig. 1 (black
points), borrowed from [8]. The authors of this very thorough experimental and theoretical work, who are
engaged in an extensive program of investigation of heterogeneous media (including lattices of empty chan-
nels and lattices containing pure absorbers and fissionable materials), have indicated that the finite channel
length could be a possible cause of the above discrepancy, which they intend to investigate.
However, in investigating the neutron leakage from a moderator block with a single channel, an ex-
pression was derived in [11] for the correction for longitudinal leakage in considering a channel of finite
*The theoretical inadequacy of Behrens' equation for DI was first indicated in [18].
157
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cs)
C.)
CI)
0
CI)
C)
'0
CL)
?-?
C.)
4,1
4,1
(3)
0
0
t=1
a)
hi)
0)
c4-1
0
a)
1:4
TABLE 1.
158
Remark
Assumption: C = 0
X
Do= 2.02-105 cm2
/sec; it is assumed
that Cri , CI and
C11, Cx equal zero
l'ransport mean free
path x = 0.431 cm
, and Cx equal
zero; x = 2. 5 cm
Do = 1.34.105 cm2/sec
X = 1.61 cm; Cx= 0
(3'
+
-I
u
It
x
u
D0=2.06.105 cm2
/sec; X=2.49;
CXII+ CI
ID? = 2.07 -105 cm2
1,037
1,145
1,362 /sec; X= 2.5 cm;
1,724 c = + C
2,268 x CI. 1
3,504
cr.
e...
(0
' C
C) .9
74 4
C.) v.
0
0?. I
CO
0 CV 0) CV ,,
CV ,-, .., CY) C.-
CO CO a, ,-.1 ,-1
1
.,,
s,
Cr,
?,
Cl
CO +I
00 ,. CV m. NV VD M
1 N
.. .e. CC . .. a.
experiment
C.>
,,
-
CC
co
CO
1,731+0,060
2,406+0,098
1,277+0,050
1,326+0,060
1,539+0,086
.
I
CD
..-4
0
CD
dd
CO
,-,
,,
,,
CV
0
0
+I
CO
CO
2,28+0,08
....1. 0 CO CO r- CO
CO
0 ,, .,, 0 0 ? 0
CD CD CD CD CD CD
0
id -El dd id dd dd di
00 CD CV M CO CV CD
CD CD CD c) 00 CV LO
0 CD .1+ CD COO?
,, CO e, ..,.C1 CO
0 CD 0 0 0 CD
- .
CD CD CD 0 0 0
+1+1-H-H-H-H
0 CD 0) V- ,, 00
u7, LC, NV N17 cI 0
,- CO .., CO CO CO
calculation
Benoist
[14],Les- Carter 1Behrens
lie [3] [13] 1[10]
C7,
co
,-i
COCI cn CO cn
cp CV CV CD ',./'
,, CV ..., ,, CO
...-q
CO
ICDCO
0,

c)
. . ,
-H 8
0 CD
ci -H
LI) 0 CD CV 00 0 CO
0 0 CV 0) 0 cA ...1+
IIIIII
I /
0, ,-, 0, 0.1 co
CD 0) 0 ...1, 0)
c0 r-- ^ CD N., V,
- ?
,. CO m. CO c.
1
1
1
CO
11 CC
cD 0tr.,
CD -
.
m; +I
CV ...1+ CV .....1" CO CD
CD NV Co Cy ..../. ,-, c,
? - ? .
..., ,-, ?, ?, ,-, ,-, ?,
IIIIII
I I
.4, ,..o tn 0) CD
00 CV 0 C- 0
in C) ,-, e, .....y.
- ? -
,, CV-,, CO ,-1
CO
CV
,,
I
I
CO
0
0
CO
if) CV cc) ,, ...1+ CO an
0 .,. CV
,-i ,, ,, e, e, ,. ...
CY) ,....r ,, In CV -../.
CV C- c0 0) Cr, 00
0 0 CV

,, ,, t, ,,,. cA
0
,-I
0-
+1 1
?,...
c.
1,19?0,030
1,375?0,030
1 , 044?0 , 030
1,117+0,030
1 , 252+0 , 030
CO
0
CD -
+I
CO
COCO
'-'
I

C..
c.
0
0
+1 -
CO
0
..
CO
0
c,..
+1
CO
,,
CV-
CO CO CO CO r CV CO
CD 0 CD CD 0 CD CD
- . ? - - ?-
CD 0 P C) CD 0 0
+I +1 +1 +I +1 +I +I
CO CO CO CO CO CO CO
CD Ma, CO CO 0 CO
- - . - - .. .
,, .., a. ..1 ?e. ... a.
r r- p 0 CO ..,T
0 0 ,., ,, CO cv
0 0 CD 0 0 0
C:CCD-O o- cc c:T
+1 +1 +I +I -H +1
r- CO CO CCC- CO
.7., CO CO CD CD,.
cp (0 m.0.) 1.0 (7,
... - ..? - .. ..
a. a. a. e. a. CO
CC CO ,
CO CO
CO CO
6. 6'
?
CO CO CO
CT> a.. GO IC M
CO 0....1+ CO -L,
CO CO 0 0 CO
O. O O O O
CO
CO
CO
c,
I
CO
CO
CO
O
.,_,
CC
CO
.-100-e.COCCOC7>
r COOCD CO r- cD
CO ..-, CO CO CO r CO
0 CO CO CO CO 0 CO
o o co o o o c,
0 CO -CCC CO CO
00 ,-, 00 CD ,-. 0
CO CO p CO CO CO
0 0 CO CO CO CO
co- OOOO O
cm Rix cm ceix
CC co
CO CO
CO CO
CO CO CO

CD CD CD 0 0
CO .07-0, CO
0,040,0, "
CC
VP
..
CC
I-
CD
CO
0
OD VP OD uP uP VD cc,
- - - -
CO...t CO.0, CC ,,n CO CO
?. ?, ? ?, "0, CO
O
c,
an CO
CCC?
-? -
CO N-.
CO CO CO CO CO
P 0 CO CO CO
- - -
CY- CY- .7, N, N.,
CO
CO
CO
I
L.O.
CO
CO
CO
CO
CD
.....1+0)0)C0c0.700)
CO CO CD CO CD CO CD
. - . - . - -
CD ., CV ,, cq ,, cq
GO CD CO CO CI CO
. - . .
CD ,, CV-CA-
0) CO
CO CO
??
CV cV 0 00 00
r r 0) oe; C6
CO
CO
CO
I
CO
CO
CO
0
0 CO r CO r- CO r
0 00 0 00 0 00 CD
,, 07- in- 0)- k.r)- c0- kr;
In v) In Le) in 0
,-4- CV-c6,77,1C--
Anisotropic medium
reference
Square lattice of?
round-section chan-
nelS in Plexiglas [1]
Same, in heavy
water [2]
Triangular lattice of
round-section chan-
nels in water [3]
Square lattice of
round-section chan-
nels in graphite [5]
Square lattice of
square-section
channels in beryl-
lium oxide [4]
Square lattice of
round-section chan-
nels in graphite [6]
Same, data borrowed
from [7]
Same, data borrowed
from [8]
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Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100002-9
TABLE 2. Measurement of the Decay Constant a in Blocks with Empty Channels
Me-B2.
dium
Characteristics of the medium
Block dimensions along the axes, cm
a, sec
102,
cm-2
Y
z (parallel
with the
channels)
1
Square lattice of channels with 5x5-cm 60,2
60,2
50,0
1709,1
0,832
sections in beryllium oxide. Lattice
75,3
90,4
60,2
90,4
50,0
40,0
1563,1
1549,4
0,747
0,740
parameters: a=15.0 cm; R=2.5 cm;
60,2
60,2
60,0
1524,6
0,733
R/X = 1.337 ; p = 0.125
60,2
75,4
60,2
75,3
70,0
50,0
1413,7
1407,2
0,672
0,662
75,4
75,3
50,0
1411,8
0,662
90,4
90,4
45,0
1365,1
0,640
60,2
60,2
80,0
1323,8
0,631
60,2
60,2
80,0
1337,5
0,631
75,4
90,4
50,0
1323,1
0,614
60,2
60,2
90.0
1281,3
0,603
60,2
60,2
90,0
1271,8
0,603
75,3
60,2
70,0
1265,6
0,587
90,4
90,4
50,0
1243,7
0,567
75,4
75,3
60,0
1221,3
0,563
75,4
60,2
80,0
1201,7
0,546
75,3
60,2
90,0
1128.1
0,518
75,3
60,2
90,0
1117,0
0,518
90,4
90,4
55,0
1140,7
0,511
75,4
75,3
70,0
1108,4
0,509
75,4
75,3
70.0
1115,7
0,509
?
90,4
90.4
60,0
1051,8
0,468
75,4
75,3
80,0
1036,3
0,461
75,4
75,3
80,0
1041,6
0,461
75,4
90,4
70.0
1033,1
0,454
90,4
90,4
65,0
985,7
0,434
75,4
75,3
90,0
978,1
0,433
75,4
75.3
90,0
981,7
0,433
75,4
90,4
80,0
956,7
0,413
90,4
90,4
70,0
932,9
0,407
90,4
90,4
70,0
936,9
0,407
75,4
90,4
90.0
885,1
0,385
75,4
90,4
90,0
894,5
0,385
90,4
90,4
75,0
888,5
0,384
90,4
90,4
80,0
863,7
0,366
90,4
90,4
80,0
875,3
0,366
75,4
93,4
100.2
840,0
0,364
75,4
90,4
105;1
828,0
0,356
90,4
90,4
85,0
823.7
0,351
90,4
90,4
90,0
803,9
0,338
90,4
90,4
90,0
805,3
0,338
90,4
90,4
95,0
770,4
0,327
2
,Square lattice of 4x4-cm channels in
48,3
60,1
44,0
1864,0
1,072
beryllium. Lattice parameters: a=12.0
60,4
60,2
60,1
60,4
44,0
60,0
1688,0
1389,2
0,939
0,745
cm; R=2.0 cm; R/X =1.342; p =0.125
60,4
60,3
80,0
1188,0
0,641
60,4
84,4
60,0
1229,5
0,625
60,4
72,4
68.0
1179,2
0,618
3
Same. Lattice parameters: a = 5. 64 cm;
64,0
64,0
64,0
72,4
64,0
56,0
2052,4 0,775
2107,3 0,680
R = 2. 0 cm; RA = 1.342; p = 1.0
56,0
56,0
84,0
2134,7 0,642
80,0
74,0
44,0
2349,6 0,621
56,0
56,0
56,0
2535,8 0,608
4
Square lattice of 3x3-cm channels in
50,0
50,0
48,0
2506,1 1,047
beryllium. Lattice parameters: a= 5.0
50,0
65,0
50,0
65,0
80,0
48,0
1975,7 0,822
1929,5 0,781
cm; R= 1.5 cm; R/X = 1.01; p= 0.5625
60,0
55,0
64,0
1830,1 0,742
5
Square lattice of 2x2-cm channels in 49,2
53,6
56,0
1798,7 0,952
beryllium. Lattice parameters: a= 4.47 58,1
40,2
62,6
53,6
48,0
68,0
1676,9 0,871
1658,6 0,865
cm; R= 1.0; RA = 0.67; p = 0,250 53,6
58,1
56,0
1648,0 0,854
length. This correction is applied by adding to the right-hand side of (3) the term -GBli [171, where
G = 1.725 Q D
1 p 0,
while Q is a coefficient dependent on the channel shape.
(7)
159
Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100002-9
Declassified and Approved For Release 2013/03/01 : CIA-RDP10-02196R000300100002-9
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