SOVIET ATOMIC ENERGY VOL. 53, NO. 3

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000300010003-8
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 83
• Document Creation Date: January 4, 2017
• Document Release Date: March 4, 2013
• Sequence Number: 3
• Publication Date: September 1, 1982
• Content Type: REPORT

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ISSN 0038-531 Y.
March, 1983
SATEAZ 53(3) 577-654 (1982)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPflIA
(ATOMNAYA ENERGIYA)
Russian_ Original Vol. 53, No. 3, September, 1982
b
C
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
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SOVIET ATOMIC ENERGY
A translation of Atomnaya, Energiya
March, 1983
Volume 53, Number 3 September, 1982
CONTENTS
Engl./Buss.
ARTICLES
Distributed. Microprocessor-Based System for Monitoring Radiation of
Nuclear Power Plants - A. A. Denisov, V. S. Zhernov,
I. S. Krasheninnikov, V. V. Matveev, N. V. Ryzhov,
and V. M. Skatkin . . . . . . . . . . . . . . . . . . . . . . .
577
131
Monitoring the Distribution of Radionuclides Throughout the
Technological Circuits of a Nuclear Power Station
- V. L. Antonov, A. A. Gruzdeva, V. S. Zhernov, S. K. Kozlov,
0. B. Lapshev,"V. V. Matveev, V. V. Pushkin, M. K. Romanichev,
A. E. Shermakov, E. P. Vargin, and L. P. Drozdova . . . . . . .
. 587
138
Distribution of the Flux Density and Hardness of the Neutron Spectrum
with Height and Over the Cross Section of the Heat-Generating
Assemblies of VVER-365 and VVER-440 Reactors B. A. Bibichev,
V. P. Maiorov, V. D. Sidorenko, and P. I. Fedotov . . . . . . . . .
596
143
Control of the Neutron Distribution in a Reactor by a Liquid Absorber
- P. T. Potapenko . . . . . . . . .
601
147
Harmonic Simulation of a Power Reactor - P. T. Potapenko . . . . . . . . . .
608
151
Refinement of Boundary Conditions in the Calculation of Close-Packed
Lattices by the Surface Pseudosources Method - N. V. Sultanov
and I. A. Zhokina . . . . . . . . . . . . . . . . . . . . . .
614
155
Gas Release from Uranium Dioxide - V. Sh. Sulaberidze
and A. V. Pershin . . . . . . . . . . . . . . . . . . . . . . . . .
619
158
Neutron Yield of the (a, n) Reaction for Multicomponent Media
- V. I. Bulanenko, V. V. Frolov, and E. M. Tsenter . . . . . . . . . .
622
160
Yields of the Photofission Products of 237Np - M. Ya. Kondrat'ko,
A. V. Mosesov, K. A. Petrzhak, and 0. A. Teodorovich . . . . . . . . .
629
164
Swelling in Cold-Deformed OKh16N15M3B Steel on Irradiation in a
High-Voltage Electron, Microscope - M. M. Kantor, V. N. Kolotinskii,
I. I. Novikov, A. G. Ioltukhovskii, V. K. Vasil'ev,
and N. Yu. Zav'yalova . . . . . . . . . . . . . . . . . . . . . . . . .
633
167
Study of the Deactivation Mechanisms for Some Constructional Steels
by Secondary-Ion Mass Spectrometry - Yu. G. Bobrov,
S. M. Bashilov, G. M. Gur'yanov, and A. P. Kovarskii . . . . . . .. . .
638
171
Optimization of Isotope-Separation Processes in Columns - V. A. Kaminskii,
V. M. Vetsko, G. A. Tevzadze, 0. A. Devdariani,
and G. A. Sulaberidze . . . . . . . . . . . . . . . . . . . . . . . . .
642
174
Determining Distribution and Concentration of Certain Elements with
the Aid of a Charged-Particle Beam - I. G. Berzina, E. B. Gusev,
A. V. Drushchits, V. S. Kulikauskas, and A. F. Tulinov. . . . . . . .
648
178
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CONTENTS
(continued)
Engl./Russ.,
Technique for'Preparing Microfilters with High Specific Capacity
G.-N. Flerov, E. D. Vorob'ev, V. I. Kuznetsov, V. A. Shchegolev,
G. N. Akap'ev,.P. Yu. Apel', T. I. Mamonova, and L. I. Samoilova . . . 652 181
The Russian press date (podpisano k pechati) of this issue was 8/23/1982.
Publication therefore did not occur prior to this date, but must be assumed
to..'have taken place reasonably soon thereafter.
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DISTRIBUTED MICROPROCESSOR-BASED SYSTEM FOR MONITORING
RADIATION IN NUCLEAR POWER PLANTS*
A.
A.
Denisov, V. S. Zhernov,
I.
S.
Krasheninnikov, V. V. Matveev,
N.
V.
Ryzhov, and V. M. Skatkin
Protection of the environment from anthropogenic actions is becoming a more urgent problem
with each passing year. With the rapid growth of nuclear power, one of the complex and spe-
cific problems in this area is ecologically safe operation of nuclear electrical power plants,
nuclear thermoelectrical power plants, AST, etc. The most important part of the problem is
creating measuring and information gathering systems and control systems, which permit monitor-
ing the changes in the environment due to the action of such objects, i.e., monitoring fac-
tors acting on the environment, evaluating the actual state of the environment at any given
time, and forecasting the possible future effect.
The presently available radiation monitoring systems [1-3] provide the necessary informa-
tioh on the radiation state of the main and auxiliary equipment, enclosures, emissions of
radioactive substances into air, water, radiation exposure of personnel, etc. However, in
the future, such systems must encompass all possible perturbing factors and must not only
provide information, but also in some cases control.
Systems for monitoring such enormous commercial objects as, for example, nuclear power
plants, include geographical and biological, impact and regional monitoring in the presence
of combined radiation, physical, and chemical perturbing factors, i.e., they on the one hand
represent the most complex and important systems for providing monitoring information and,
on the other, they are the most advanced (developed) systems that lay the path for developing
other similar monitoring systems.
Aside from expanding the functions and increasing the amount of monitoring and control,
further development of such systems is directed toward increasing the measuring capabilities,
since measurement of physical parameters is the primary function of these systems. The ac-
curacy of measurements can be increased by decreasing the influence of external background
and the background accumulating at the monitoring points, eliminating systematic error, and
including automatic compensation of the nonlinearity of the detectors.
The economic factors in creating and using such systems are an important aspect. The
cost of the systems is in many ways determined by the cost of replacement parts, communica-
tion lines, assembly, and startup operations. The operational cost is determined by the
cost of maintaining constant parameters of the system by the service personnel, the number
and quality of personnel, and their errors.
Increasing the requirements for reliability, accuracy of measurements, especially in
real-time, and fast response, expanding the functions together with the economic factors de-
termine the requirements and criteria for constructing modern systems, choosing the structure,
elements, and composition of the main and peripheral installations and the organization of
their communication.
The development of computer technology and the advent of accessible, inexpensive micro-
processers and microcomputers permit new solutions to these problems and may permit taking
the next qualitative step in creating and improving radiation monitoring systems in nuclear
power plants. The success in solving the monitoring problems is in many ways determined by
the state of knowledge about the object, the choice of an appropriate information and measur-
ing model with optimum monitoring capacity for the given object.
*This paper is based on a report at the 2nd Conference of Member-Countries of the Council
on Mutual Economic Aid on Radiation Safety of Nuclear Power Plants, Vilnius, May 18-21, 1982.
Translated from Atomnaya Bnergiya, Vol. 53, No. 3, pp. 131-138, September, 1982.
0038-531X/82/5303-0577$07.50
1983 Plenum Publishing Corporation 577
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The pragmatic side of constructing modern systems is the development of a complete,
basic set of functional installations, which permit creating in a planned manner an object-
oriented system with optimum functional capacity, control points, equipment for maintaining
operation, i.e., making it possible for the planners of radiation safety monitoring complexes
to account for the characteristics of the object without considerable additional expenditures.
In this paper, we examine the problems of constructing modern systems for monitoring
radiation in nuclear power plants. We emphasize the problem of operational radiation monitor-
ing and we demonstrate, using this problem as an example, the possibilities of microprocessors
and microcomputers and distribution of functions over. subsystem levels.
Radiation Monitoring System Structure. The structure of the system for monitoring ra-
diation in a nuclear power plant is based on realization of two basic planning principles:
separating in the overall problem the most independent parts and introducing a hierarchy of
ordered levels for solving it. Both..principles are effectively satisfied in the radiation
monitoring system: first, due to the possibility of solving the overall problem in the form
of a parallel construction of the entire set of weakly coupled.(from the point of view of the
interaction dynamics) problems: radiation monitoring of enclosures and equipment in the power
block; radioecological monitoring of adjacent territories; monitoring pass-through and exit
paths; individual dosimetric monitoring of nuclear power plant personnel; and, second, the
specific nature of each problem is reflected in the choice of the optimum number and organiza-
tion of levels in its solution.
Figure 1 shows the structure of the complex of radiation monitoring apparatus in the
form of a three-level, hierarchial system for a two-block nuclear power plant with a water-
cooled water-moderated power reactor.
The use of standard computer equipment in the system (microcomputers and microprocessors)
permits automating most of the routine work in the operation of the complex and leads to a
more flexible interaction of the operator (dosimetrist) with the system due to the use of
a dialogue mode instead of functional-keyboards. The program realization of the system func-
tions decreases the range of technical equipment and improves its adaptation to the character-
istic of the object. The use of standard peripheral equipment at operator stations permits
broad standardization of the methods for recording and displaying the state of the object
and permits using standard forms of report documentation. Each problem is realized on a
separate subsystem of the technical equipment, and the high-frequency dynamics of the object
are localized in them. The interaction of subsystems at the upper level of the system re-
presents its low-frequency component.
We shall examine the structure of the subsystems for solving the problems enumerated above.
Radiation and radioecological monitoring is characterized by a large number of monitoring
points (300-500) distributed over enclosures and the territory encompassed by the power plant,
continuity and efficiency, and requirements for minimum delays in transformation [1, 2]. The
choice of structure for a subsystem with two processing levels is determined by the economic
saving due to the reduction of cable lengths, which is achieved by placing the processing
equipment closer to the monitoring points. The lower level of the subsystems consists of
stations for collecting data, containing the primary transducers including the detection
blocks, weather sensors, flowrate meters, as well as systems for local alarms and control,
radially connected to the base modules. At this level, the parameters being monitored are
measured and calculated in real-time, the control actions are drawn up, the working order
of the equipment is checked, and data is formed for transmitting to the upper level of the
subsystems.
The base modules form a distributed computed system, in which several loops and modules,
cascade-connected by communication lines in series with an interface, according to GOSTu
23765-79, are separated. Each loop begins and terminates in the executive module, the loop
control. In contrast to the structure in [4], the use of an executive module in the loop
permits organizing horizontally independent groups of computers (for example, for solving
subproblems involving monitoring of protective shields in the first and second loops or in
the auxiliary equipment), radially connected by lines from a series interface to the upper
level of the subsystem. One loop can encompass 100 monitoring points. The survivability of
data collecting stations with a breakdown in the communication lines to the series-connected
interface is ensured by retaining the measurement, alarm, and control functions of the base
modules and the possibility for controlling the operational modes of the module through its
built-in digital display.
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The operational control and display functions, introduction of operational records and
transmission of data to upper levels of the system for centralized display of the monitoring
processes and introduction. of the main radiation monitoring system records are executed in
the upper level of the subsystems. Radioecological monitoring of the adjacent territory in-
cludes group analysis and accumulation of data from measurements of soil, water, and other
samples, which the operator introduces at the second level of the subsystem from results
of laboratory measurements.
Monitoring of the pass-through and exit paths for contamination of hands, body, clothing,
and transport is characterized by short permissible computing time and high reliability of
the decisions adopted. The subsystem contains one level of technical equipment, whose high
capacity is achieved by local concentration of computers. The link to the upper level of
the system is established when necessary by centralized recording to contamination events.
The subsystem for individual dosimetric monitoring of nuclear power plant personnel con-
sists of two processing levels. Data collected from the ionization and thermoluminescence
dosimeters, as well as information on the content of radionuclides in the body are collected
and preliminarily processed and the personnel are identified. The results of measurements
are processed at the upper level, where an intermediate data file is formed, which is then
sent to the upper level of the system into a data bank for individual dosimetric monitoring
of nuclear power plant personnel. Operational information on random (in time) queries, for
example, in the case of regulation or repair and preventive work, as well as a periodic list-
ing of the exposure of the nuclear power plant personnel to external and internal irradiation,
are displayed by the display systems in the upper subsystem level. The data band contains
information on each worker: the y, 1, and neutron irradiation doses over a ten-day period,
the current month and year, over the time of work in the nuclear power plant, and from the
beginning of professional work together with an indication of the last name, name, the depart-
ment, section, specialty indication, and classification number.
Centralized radiation monitoring systems permit concentrating at the operator or dosi-
metrist total information on monitoring processes and radiation conditions at the plant [3].
However, increased attention to the radiation safety of nuclear power plants has increased
the number of monitoring channels up to 200-300 for each block in the nuclear power plant
and approximately to 500 in the two-block plant. Information is given to the operator in
the form of signals showing an increase above the warning and accident thresholds and reports
on the working order of the channels, translating them into the verification regime and other
auxiliary regimes (in all there are about 1500-2500 positional signals), as well as in the
form of results of measurements for each channel. Receiving this quantity of information
and adopting operational solutions for normalizing the radiation state at the nuclear power
plant leads to appreciable psychological pressure on the operator and operator fatigue. The
general problem of man-machine dialogue requires finding an optimal solution for the problem
of representing incoming information in a convenient and compact form with preliminary selec-
tion by importance and management efficiency.
Possibilities have recently been discussed for comprehensive representation of the diverse
information on radiation conditions at the nuclear power plant using colored CRT displays [4].
The information content of reports is increased and the time required by the operator, who
is responsible for the safe operation of the nuclear power plant, for analyzing events and
making decisions is decreased by the colored displays in separate channels automatically
changing in accordance with the program loaded into the microcomputer.
We can consider the application of a single colored display with variable display format
or simultaneously two and even three display formats, for example, for a two-block power plant,
etc. In order that the operator can rapidly comprehend and evaluate the background or the
changing radiation conditions, it is first necessary to display the presence or absence of
alarm signals (accident, warning, or malfunction signals), using for this purpose contrast-
ing colors and positioning of symbols convenient for perception.
The format shown in Fig. 2 consists of 300 rectangles, grouped either according to
channel number, for the channels used at the power plant (variant I or II), or according to
the connection to some base module (variant III). For normal conditions at the nuclear power
plant, all rectangles are green. When the first threshold has been exceeded in some channel,
the color changes to a blinking yellow color and when the second threshold is exceeded to a
blinking red color. In order to make the work of the operator easier, these channels are
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^
Fig. 1. Structure of the complex for monitoring ra-
diation safety at a nuclear power plant: 1) central
console of the radiation monitoring system; 2, 3, 4)
subsystem for.individual dosimetric; radioecological,
and radiation monitoring, respectively; 5) subsystem
for monitoring contamination; 6) dosimetrist's console;
7) operating console; 8) contamination monitoring
units; 9) primary processing units; 10) data collection
stations.
0 9 10 19 20 29 30 39 40 49 50 59 60, 69
0000000000 D ... 0 0 ... 0 0 ... 0 Lug 0 ... 0 0000000000
0 9
00^^^00100^
^^00^0^00^ 116 TK2.113 1,5 x 104Bq/rh'
^ ^^^ ^ ^^ ^ ^ ^
^00^^^^^00 225 RB 2. 027 32,0 x 10-tSA/kg
^ 0000 0000 ^
DDDDDDD000 358 TK1.105 4,4 x 10 s 1 sec
^^^000^^^^ ,
90000000000 / RB%.._. x1_ ti/kg
u~.oo^ooo
3 ooooaooo
4
u o^ooaooo~ ???
K`1..... ?:x
q;m
Fig. 2. Format of states: ...) blue; -) red;
---) yellow.
automatically displayed on the screen for continuous measurements with the appropriate color.
In so doing, the alphanumerical label of the channel, used for the given power plant within
the scope of a unified automated control system, as well as the physical dimensionality of
the parameter measured is indicated. The operator can put the indication manually into a con-
tinuously lit state, so as to make it possible to evaluate rapidly the change in the conditions
in other channels (according to the blinking display). If a threshold has been exceeded in
some channel and then the monitored quantity has returned to the norm, then the corresponding
rectangle is transformed into a green triangle (the fact that the threshold has been exceeded
in this channel is remembered). When a malfunction is discovered in the channel, the color
of the rectangle changes to blue, and while the channel is switched-off for the time period
required to make a check, the rectangle has a light-blue color. Priority in the representation
of information is given to the blue color, and then light-blue, red, and yellow. At the same
time, the operator can query the measurements in any other channel, which will be displayed
by a green color. This format must be constantly present for efficient evaluation of the
overall situation at the power plant.
In addition to the format presented above, it is also useful to have a second format
in the form of a group analog histogram (Fig. 3), which indicates the current values of the
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Illil
1111111
125 RB2. 027 187 x 10-9A/kg
Fig. 3. Format of the group
histogram on a black and white
display.
Above threstnld
225 TK2.113 10% 241 273 RB2.0Z7 40%
hil
z I! 111111 IIII !i.ll llllllllll 111JI11111 1111111111 ,
a J II 111!11!1!!
s' llllllllll
7
Fig. 4. Group histogram format on color display.
level of measured parameters in a chosen group of channels in the form-of vertical lines.
The number of channels in such a group is limited by the resolution of the CRT and is usually
about 100 for black and white displays [5]. For more efficient evaluation of information
in channels where the first or second thresholds have been exceeded, the corresponding channel
is transformed into the blinking line mode and can be represented in digital form on the same
screen.
The colored display increases the information content of such a format. Here, it is
possible either to increase the number of channels in a group to 250, changing at the same
time the color of the lines from green to yellow and red (when thresholds in separate channels
are exceeded), or to remain in the 100 channel format (using different colors) while introduc-
ing different information.
Figure 4 shows the format used in monitoring radioactive inert gases, for which each de-
tection block is used for measurements in several enclosures by means of remote switching of
air ducts. In addition to the colored histogram, a picture is shown on the format indicating
the open valve and the number of the enclosure from which the gas being monitored is entering.
If the threshold has been exceeded in some channel, then the number of this channel and the
value of the excess above the threshold level in percent, calculated using the equation
Ameas -Athres .100
A tires
where Ameas is the current value of parameter being monitored and Athres is the threshold
setting, are displayed automatically on the screen in an appropriate color.
The operator can also call up manually on the same format the reserve up to the threshold
level, defined according to the equation
AttiresAmeas 100,
A thres
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Fig. 5. Structure of the subsystem for monitoring ra-
diation in the power block: 1, 2) digital and operational
display, respectively; 3) printout: of group data; 4)
control panel; 5) data library storage; 6) input-output
control; 7) central console for the radiation monitoring
system;.8) central processor; 9, 10) operational and per-
manent system memory,- respectively; 11) common bus; 12)
input-output control for the sequential interface; 13)
control module with microprocessor; 14) data collecting
station; 15) base module with microprocessor; 16) detec-
tion blocks, alarms, control units; 17) sequential inter-
face.
if the threshold has not been exceeded in this channel.
All of these formats and colored displays greatly improve the operation of the man-machine
link. However, in order to maintain high reliability of the monitoring, it is useful to
provide the traditional simple and reliable general alarm systems (indicating that the first
or second threshold has been exceeded or a malfunction has occurred), signals from which can
also be used to switch-on-automatically the formats of the color displays above.
Subsystem Monitoring Radiation in the Power Block. All processing and preliminary in-
formation functions are transferred to the lower level of the system, while operational dis-
play; recording, and collecting data concerning the state of the object, and communication
with the operator and the upper level of the complex are performed in the upper level. Figure
5 shows the organization of the upper subsystem level (operating station) based on the common
bus of the Elektronika-60 microcomputer. The subsystem is constantly in the main state, in
which sequential scanning of all monitored points and automatic output of information in
analog form on a CRT (operational) display screen for all monitored points of the operator-
chosen loop (channels, in which the threshold has been exceeded, are distinguished by color
and blinking display), as well as in digital form for channels in which the threshold has
been exceeded, and selectively for any monitored point in both displays, occur. The monitored
parameters are periodically listed in red for those channels where a threshold has been exceeded
and the procedure for introducing the operational records and processing queries from the upper
level of the complex is performed automatically.
The operator interacts with the subsystem, forming with the help of a keyboard in the
control panel over several steps of the dialogue on theCRT display screen a query for opera-
tional or recorded information in the form of charts, graphs, and tables, grouped according
to the indicators of the monitored parameters, giving the type, logical and boundary condi-
tions for data output. All control actions by the operator are recorded on the printer.
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Let us examine the interaction of the components, levels of control, and organization
of the given subsystems.
The lowest level of the subsystem contains up to five loops of the base modules. The
loops operate in parallel and each of them is connected at the upper level of the subsystem
to a digital display, controllers of the input-output operational display, printer, accumul-
ator of record data on a magnetic tape, controller of input-output of the sequential inter-
face, and is closed in the executive module of the loop. In the basic state (throughout
scanning), the loop control functions are transferred to the upper level of the subsystem
in the executive modules, which sequentially increment the number of the loop channels and
translate the records of the channels on the output device in the upper level. The pro-
cedures for servicing the queries for data output from the operational records are performed
at the upper subsystem level, independent of the lower subsystem level.
Queries for output of required operational information (for example, printing the tech-
nological monitoring channels, where.a threshold has been exceeded) generate a sequence of
control commands for the loops in the base modules. Each of them can be represented as a
processor, which performs the current job, while the executive module acts as an interpreter
of the commands from the upper level. It obtains commands from the controller of the se-
quential interface and executes them on the processor (loop). When the current command has
been performed on the processor, the executive module returns control upwards outputting the
results of performing the command, entering into the output devices of the upper level. In
this state, the process of sorting and merging of channel records occurs in each loop and
between loops. In the base modules, its records are selected according to qualifying indica-
tions (for example, according to type of parameter monitored), sorted according to a fixed
sort key, and if the given relations between the trace transmitted through the interface and
the upper record formed in the selection module are satisfied, they are outputted into the se-
quential interface of the loop. Analogous interaction processes occur between the executive
modules of the loops. The termination of the regime is.indicated by complete rotation of the
same record through the loop.
The information collected, computed, and sorted by the subsystem forms the data base for
operational radiation monitoring and on a logical level is represented in the form of files
of actual data from the lower level and operational record data. The records contain data
on each monitored point: its identifying number, type of monitored parameter, value, scale
coefficient, two threshold settings, and state indication (passage through a threshold, equip-
ment malfunction).
Structure of Base Module. The required productivity of the lower level of the radiation
monitoring subsystem is achieved by separating it into a set of base modules. Each of them
contains a complete collection of functions, transferred to the level, and is related to
neighboring modules only by the transfer function.
The structure of the base module shown in.Fig. 6 reflects two aspects of its operation:
functions and logic. The functions form the external characteristic of the module, and most
of them vary with the specific planning of the subsystem. Their designation depends on the
types of connected detection blocks and stored processing algorithms. The logic of a module
is reflected in the organization of the coupling of its components (structure). The multi-
level structure of a module separates its permanent and variable functions. The permanent
functions are the measuring and control procedures. Their realization is organized on sepa-
rate microprocessor sections and is fixed in the permanent microprogrammed memory. The vari-
able functions are separated into semipermanent, which are changed during the operation of
the module, and fixed for a given module (but not necessarily the same for neighboring modules).
These functions are realized on the upper level of a module (its central microprocessor) and
differ according to the storing procedures, viz., in permanent, semipermanent, or operational
memory.
The measuring procedures are fixed in the permanent microprogrammed memory of the multi-
channel average frequency meter (MAFM), realized on the microprocessor sections. The MAFM
has up to 32 independent galvanically decoupled frequency inputs, in each of which the input
frequency can vary over a range covering four orders of magnitude from 0.5 to 5.103 pulses
per second. The model presented in [6] is chosen as one of the basic algorithms for realizing
the MAFM program. The procedure for measuring in each channel is described by the following
recurrence expression:
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
Y(niT)= X(s T) -+ -Y[(m-1)TJexp(-TIT),
where mT are the discrete time intervals fixed by the timer; m = 0, 1, 2, ...; X(mT), number
of pulses from the detecting block over the interval mT; T measuring time constant; Y[(m -
1)T], value of the average frequency calculated up to the time mT and stored as a result of
the measurements; Y(mT), new value of the average frequency calculated at time mT.
Expression (1) describes the digital equivalent of the integrating RC circuit, which
when measuring randomly distributed pulses gives a statistical error, calculated from the
equation
1/1T2nT, (2)
where n is the average frequency of the.pulses.
The condition for optimum measurements in the system operating in real time can be taken
as
which ensures constant accuracy of the measurements over the entire range and minimum delay
in the measurements. The operands in MAFM are represented in a floating point binary system,
which permits measurements over a wide range with the required accuracy. The format of the
fractional part is determined by the dynamic range of the input frequency and constitutes 16
binary digits and the integer part constitutes.8 binary digits.
The process of making measurements in each channel consists of periodic multiplication
of the information accumulated in the channel by a-coefficient, less than 1, and adding the
result to that contained in the input buffer of the given channel, after which the buffer is
tripped and accumulates the next portion of input pulses, while the final result is stored
up to the next processing cycle. The quantization period is fixed by a timer with a quartz
resonator; T and the capacity of the input buffer Bi are related by the relation
ntmaxT11 > M)
Eq. (9) has the analytic solution [7]:
q'* (r) -IlKo(r1T~
nr
(7)
where Ko is the zero-order Bessel function of the second kind and B is a normalization factor;
upon introduction of a reactivity of 0.010 the change in the average integrated neutron flux
$(r) should be 1% of the nominal value.
The steady-state static. influence function of a critical reactor with a negative power
reactivity coefficient Kp = dk/dcq is determined for a zone with an equalized ND from the equa-
tion
V2ip M' q)= - M.~ k,
whose solution in cylindrical geometry is analogous to the solution of Eq. (7):
( j/KpQ)
cP (r) = DKo r )
M ,
the coefficient D is determined by the following condition: upon introduction of a reactivity
p the average neutron flux (D should increase by p/Kp.
The necessary accuracy of the simulation depends on the type of equations being solved.
Thus when analyzing the stability of a system of local automatic regulators (LAR) in an RBMK
models with accurate simulation of two-three harmonics of the ND prove to be satisfactory [4].
It is sufficient to model deviations of the ND in the range ?10%. Larger deviations are not
permitted by the emergency protection.
Let us estimate the systematic error of the model (1), taking into account that the first
v harmonics in it are simulated without systematic error. Let the values of the amplitudes
of the first v harmonics be equal to (Dj in the case of a unit local perturbation of the reac-
tivity (p = 13). With such a perturbation the instantaneous components of the remaining har-
monics do not exceed Kj/(1 + Kand their steady-state values with the power reactivity
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I FT_
2-J
Fig. l:- (a) Structural layout of the
analog model and (b) the basic layout
of the i-th node of the grid: 1) ress-?
.tive grid; 2) units for simulation of
the harmonics.
coefficient taken into account are (Kj /(1 + KjKp-0/S) [4-6]. Since Kj > Kj+1f the relative
simulation error does not exceed
2( Kj . KK Kv+i (1 I Kp~P/S) KJ
v+1 1-KiKpU)/p 1+ i v4 f (1 Ki) (I - K T/Ii) -IF
V o0
1-K K a)/(3
Strengthening the inequality, we obtain
G'
- KSKp'i'l11
F < Kv.+t (1-I-- Kph/(3)= 1000 (1 } KpW/f3)/aj.112, ?,n. (10)
Thus, if the entire simulation range is ?10% of the nominal ND and a simulation accuracy of c
is specified, then in the model (1) one selects the v first harmonics which satisfy the con-
dition
1/a4M2 > 9/1013(14- Kp (U/(3). (11)
In accordance with this, taking the eigenvalues of the first most important harmonics into
account [4, 8, 9], the accuracy of the model (1) for an RBMK is no worse than 3% if one in-
cludes the fundamental, first, and second azimuthal harmonics in the number v. When simulat-
ing slow variations of the radial energy distribution of the.VVER-1000, the equations of sub-
critical reactor of the type (8) can be adopted as the model.
Digital modeling of the ND of a specific reactor requires satisfaction of the following
preparatory operations: 1) calculation of the matrix M and writing it into the memory device
(MD) of the computer; 2) calculation of the v first eigenfunctions of the steady reactor and
writing the corresponding elements ai [see Eq. (2)] of the numerical matrices Aj for these
im
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 Declassified and Approved For Release 2013/03/04: CIA-RDP1O-02196ROO0300010003-8
6 5 4 3 2 1 0 1 2 3 4 5 5 0 18 36 54 7Z 90 108 126 144 162
Radius, m Degrees of azimuth
Fig. 2. Instantaneous influence functions of the LAR rods of an RBMK in the (a)
radial and (b) azimuthal directions and (c) a chart of the placement of the de-
tectors (0) and the seven LAR rods IS): -) digital simulation; ---) analog
grid model; -?---) experiment in a reactor.
harmonics into the MD; and 3) calculation of the transfer functions Jj(p) or formulation of
the differential (difference) equations corresponding to them. Naturally, computer simula-
tion consists of multiplication of the transfer matrix )W(p) and the reactivity vector:
V% (n) [M S; J, (P) A.i] P (P)? (12)
The operations written here in'terms of the Laplace transformation are conveniently
carried out on a computer with the help of the apparatus of state space [10]. In order to
obtain the matrix M, for example, from Eq. (5) [we set ay/8t 0], the operator 0'1Q* is
written in difference form, as a result of which the matrix equation
(D--K[31)q*- 1D(1-P)k
(13)
is obtained, where I is the unit matrix, D is the difference matrix, and (D is the diagonal
matrix of the nominal ND. Since for. model (5) the reactor is subcritical, then the matrix
(D - KW-1 is not singular, and
M== --(D-,KP1)- (1-S), (14)
Effective programs exist for the inversion of sparse matrixes in a multiplicative formula and
for storing them in an MD using packing in the form of a coherent copy [11].
An analog model [12] implementing the proposed simulation method consists of a resistive
grid and v operational amplifier units connected to it also through resistors (Fig. la). One
operational amplifier each is provided for each node of the grid in a traditional analog sim-
ulation.
One of the nodes of the resistive grid is presented in Fig. lb, which simulates, in ac-
cordance with the outlined procedure, a subcritical reactor; more accurately, its equalized
control zone, where the detectors and rods are mounted. The equation for the i-th node of
the resistive grid (see Fig. lb) is
R R
R Uif Ei
eq i
dUi
C dt
where Ui is the voltage at the i-th node, which simulates the deviation of the ND; n, number
of the four nodes adjacent to the i-th one; Ei, source voltage, which simulates the deviation
of the safety and control rod (SCR) from its base value (reactivity); R, resistance of the
grid resistors; and Req, resistance of all the resistors connected in parallel to the i-th
node:
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Re4 = Rin +-Rint+Rout -hRZ (16)
where Rin and Rout are the resistances of the resistors which connect the node to the inputs
and outputs of the amplifier units, and RZ are the resistances of the load, for example, adetector model. Of course, not all the nodes of the grid are equipped with all the elements
presented in Fig. lb; only the resistors R of the grid are naturally obligatory.
If one writes the operator V2 in Eq. (5) in finite-difference form, then for a zone with
a balanced ND it is transformed to the form
h2f3cp"? + h2k; (
-i =i1z2 a &
where h is the partition step expressed in migration units. The computational relationships
for the grid parameters follow from a :comparison of..Egs. (15) and (17) and .the adopted scales
for k and T*
U` =Mwcpf; Et =MkDtki;
RC = tih2; R/Req = h2?;
RMk !RjM, = h2 (1- P).
As has been shown by Ya. V. Shevelev [8], a reactor with a large equalized zone.can be
replaced with good accuracy by a reactor with a completely equalized ND and a boundary which
passes halfway between the reactor boundaries and its equalized zone. In this case the bound-
ary nodes of the resistive grid should be "grounded" through the resistors Req but not through
R. The test for.regulation of the boundary "grounded" resistors is: the variation in the
neutron flux averaged over the reactor'due to an introduced reactivity of p 0.01 should
amount to 1%.
The transfer functions of the amplifier units are selected so that together with the
.resistive grid they reproduce the transfer functions of the appropriate harmonics. For ex-
ample, the appropriate unit to reproduce Wot(p) -[see Eq. (4)] should have a transfer function
for the voltage of 2/(Top + 1). For each of the two azimuthal harmonics (sinjy, cos J(P) one
unit each is provided; the conductivities of the resistors Rin and Rout are chosen to be
proportional to the value of the harmonic being simulated for the reactor cell corresponding
to.-the. i-th node.
Examples of the Results. The procedure described has been implemented with digital and
analog models of a reactor, the main purpose of which is the investigation of systems for ND
Regulation. For example, a programt has been written for digital simulation of the instan-
taneous component of the ND in an RBMK with a spatial grid spacing of 25 cm, and a grid analog
model with a spacing:of 50 cm is produced. For illustration the instantaneous influence func-
tions are given in-Fig. 2 for the central and peripheral LAR rods of an RBMK [13] when they
are withdrawn by 0.010 as obtained with these models and experimentally on an RBMK.
The matrix of the instantaneous discontinuity,.supplemented by a factor which takes into
account the prompt neutrons, which is needed to calculate the LAR within the framework of the
first adiabatic model [4], follows from the data and chart of the placement of the LAR rods
and detectors which have been.given (Fig. 2c):
5.0
1.3
0.4
0.2
0.4
1,3
1.0
1.3
5.0
1..3
0.4
0.2
0.4
1.0
0.4
1.3
5.0
1.3
0.4
0.2
1.0
2
0
4
0
3
1
0
5
3
1
0
4
1
0
1
.
.
.
.
.
.
.
%
0.4
0.2
0.4
1.3
5.0
1.3
1.0
P+1
1.3
0.4
0.2
0.4
1.3
5.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
3.0
tThe program and calculation are the work of 0. L. Bozhenkov.
According to the data of V..V. Postnikov [4].
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
As has been shown [4], when the LAR of the correcting inverse matrix M-' is incorporated
into the system (between the mismatch amplifiers and the comparison elements), autonomy of
the local regulators is achieved.
I11t is important to emphasize that the matrix M of the instantaneous discontinuity does
not depend on inertial feedbacks (temperature, vapor, poisoning). Therefore simulation of
ND deviations at different power levels requires appropriate fine adjustment of the param-
eters of model (1) only for the v harmonics being taken into account. The. described harmonic
model has been effectively used in connection with the development of algorithms for ND control
in a reactor of the Beloyarskaya nuclear power plant [14] and trainers for instruction in the
control of RBMK reactors.
Thus, the simulation procedure consists of calculating the steady ND of subcritical
reactor and simulating the behavior of its first v harmonics. It permits shortening the
machine time for digital simulation and reducing the amount of equipment needed for analog
simulation in comparison with direct programming of the nonsteady equations describing the
behavior of the ND.
1. P. T. Potapenko, At. Energ., 27, No. 3, 189 (1969).
2. A. A. Anikin and Ya. V. Shevelev, Vopr. At. Nauki Tekh., Ser. Fiz. Tekh. Yad. Reaktor.,
No. 3 (12), 35 (1980)-
3. I. Ya. Emel'yanov, P. A. Gavrilov, and B. N. Seliverstov, Control and the Danger of
Nuclear Reactors [in Russian], Atomizdat, Moscow (1975).
4. E. V. Filipchuk, P. T. Potapenko, and V. V. Postnikov, Control of the Neutron Field of
a Nuclear Reactor [in Russian], Energoizdat, Moscow (1981).
5. P. T. Potapenko, At. Energ., 41, No. 1, 25 (1976).
6. P. T. Pbtapenko, At. Energ., 50, No. 1, 8 (1981).
7. R. Megreblian and D. Holmes, Reactor Theory [Russian translation], Atomizdat, Moscow
(1962).
8. Ya. V. Shevelev, Vopr. At. Nauki Tekh., Ser. Fiz. Tekh. Yad. Reaktor., No. 3, 23 (1980).
9. L. P. Plekhanov, At. Energ., 42, No. 4, 268 (1977).
10. Yu. Tu, Contemporary Control Theory [in Russian], Mashinostroenie, Moscow (1971).
11. R. P. Tewarson, Sparse Matrices, Academic Press (1973).
12. P. T. Potapenko, Inventor's Certificate No. 711879, Byull. Izobret., No. 26, 309 (1981).
13 I. Ya. Emel'yanov et al., At. Energ., 49, No. 6, 357 (1980).
14. 0. L. Bozhenkov et al., At. Energ., 51, No. 2, 91 (1981).
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
REFINEMENT OF BOUNDARY CONDITIONS IN THE CALCULATION OF
CLOSE-PACKED LATTICES BY THE SURFACE PSEUDOSOURCES METHOD
N. V. Sultanov and I. A. Zhokina UDC 539.125.533.348
In reactor calculations it is frequently necessary to solve the kinetic equations in,
square and hexahedral cells. As a rule these calculations are made in the Wigner-Seitz ap-
proximation, replacing the actual cell by a cylindricalized cell with an equal area. In
close-packed lattices where the optical thickness of the moderator is less than one neutron
mean free path, the details of the boundary conditions at the outside boundary of the cell
begin to have'a substantial effect on the integral characteristics of cells [1, 2]. By as-
suming isotropic reflection of neutrons at the outside boundary of a cell, the Wigner-Seitz
approximation can be extended to the calculation of cells in close-packed lattices [1, 2].
But even this condition has limited application, particularly if the materials of the inner
regions of the cell are strongly absorbing (Table 1). By using the first collision prob-
ability method the outer region of the actual cell can be divided into small subregions, and
the problem can be solved in two-dimensional geometry [2]. This procedure complicates the
calculation and requires increased machine time. Within the framework of the surface pseudo-
sources method [3] we propose boundary conditions which extend the range of application of
the Wigner-Seitz approximation for calculating close-packed lattices with practically no in-
crease in machine time.
Using the surface pseudosources method we solve the one-velocity transport equation in a
multiregion cylindrical cell. Each region is characterized by constant scattering,(Es) and
absorption (Ea) cross-sections. Neutron scattering is assumed isotropic. A constant neutron
source density q is specified in each region. Within the framework of the surface pseudo-
sources method Laletin [31 used a "sink at infinity" condition on the outside boundary of the
cell to calculate cells with optically thick outer moderator regions, but this method leads
to relatively large errors in calculating close-packed lattices (see Table 1). Calculations
showed that the "isotropic sink" condition at the outside boundary of a cell formulated in
the present article gives results close to those obtained with the isotropic reflection con-
dition (see Table 1), and the "combined sink" condition leads to results-close to those ob-
tained with the reflection condition in actual cells (Tables land 2).
To formulate the neutron reflection condition at the outside boundary of a cell we write
the neutron distribution function in the outer region in the form
(p, 1)=4/Ea 1 Gi yn (fl) b'n'm'G'n%m (PlPx_f) +A'F si (p, Q), (1)
n, m n', m'
where the YnW) are spherical harmonics normalized in the usual way [4]; the Gn1m ,(p/p )
are the angular moments of the Green's function [3] for an infinite homogeneous on a surface
of radius p from a source on a surface of radius pH_.j the gn',m' are the angular moments of
the surface pseudosource on the inside surface of region H: Y'si(p, 0) is the contribution to
`Y(p, 0) from the external neutron sink; A is a constant which is chosen from the condition
that there is no net neutron current at the outside boundary of the cell.
In the surface pseudosources method a subsidiary problem is considered for each region,
which leads to a problem in an infinite homogeneous medium with the material of the chosen
region, and the effect of adjacent regions is taken into account by introducing neutron pseudo-
sources on the boundaries or at some other place. A "sink at infinity" means that the neutron
sink is much farther away than one neutron mean free path.
An "isotropic sink" is represented by placing a sink with an isotropic angular distribu-
tion of neutrons (S2n) on the outside boundary of the cell, where n is the normal to the out-
Translated from Atomnaya Energiya, Vol. 53, No. 3, pp. 155-158, September, 1982. Original
article submitted November 3, 1981.
614 0038-531X/82/5303-0614$07.50 ? 1983 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
TABLE 1. Disadvantage Factors
Boundary condition and approximation
Monte
,Specular reflection, hexahedral cell
1,145x
1,297X
1
651 x
2
453x
Carlo
x (1?0,4.10-2)
X(1?0,5.10-2)
,
X(1:0,4.10-2)
,
x (1?0
4.10`2)
Isotropic reflection, cylindricalized
1, 130 x
1,264X
600x
1,
,
2,326X
cell
X(1?0.4.10 2)
X (1?0.5.10-2)
4. 10-2)
X(1?0
4.10_2).
X (1?0
Surface
(-1,3)*
(-2,5)
,
1) *
(-3
,
(-5
2) *
pseudo-
sources
Sink at infinity
G1 *
1,195
1,388
,
1,818
,
2,785
method
(4,4)
(7,0).
(10,1)
(13,5)
G3 *
1,165
1,340.
1,731
2,616
(1,7)
(3,3)
(4,8)
(6
6)
Isotropic sink
1,146
1,288
1,620
,
2,390
(0,1)
(0,8)
(1,9)
(2;7)
1,131
1,273
1,589
.2,318
(0,1)
(0,7)
(-0,7)
(-0
3)
Combination sink
G1 *
1,164
1, 325'
1,694
,
,
2,.539.
(1,7)
(2,2)
(2,6)
(3,5).
1,143
1,300
1,644
2,434
.(-0,2).
-0,2)
(-0,4)
(-0,8)
*Numbers in parentheses are percentage. deviations. from results for.a.hexahedral cell
calculated by the Monte Carlo Method.
tNumbers in parentheses are approximate percentage deviations from results. for a cylin-
dricalized cell with isotropic reflection calculated by the Monte Carlo method.
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
TABLE 2. Disadvantage Factors
Method or pro
ram
Boundary condition and
g
. approximation
K2
Monte Carlo
Specular reflection, square
1,62 (1?0,8x
.1, 156 (1?0,5 X
1,147 (1?0
5x
1,157 (1?0,3x
cell
X 10-2)
X 10-2
,
X JO-2)
x40-2)
CELTIC [2]
U
1,170
1,160
1,155
1,152
(0,7) *
(0,4)
(0,7)
(-0,4)
PNF-2 [7]
1,160
(--0,2)
Surface pseudo-
sources method
Skin at infinity
Gl
1,192
1,179
1,183
1,199.
(2,6)
(2,0)
(3,1)
(3,6)
Ga
1,176
1,167
1,161
1,168
(1,2)
(1,0)
(1,2)
(1,0)
Combination sink
1,164
1,174
1,154
1,188
(0,2)
(1,6)
(0,7)
(2 7)
1,163
1,161
1,145
1,155
(-0,1)
(0,4)
(0,2)
(0,2)
*Numbers in parentheses are percentage deviations from results calculated by the Monte
Carlo method.
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
side boundary of the cell. Then, using the Green's function for an infinite homogeneous
medium, we can write the function 'si(p, 1) in the form
Tsi (0, 0) _ I Ym (0) Gi' l'l (pip,),
n, m
to
A= : gn', m'G,i:.'m' (ptt pu-i)/Gt: (4 11/011).
n', m'
(3)
To represent a "combination sink" we use the fact that the angular distribution of neu-
trons entering the cell is shaped in its immediate vicinity at a distance of approximately
one neutron mean free path. Since we are considering an infinite uniform lattice, surface
pseudosources corresponding exactly to the surface pseudosource of the selected block are
distributed over the surfaces of the nearest set of fuel elements.
We note that the component of the neutron flux at the cell boundary arising from the
pseudosources of the adjacent fuel elements K contains axial spatial harmonics. Because of
symmetry, axial harmonics which are multiples of K remain. In the approximation under con-
sideration we retain only the harmonic with K = 0. The effect of the remaining sets of fuel
elements is replaced by a "sink at infinity." Then the function 'Ysi(p, Q) takes the form
l'sl (P, Q) - Yn (0) 1. A 2 gn', m'Gn mm 'PO (PIpn_ir) f Gas n' (P/P.)
n' m n', m'
where the Gi11T1'? (P/pH-1) are the angular moments of the Green's function from the adjacent
n ,m ,o -
block in the coordinate system of the chosen block [5]; the GaSm (p/pm). are the angular moments
of the Green's function from the "sink at infinity"; k is equal to 4 and 6 for square and
hexahedral cells respectively; r is the distance between the centers of symmetry of. the chosen
fuel element and the fuel elements surrounding it.
A = 11 en', m' [G;,'Om' (PH/P11-t) -I-kGn:?,,' (pii/pit-Ir)I/Gaso(p,,/p,)?
n', m'
Thus, the "combination sink" condition reduces the two-dimensional problem to that of
calculating a one-dimensional cylindrical cell.
The modified boundary conditions were introduced into the PRAKTINETs-3 program [6], which
was used to calculate two-region hexahedral and square cells. The results were compared with
those calculated earlier by the Monte Carlo method for hexahedral and equivalent cylindrical-
ized cells and forsquare cells [2]. The specular reflection condition was used in calculat-
ing actual cells by the Monte Carlo method, i.e., the axial dependence of the neutron distribu-
tion was taken into account.
The following initial prameters were assumed for all hexahedral cells: pl = 0.3 cm,
P2 = 0.42 cm, Ea = 0.02 cm 1, Es = 2 cm 1, Es = 0.3 cm 1, q'? = 0, and q2 = 1. For cells
numbered rl-r4 ,Ea = 0.5, 1, 2, and 4 cm 1, respectively. Table 1 lists the values calculated
for these four cells. It is clear that the values obtained by the surface pseudosources
method for an "isotropic sink" are close to those found for isotropic neutron reflection (less
than 1% error in the G3 approximation). The results calculated for isotropic reflection dif-
fer by 1-5% from data obtained in calculating actual cells. By using the "combination sink"
condition the disadvantage factors are calculated with less than.1% error.
The following initial parameters were taken for all the square cells; pl = 0.381 cm,
Ems' = 0.387 cm 1, Etot = 0.78 cm 1, q1 = 0, q2 = 1. For cells'Kl and K2 P2 = 0.86 cm; for
K3 and K4 P2 = 0.645 cm; for Kl and K3 Ea = 0.0088 cm 1; Etot = 1.0618 cm 1; for K2 and K4
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Ea = 0.00587 cm 1, and Etot = 0.70787 cm-1 (see Table 2). For the cells treated by the sur-
face pseudosources method a "sink at infinity" can also be used; by changing to a "combination
sink" the disadvantage factors can be calculated with less than a 1% error. Taking account
of the fact that the machine,time required under these conditions is practically the same,
(the computation time on a BESM-6 computer was increased by 0.005 sec), the "comb ina~t1i%n`'s~nk"
is the better choice. In the G1 and G3 approximations the calculation of a single region re-
quires 0.15 and 0.27 sec, respectively, on a BESM-6.computer.
We have used the isotropic and "combination sink" conditions within the framework of the
surface pseudosources method. By using these conditions the Wigner-Seitz approximation can
be extended to the domain of close-packed lattices, and the disadvantage factors in the cells
considered can be calculated with an error of less than 1% for isotropic reflection in cy-
lindricalized cells and for specular reflection in actual cells. We propose to use the re-
flection conditions.in a multigroup calculation of cells in the MG PRAKTINETs programs [8],
which employ the method of decomposition of the operator, with the spatial-angular part of
the problem solved by the surface pseudosources method [9, 10].
In conclusion the authors thank N. I. Laletin for his interest in the work and for
valuable comments. The results of the calculations of hexahedral and cylindricalized cells
by the Monte Carlo method were kindly supplied by the late A. D. Frank-Kamenetskii.
LITERATURE CITED
1. H. Honeck, Nucl. Sci. Eng., 18, 49 (1964).
2. J. Wood and M. Williams, J. Nucl. Energ., 27, 377 (1973).
3. N. I. Laletin, Preprint IAE-1374, Moscow (1967); in: Methods of Calculating Thermal
Neutron Distributions in Reactor Lattices [in Russian], Atomizdat, Moscow (1974), p.187;
At. Energ., 28, No. 3, 242 (1970).
4. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic
Press, New York (1965).
5. N. I. Laletin and N. V. Sultanov, At. Energ., 46, No. 3, 148 (1979); N. V. Sultanov,
Preprint IAE-3005, Moscow (1978).
6. N. V. Sultanov, Preprint IAE-2144, Moscow (1971).
7. V. Yu. Plyashkevich, Preprint IAE-2549, Moscow {1975).
8. N. V. Sultanov, Preprint IAi-3376/5, Moscow (1981).
9. N. I. Laletin, Vopr. At. Nauki Tekh., Ser. Fiz. Tekh. Yad. Reaktor., No. 5 (18), 63 (1981).
10. N. V. Sultanov, ibid., 69.
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
V. Sh. Sulaberidze and A. V. Pershin UDC 621.039.524.44:621.039.542.342
The working parameters of nuclear reactor fuel elements are such that an appreciable
part of the fuel doses not reach the temperature at which columnar grains are formed (1900-
2000?K). Under such conditions the level of gas release is not determined by the volume dif-
fusion of gaseous fission products (GFP) in the fuel, but by other mechanisms. This is man-
ifested in the change of the temperature dependence of gas release, a complication of the
dependence of the relative yield of GFP radionuclides from the fuel on the radioactive decay
constant.
The experimental value of the GFP diffusion coefficient is a certain effective param-
eter reflecting the combined effect of several gas-release mechanisms. It depends also on
a_number of factors characterizing both the fuel (oxygen content, microstructure) and the
experimental conditions (fuel burnup, GFP concentration in'the fuel, fission density) [1].
Therefore, in calculating the GFP yield from uranium dioxide in specific fuel elements it is
necessary to employ diffusion coefficients obtained for fuel with-similar characteristics.
We have determined the temperature dependence of gas release from compact uranium
dioxide in the range 770-1700?K for a burnup of up to 1% of the uranium atoms. The GFP yield
from a fuel sample was studied by an in-pile method. The experimental arrangement consisted
of an irradiation device with the sample and an open helium loop. Gas samples were analyzed
with standard spectrometric apparatus using a (Ge)Li.detector. Gamma spectra of 87Kr, 88Kr,
85mKr, 133Xe, 135Xe, and 138Xe were identified.
The fuel was 10% enriched in 235U, had a density of 10.45 g/cm3, an 0/U ratio of 2.006,
a mean nominal grain diameter of 6.9 pm, a ratio of volumes of bare and clad surfaces 0.19,
and a calculated specific pore surface equal to 460 cm2/cm3. The' temperature at the center
of the sample and on its surface was measured with thermoelectric thermometers. The relative
changes of the neutron flux at the sample location were determined from readings of a direct
charge transducer with a 103Rh emitter. The absolute value of the thermal neutron flux den-
sity in the central cross section of the channel was found from the results of neutron-phys-
ical measurements. The error in the measurement of the temperature in the device was ?1%,
in the relative change of the neutron flux at the sample location, taking account of the un-
certainty of its position in the channel ?1%, in the average fission density in the sample
?15%, and in the release rate of GFP radiopuclides from the fuel ?20%.
Changes in the irradiation conditions of the sample were produced by changing its height
in the channel, the power of the electric heater, the gaseous medium, and the evacuation of
the channel cavity. Three identical samples were irradiated. Sample No. 2, for which the
most detailed investigation of the temperature dependence of gas release was made, was irra-
diated to a dose of 2.4.1020 fissions/cm3, with a maximum fission density fmax - 8.9.1012
fissions/cm3?sec.
The dependence of gas release on.the fuel temperature was similar for all nuclides in-
vestigated. Figure 1 shows the relative yield of 85mKr(F) from samples as a function of the
mean bulk temperature of the fuel Tv. In the temperature range 770-1200?K gas release is in-
dependent of the temperature, in good agreement with results in [2] obtained by a similar
method.
It should be noted that in investigations by the method of postirradiation annealing the
temperature dependence of gas release appears at a lower temperature. Calculations using
relations obtained by such a method underestimate the low-temperature yield of GFP, since
under in-pile irradiation surface mechanisms ensure a level of gas release appreciably higher
than these relations give.
Translated from Atomnaya Energiya, Vol. 53, No. 3, pp. 158-160, September, 1982. Orig-
inal article submitted January 19, 1981; revision submitted February 23, 1982.
1983 Plenum Publishing Corporation 619
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 Declassified and Approved For Release 2013/03/04: CIA-RDP10-02196R000300010003-8
90 2
900 1000 1200 1400 TV, ?K
Fig. 1. Relative yield of esmKr as.a function of
the mean bulk temperature: ?) sample No. 1;0 , (3 t,Q) sample No. 2 (burnup equal to 0, 0.3-0.22,
0.22-0.46, 0.83-1.0, and 1.04%, respectively); ?)
sample No. 3; the experimental points over which
the averaging was performed are numbered.
At a higher temperature the relative yield. of GFP increased with increasing temperature.
The spread of points corresponding to a different fission density lies mainly within the
limits of error of the determination of F; i.e., in the range (2.7-8.9)?1012 fissions /CM3 -sec
the GFP release rate is. proportional to the fission density.
The observed dependence of the gas release rate on the fission density for a mean-bulk
fuel temperature Tv 1200?K is consistent with the diffusion of GFP uranium dioxide.
Table 1 lists values of the activation energy for the diffusion of GFP in the range.1200-
1700?K for a burnup of 0.03-0.22% (results of processing data on the GFP yield for sample No.
2 by using the Booth model), kJ/mole.
For a fuel burnup of 0.22-0.46 and 0.83-1.0% the activation energy does not differ ap-
preciably from the values presented (see Fig. 1). Similar values of the activation energy
for the diffusion of nuclides of a single element indicate that thermally stimulated diffusion
is the predominant mechanism for the release of GFP from uranium dioxide for Tv '> 1200?K and
f = (2.7-8.9).1012 fissions /cm3?sec. However, the activation energy in this case turns out
to be lower than the activation energy for volume diffusion, and is essentially an effective
parameter taking account of the effect of several gas-release mechanisms.
Figure 2 shows the relative yield of GFP having various radioactive decay constants for
three values of the temperature. The experimental results were normalized to the relative
yield of,133Xe. The figure also shows the theoretical dependence for a temperature of ti1700?K
predicted by the Booth model, based on the volume diffusion of GFP in fuel. The difference
between the experimental and theoretical values, noted in a number of papers, is accounted-
for by the more effective trapping of short-lived nuclides in fuel [3],. the effect of grain-
boundary diffusion [4], the trapping of GFP in closed porosity [2], and the diffusion of GFP
precursors [5].
Calculations showed that no one mechanism describes the observed dependence of the rela-
tive GFP yield on the decay constant (see Fig. 2). The variation of the relative yield of
Xe and Kr with the decay constant in the range 10-6-10 3 sec-1 is better described by a model
which takes account of volume diffusion, grain-boundary diffusion, and the diffusion of GFP
precursors (curve 5 of Fig. 2). A similar conclusion was drawn by Turnbull and Friskney [6].
At a low temperature the general level of gas release and its dependence on fission density
and the radioactive decay constant indicate the action of a mechanism of the "knockout" type.
Thus, for in-pile irradiation low-temperature gas release from fuel contained in a shell with
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TABLE 1. Estimates of the Spread
of the Regression Coefficients and
the Mean-Square Deviation of the
Average Values
a5mKr
275 ? 16
98Kr
279 ? 19
" Kr
258 ? 19
Average
270 ? 11
135 Xe
249 ? 14
133Xe
.226?14
Average
237 --'i6
D 2
90-6 70-'f 70-4 . 70-3
Radioactivity decay constant, sec-1
Fig. 2. Reduced relative yield of GFP (Y) as a
function of radioactive decay constant. Experi-
ment: ?) Tv 3000?K; (3) Tv = 1300?K; 0) Tv =
1700?K. Calculation: 1) volume diffusion; 2)
grain-boundary diffusion; 3) diffusion of GFP pre-
cursors; 4) trapping of GFP in closed porosity; 5)
grain-boundary diffusion (2). And diffusion of pre-
cursors (3); 6) "knockout."
a small gap is due to the mechanisms of the type indicated. The temperature dependence of
gas release from uranium dioxide directly in the irradiation process appears at a temperature
above 'l200?K, and this temperature limit varies slowly for fission densities from 3.1012 to
1013 fissions/ cm3?sec. Between 1200 and 1700?K the GFP yield from compact uranium dioxide
is determined by volume and grain-boundary diffusion of GFP and their precursors.
The activation energy for the diffusion of krypton and xenon in the fuel element samples
investigated was 270 ? 11 and 237 ? 16 kJ/mole respectively, and did not change for a burnup
of up to 1% of the uranium atoms.
1.
G.
Lawrence, J. Nucl. Mater., 71, 195 (1978).
2.
C.
Friskney and J. Turnbull, J. Nucl. Mater., 79, 184 (1979).
3.
A.
A. Khrulev et al., Vopr. At. Nauk Tekh., Ser. Energ. Tekhnol., No. 2(7),
55 (1977).
4.
J.
Turnbull and C. Friskney, J. Nucl. Mater., 58, 31 (1975)..
5.
J.
Turnbull et al., ibid., 67, 301 (1977).
6.
J.
Turnbull and C. Friskney, ibid., 71, 238 (1978).
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 Declassified and Approved For Release 2013/03/04: CIA-RDP1O-02196ROO0300010003-8
NEUTRON YIELD OF THE (a, n) REACTION FOR MULTICOMPONENT MEDIA
V. I. Bulanenko, V. V. Frolov, UDC 550.35:357.591
and E. M. Tsenter
There has been a steady rise in the production and use of a-active nuclides in nuclear
engineering, and it is necessary to know the accurate neutron. yield Q for the solution of
many practical problems, a detailed and reasoned list of which is given in the review [1].
The components of Q are spontaneous nuclear fission and (a, n) reactions in light elements
with Z < 20. The importance of taking (a, n) reactions accurately into account is illustrated,
e.g., by the result of [2], in which a sharp increase in yield and hardening of the energy
spectrum of neutrons when light elements are present in the compounds is demonstrated.
In view of the difference in composition of the set of materials and components actually
used, it is preferable to obtain accurate information by calculational means. Whereas the
calculation of the neutron yield of spontaneous fission with known nuclear data is not dif-
ficult, the calculation of the neutron Yieldof the (a, n) reaction Qan is far from obvious.
Individual aspects of determining Qan and its'dependence on the a-particle energy and composi-
tion of the medium have been considered in a series of works [3-21], but nevertheless there
are no published data on the systematic and critical analysis of these calculations, and also
on the analysis of sources of error and the possibility of reducing them.
Calculation of the Neutron Yield Qan Theoretical Formula
It is known that chemical compounds and solutions may be regarded as homogeneous-media.
Suppose thatthis medium contains a single radioactive nuclide, emitting r groups of a-particles
with initial energy Eoi and intensity Ii, and the number of components at whose nuclei (a, n)
reactions occur is Z. Then, for a homogeneous medium, the neutron yield of (a, n) reactions
at nuclei of type j will be
r Foi
a'
Qj =Anj li
i-~ B.1
rr (E) dE.
(-dE/d.r)
where A is the activity of the a emitter; nj, number of nuclei of type j in unit mass of com-
pound; aj(E), cross section of the (a, n) reaction at'elements of type j; (-dE/dx), energy
loss of the a particles in the ionization and excitation of atoms in the medium; Bj, threshold
of (a, n) reaction for the j-th nuclide.
Using the Bragg-Kleman sum rule for the stopping power, the neutron yield for a multi-
component medium is obtained
r i Poi
Qan ANA, I i I
i=1 j=1 Bj
"j(E) fj(E)dE.
M1 (- dEldpr)1
Here NAv is Avogadro's number; Mj, mass number of atoms of type j; f1-(E), weighting factor
determined by the composition of the medium and expressed in terms of the ionizational a-
-particle losses in an element of type j in mass units (-dE/dpx)j and the gravimetric fraction
of the atoms
fj(E)?-_F
s
j (-dEl(lpx)jl.Y ?i, (--dE/dpx)h.
Translated from Atomnaya nergiya, Vol. 53, No. 3, pp. 160-164, September, 1982. Orig-
inal article submitted November 28, 1980; revision submitted February 22, 1982.
622 0038-531X/82/5303-0622$07.50
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A similar expression for fj(E), expressed in terms of the mass range pR, was obtained in [11].
Equation (3) for fj is valid for any compounds, including aqueous solutions and finely
disperse mixtures. For chemical.compounds, a weighting factor expressed in terms of the
relative atomic stopping power Sj is more expedient, as follows:
8
NjSi (E)% f. NkSh (E),
k=1
(4)
where NJJ?. is the relative proportion of atoms of type j. Using Eq. (3) or (4), Eq. (2) allows
Qan to be calculated, in principle, for any arbitrary composition. However, such calculations
are found to be difficult.
Approximate Formula [3]
It is quickly evident that, when the weighting factor fj is independent of the a=particle
energy, Eq. (2) transforms to the formula proposed in [3] and distinguished by its significant
simplicity in practical applications:
r I
Pan = A Ii 4i (Eoi) fj (Eoi).
i=i j=1
Here gj(Eoi) is the maximum specific neutron yield from a thick target at an energy Eoi, and
is
NAv Qi (E)
4i (E01) Mj J (-dEldpx)i dE.
Bi
Essentially, qj' is calculated under the condition that the neutron yield is referred to the
pure material of type j of the target in which (a, n) reaction is possible, i.e., with fj - 1.
The basis of this approximation is that the relative stopping power does not change much
as a function of the energy. In fact, the dependence S(E) is steepest in the low-energy re-
gion. At the same time, the cross section o(E) is small at these energies. Therefore, the
real contribution to the neutron yield from low-energy a particles is slight. Calculations
of Qan for binary compounds of type PuBe13, Pu02, etc., according to Eqs. (2) and (5) show
that Eq. (5) overestimates Qan by no more than 3%. If values of S averaged over the energy
range from B to E0 are used, the accuracy of calculations based on Eq. (5) is increased.
According to [20], the energy dependence of f may be neglected in calculating Qan from Eq.
(5) if the value'of the ionizational losses is taken at E0 = 5 MeV. For natural a 'emitters,
this gives an additional error of less than ?5%, which is considerably less than the inde-
terminacy existing in (-,dE/dpx).
Of course, the limited dimensions of the medium reduce the neutron yield, since some
of the a particles of the surface layer do not lead to neutron formation. Since the a-particle
path is very small ( 1-25 mg/cm2) [11], this effect appears for compounds of small mass ('0.15 g
and less).
Hence, Eq. (5) gives a sufficiently good approximation in calculating the neutron yield
for multicomponent media. At the same time, the semiempirical Eq. (5) is markedly preferable
to the theoretical Eq. (2), since it is based on q, which may be determined not only by cal-
culationbut also by experiment, and may be. tabulated. This allows Qan to be calculated in
a considerably shorter time for any chemical compound. Thus, calculating Qan from Eq.
(5)
reduces to the separate determination of q, f, A, and I. The components of the error
in
calculating Qan are also considered in accordance with this division.
The Error SQ
The maximum specific neutron yield for the a-particle energy q may be calculated from
Eq. (6). Such calculations for several nuclides [5, 9, 10, 13-15] have shown that the de-
pendence of q on the energy is complex.
623
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10 ",
3 4 5. . 5 7 B
a particle energy, MeV
Fig. 1. Dependence of the maximum neutron yield per
106 a-particles for a thick beryllium. target on the
a-particle energy, according to the data of [13]
(-), [12] (---), [6] (-?-?-), [7] (....), and [15]
(-??-) and the experimental data of [13] (0), [12]
(x), [4, 6] (A), and [18] (0).
The use of Eq. (6) has certain limitations. First, the detailed structure of the cross
section o(E) is measured for a restricted number of nuclides, mainly at an energy of