SOVIET ATOMIC ENERGY VOL. 48, NO. 3

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• Document Creation Date: December 23, 2016
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• Sequence Number: 3
• Publication Date: March 1, 1980
• Content Type: REPORT

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1JJ11 WUJU-JJ1 S
Russian Original Vol. 48, No. 3, March 1980
September, 1980
SATEAZ 48(3) 153-222 (1980)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPrIA
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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vv.. ,~cv....c. ,irryy la Q UQIIDICLIUll U1 /'ilU/////dyd Cnergiya, a
,V V't-'publ.ication of the Academy of Sciences of the USSR.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
September, 1980
Volume 48, Number 3 March, 1980
CONTENTS
Engl./Russ.
ARTICLES
Technology of Increasing the Quality of Uranium Ore during Extraction
and Primary Processing - M. A. Temnikov . . . . . . . . . . . . . . . .
153
139
Using Determinations of Protactinium when Assessing Uranium Showings at
the Prospecting Stage - G. N. Kotel'nikov and I. P. Shumilin .. . . . .
159
144
Problems of Diagnostics of Physical Characteristics of RBMK.Reactors
according to Neutron Noise - B. A..Vorontsov, I. Ya. Emel'yanov,
L. N. Podlazov, V. D. Rogova, V. I. Ryabov, and B. M. Svecharevskii .
161
145
Comparison of Certain Methods of Calculating Neutron Fluxes in a Reactor
Fuel Channel - Yu. P. Elagin, A. S. I1'yashenko, V. A. Lyul'ka,
T. S.,Poveshchenko, V. A. Lyul'ka, T. S. Poveshchenko,
and N. V. Sultanov . . . . . . . . . . . .
165
148
Calculation of Effective Boundary Condition at the Surface of a Multiregion
Cylindrical Slug - B. P. Kochurov . . . . . . . . . . . . . . . . . . . .
169
151
Neutron Importance and Sensitivity Coefficients in Iteration Synthesis
Methods - A. M. Kuz'min, K. S. Rafaev, and V. V. Khromov . . . . . .
172
154
Production of Defects in Molybdenum by a Deuterium Glow Discharge Plasma
- V. N. Chernikov, G. A. Arutyunova, Yu. N. Sokurskii,
and A. P. Zakharov . . . . . . . . . . . . . . . . . . . . . . . .
. 176
157
Erosion of the First Wall of Tokamaks - M. I. Guseva, E. S. Ionova,
and Yu. V. Martynenko . . . . . . . . . . . . . . . . . . . . .
182
162
Measurement of Spectrum Flux of Ultracold Neutrons by Magnetic
Integrating Spectrometer - Yu. Yu. Kosvintsev, Yu. A. Kushnir,
and V. I. Morozov . . . . . . . . . . . . . . . . . . . . . .
187
166
Diiodide Crystals for y-Ray Detectors - V. M. Zaletin, I. N. Nozhkina,
V. I. Fomin, N. V. Shustov, and I. I. Protasov . . . . . . . . . . . .
191
169
LETTERS
Concerning the Choice of Graphite for Stacking of High-Temperature
Gas-Cooled Reactors - Yu. S. Virgil'ev and V. P. Shevyakov . . . . . .
195
174
Use of Thin Films to Study Pore Distribution Over Depth of Range
of Ar+ Ions in Nickel - A. G. Guglya, V. A. Gusev, V. F. Zelenskii,
B. V. Matvienko, and I. M. Neklyudov . . . . . . . . . . . .. . . . .
197,
175
Diffusion of Actinides and Some of Their Fission Products in High-Melting
bcc Metals - V. N. Zagryazkin . . . . . . . . . . . ... . . . . . . .
200
177
Nitrogen Determination in Mixed Uranium-Plutonium Fuel after
14N(a,py) Reaction - V. I. Melent'ev and V. V. Ovechkin . . . . . . . .
202
179
Obtaining Assessment Data on Euqally Probable Intragroup Sections
for Protection Calculations from Basic Libraries by the Monte-Carlo
Method - V. E . Kolesov and N. A. Solov'ev . . . . . . . . . . . . . .
205
180
Helium Blistering and Hydrogen Absorption by PT -7M and PT-3V Titanium
Alloys - V. M. Gusev, M. I. Guseva, E. S. Ionova, N. G. Lemke,
V. I. Syshchikov, P. A. Fefelov, B. B. Chechulin,
and 0. I. Chelnokov . . . . . . . . . . . . . . . . . . . . . . . . .
208
182
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CONTENTS
(continued)
Engl./Russ.
Energy Characteristic of Silicon Neutron Accident Dosimeters.
- V. V. Golub . . . . . . . . . . . . .
.210
183
Features of Standardization of Plutonium Isotope Mixture. Formed
in Nuclear Power Reactors - R. Ya. Sayapina, V. I. Bad'in,
R. Ya. Sit'ko, and S. V. Petrov . . . . . . . . . . . . . . . . . . .
212
185
Physical.Aspects of Injecting System for Large Tokamaks and Open Traps
- A. I. Krylov, V. V. Kuznetsov, and N. N. Semashko . . . . . . . .
. 214
186
Possible Control of Neutron Flux by Molecular Layered Compounds
I. G.-Gverdtsiteli, A. G. Kalandarishvili, S. D. Krivonosov,
V 'A.'Kuchukhidze, and B. A. Mskhalaya . . . . . . . . . . . . . .
217
187
Energy Distribution of Fast Neutrons in the F-1.Uranium-Graphite
Reactor.- V. A. Kanareikin, V. M. Tyryshkin, and V. S. Yuzgin . . . . .
219
189
Approximation of Control in Optimization of Xenon Transient Processes
- V. I. Pavlov and V. D. Simonov . . . . . . . . . . . . . . . . .
221
190
The Russian press date (podpisano k pechati) of this issue was 2/25/.1980.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
TECHNOLOGY OF INCREASING THE QUALITY OF URANIUM
ORE DURING EXTRACTION AND PRIMARY PROCESSING*
M. A. Temnikov UDC 622.349.5:622.79
The expansion in nuclear power engineering calls for an increase in the extraction of
uranium ore, and consequently in the productivity of mines. This has led to the use of a
system for processing deposits involving mass methods of breaking down ores and completely
working out the ores. The cost of hydrometallurgical processing of such ores is high, but
it can be reduced by chemical concentration methods.
The present article examines the use of radiometry methods for increasing the quality of
the ore during extraction and primary processing.
Figure 1 gives a scheme for checking the quality of the ore in systems involving selec-
tive and mass breakdown of the ore respectively. The roman numerals denote the radiometric
methods for increasing the quality of the ore. These are based on hydrometallurgical proces-
sing.
Let us now examine each of these methods in greater detail:
We know that the gamma radiation from uranium ores can be used to determine the concen-
tration of uranium directly in the ore body by a radiometric method. The method of deter-
mining the uranium content and power of mineralization at the outcrop of the ore is conven-
tionally known as gamma sampling, in the same way that determination in cores and boreholes
is known as core gamma sampling or gamma logging [4-6].
The gamma sampling of a shothole is used during selective cutting of ore and rock to
determine the contours of the ore body. The holes are drilled at the points at which the
samples are needed. Gamma sampling is carried out either by determining the difference in
effect achieved by the use of special lead screens installed on the detectors of portable
radiometers, or by the radiometers of a directional y-radiation detector.
*A version specially written for this journal of a paper read at the MAGATE symposium on
estimating reserves of uranium and mining techniques, Buenos Aires, 1-4 October, 1979.
TABLE 1. Experimental Data on the Sorting
of the Same Ore Mass in Dumpers on Route
to the Ore Chute and in Rail Wagons (RTS)
after Leaving the Ore Chute
Wa oin
Fa
E
sorting
cess. %
pro-
w s?
0
stope
Notes
E
(fce)
sort-
ing
R,t,S
Horizontal
bed, cutting
downwards
Substage
stoping
Substage and
53
0
34,0
19,0
Averaged data
Separate ex-
(artial)
bed
,
4,2
1,7
2,5
periments
.
breakdown
27,0
0,0
27,0
17,3
10,8
6,5
25,4
11,6
13,8
Averaged data
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 139-143, March, 1980. Original
article submitted December 7, 1979.
0038-531X/80/4803-0153$07.50 ? 1980 Plenum Publishing Corporation 153
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Systems of processing and selective mining of ores
I L Gamma analysis of deposits I
Fine-core drilling. of deposits
ILCore gamma sampling
ILL Face sorting of rock in the dumpers
during transport to ore chutes
1V. Rapid gamma analysis of ore
(rock) at RTS
Barren rock
to waste. or
tailings
V. Unsorted
ore to radio-
metric enrich-
ment
ommercial (rich
ore to chemical
conversion
Enriched
product
Open-cut and underground workings for mass ex-
traction of ore
III Face sorting of rock in the excavator buckets
during loading into dumpers or in the dumpers during
transport to. ore chutes
Drilling of blocks (chambers)
I
IIL Gamma logging of shotholes
I (rock) at. RTS
IV. Rapid gamma analysis of ore
Barren rock
to waste or
tailings
V. Unsorted ores
to radiometric
enrichment
1
Commercial
(rich) ore to
chemical
conversion
Enriched
product
Fig. 1. Scheme for checking the quality of uranium ore during mining and primary
processing (RTS: radiometric test,station).
Shothole gamma sampling is used for the quantitative assessment of mineralization and
for defining the boundaries of ore bodies, using the holes drilled for blasting. The shot-
holes are. checked for the correct charge of explosive to ensure selective cutting of the
rock.
The fact that the results are obtained directly at the measurement site, coupled with
the simplicity and availability of the methods used, has ensured their widespread use as
a means of increasing ore quality.
Gamma logging of holes is used during the development of deposits by systems that in-
volve mass recovery of the ore. The shotholes are gamma logged prior to being charged with
explosive, in order to-define the boundaries of mineralization and to select the sites for
TABLE'2. Results of Tests on Various
Types of Uranium Ore
Type of
ore
No.of Rel.error in analysis,d?
containers of whole lav. oin- max.individual
meas. ore batc dividual analy.
analy.
59
-0,7
?31,0
+90,0
-36,0
II
50
+1,4
?23,0
+72,0
-31,4,
III
137
0,0
?6,9
+22,5
-26,6
IV
85
-5,1
?6,9
+43,3
-66,7
V
42
-6,0
+22,7
+38,5
-62,3
.VI
18
+5,8
?22,4
+91,3
-36,9
VII
25
+1,2
?24,0
+36,0
-43,8
VIII
7
-1,8
?18,1
+56,2
-43,4
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-200
.1
Milling
it
Washing and cutting
-200 +50 mm -50 +23rmm
i
Separation
Sands Drainage
Waste and tailings
Muds Drainag
1 ..
Commerical ore to hydrometallurgical plant
Fig. 2. Ore enrichment scheme.
the setting of charges. This enables one to carry out shot firing with minimum disturbance
and mixing of the ore.
By gamma logging the holes and selectively cutting the rock and ore in a single deposit,
we can achieve a considerable enrichment (18%) of the extracted ore in certain parts of the
chamber, compared with bulk mining throughout the whole depth of the fold. Under these cir-
cumstances, the output of the unconditioned ore mass can be increased by a factor of 1.38.
Radiometric sorting of the extracted ore mass in the face, by taking measurements in
the excavator buckets or in the dumpers, can be used as a means of primary enrichment of the
ore. This technique is being rapidly developed, due to the use of large wagons, dump trucks,
and rail dumper cars in uranium mines and quarries. Unfortunately, the radiometric contrast
or the variation in the distribution of the radioactive component of the ore tends to fall
with an increase in the size of the loads subject to sorting. At the same time, radiometric
sorting of extracted ore at the stope in turn enables one to mine whole formations or just
individual parts of the formations, or in certain cases to abandon unproductive systems of
selective mining and change over to more productive systems of mass or semimass mining.
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Fig. 3. "Granat" separator for sorting ore size -200+50 mm: 1) sorting
hopper; 2) electropneumatic valve; 3) radiometer detector; 4) fixed
spiral.of conical pick-up feeder; 5) conical pick-up feeder; 6) vibro
feed; 7) bunker;-8) drive to conical pick-up feeder; 9) frame of separa-
tor.
The extracted ore is sorted in the buckets of the excavators by means of special instru-
ments, each consisting of a control board mounted in the cabin of the excavator and detec-
tors with special shock absorbers mounted on the bucket and equipped with special protective
screens made of steel and-lead.
The following data serve to illustrate the effectiveness of bucket screening. The
average depletion factor of ores in opencut workings was 25.1-31.0% prior to the introduc-:
tion of bucket sorting (as high as 48% in certain blocks), with a standardized depletion of
20%. The introduction of bucket radiometric sorting enabled this to be reduced to 19.2% on
an average, with a maximum of 22.8%.
As we have already noted, the output of tailings and the content of uranium in the com-
mercial ore become lower as the mass of the sorted portion of ore deposit is increased, for
a constant minimum workable content of uranium. For example, when a six (cubic) meter exca-
vator bucket was replaced by four meter and three meter buckets on one quarry, the tailings
of'the sorting process increased by 3 and 5-5.5%, respectively. At the same time, the con-
tent of uranium in the ore increased by 3.3 and 5.7-6.0%, while the depletion factor fell
by 2.9 and 5.2%, respectively.
Increasing the efficiency of the radiometric sorting in the excavator bucket in some
cases facilitated a reduction in the height. of the excavator berm. For example, drilling
and blasting is carried out at a height of 15 m, while the ore is excavated in two or three
subberms, i.e., at a height of 7.5 or 5 m.
In the case of underground uranium workings, the quality of the ore loaded in the dump-
ers is determined at the instant it is moved to the ore chute, with the aid of a radiometer
mounted on the machine. The machine will then load the material in one chute or another,
depending upon its quality (ore or waste). Stope or face sorting avoids the need to move the
rock to the ore chute for measurement, acting virtually as a primary enrichment process for
the extracted ore.
Table 1 gives experimental data on stope sorting prior to the ore being transported to
the ore chute, together with rapid gamma analysis of the same ore mass after leaving the ore
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chute. We can see from the table that radiometric sorting ahead of the ore chute leads to
an increase in the tailings of 9.5-16.5%, which in turn leads to an increase of 8-15% in the
uranium content of the ore.
Rapid gamma analysis of the rock in the transport containers (rail wagons, dumpers,
etc.) has long been an integral part of ore processing for the rapid sampling of the ore
mass as a whole. A high degree of accuracy in the sampling of the ore in wagons, and the
possibility this offers of changing the content of the sorted rock being carried, enables
us to treat the rapid ore analysis method as a primary method of ore enrichment, in much
the same way as radiometric sorting. Radiometric test stations for rapid gamma analysis
have been set up both underground and on the surface for sorting the extracted rock and for
calculating the uranium content of the extracted ore. Radiometric test stations are equipped
with special radiometers based on gas-discharge or scintillation counters [3, 41. Where
necessary, the stations are equipped with balances, and in recent years they have been fur-
nished with equipment for recording analytical data on magnetic or punched tape, and with
teletype machines for transmitting the data to a computer for processing.
The error in gamma analysis depends upon the uniformity in the distribution of the
uranium throughout the ore, the dimensions of the portion of ore being analyzed, the state
of radioactive equilibrium, the radon emission from the ore, the weather conditions, and
other factors. It can reach a level of ?20-30% in individual analyses. However, the error
in analyzing batches of ore does not exceed ?5-6% and satisfies the conditions for the chemi-
cal analysis of uranium ore.[3] (Table 2).
Where there is no provision for face or stope analysis at the mine, its function can
be taken over by the radiometric test station, generally by testing the whole of the extrac-
ted rock. The quantity of waste that is generated by this method of sorting comprizes from
0 to 34% (see Table 1).
Consequently, the use of radiometric methods as part of the ore processing cycle of the
mine and the use of various types of electronic apparatus lead to a significant primary en-
richment of the ore, either during the blasting operation or during the transport of the
extracted ore.
This type of sorting operation is carried out prior to chemical refining operations
and more thorough sorting or radiometric separation (enrichment) of the industrial ore is
carried out on radiometric test stations at a radiometric enrichment plant [2]. Radiometric
separation relies on the same properties of the uranium ore as are employed in gamma sam-
pling and borehole logging, face sorting and rapid analysis of ore in the dumpers. For
roughly half of the type of uranium ore, radiometric separation is not just a method of
primary processing, it is the only method of mechanical enrichment employed. The advantages
of this process lie in its cheapness, and also in the fact that it does not require milled
ore, does not use reagents, requires very little electrical energy, and produces virtually
no products that are harmful to the environment.
The most serious of the drawbacks to radiometric separation is the limited enrichment
that is possible with low grade ores. For this reason, it is very important not to overre-
duce the ore when blasting and to strive for the range of sizes most suitable for separation:
-150+30 mm.
The technology of radiometric separation has its own special features. Figure 2 gives.
the schematic of a radiometric enrichment plant. We can see from this that such plants in-
volve the following main operations [1]:
1) reduction (this plays an insignificant role). The purpose of the reduction process
is to ensure the maximum size of rock suitable for separation, usually not larger than 200-
250 mm. Only the larger rocks (+200 mm) are crushed;
2) screening, which is one of the basic preparatory operations for separating the un-
sorted fines (particles below 15 mm, for example) and dividing the sorted material into two
or three "machine" size classes in order to eliminate any large differences in the weight
of the rocks passing through the machines;
3) washing the machine classes to remove any radioactive mud coating the rocks. Other-
wise, barren material would become radioactive and would not be rejected. Sometimes, the
operations of screening and washing are combined, since they can be carried out on the same
piece of apparatus;
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4) the sorting of the "machine" classes, i.e.; dividing them into concentrate (commer-
cial ore) and waste, is carried out on-ore-sorting machines known as radiometric separators.
Despite the range of structural designs employed for this purpose, all separators have the
following basic parts, used for the same purposes (Fig. 3):
a bunker outlet'for ensuring an even flow of material from the bunker for sorting;
a vibratory feed with an electromagnetic drive;
a cone-shaped pick-up feeder with a fixed spiral for spreading out the rocks through-
out the measurement zone;
a radiometer with scintillation counters and a count-resolving system, to provide a
quantitative estimate of the content of radioactive component in the rock and to send
a signal to the actuator;
an actuator (pneumatic valve or throttle) for mechanically segregating the rocks;
a sorting discharge hopper for accumulating the sorted material and passing it to the
appropriate conveyer.
The throughput rate of the separators varies from 40 to 100 tonnes/h for the size class
-200+50 mm , 10-15 tonnes/h for class -50+25 mm, and 4-5 tonnes/h for class -25+15 mm.
'The radiometric enrichment plants in existance at the present time generate wastes of
from 2.5 to 43% of the original ore, or from 50 to 80% of the sorted class, the output of
which varies from 45.0 to 64.5% for the various types of ore. The content of uranium in
the waste'from'the radiometric separators varies from 0.010 to 0.015%. Under'these circum-
stances, the enrichment factor of the final.. product leaving the plant for chemical proces-
sing equals 1.25-1.64.
Consequently, the concept of increasing the quality of extracted uranium bearing ores
by the widespread introduction of radiometric methods and instruments during-the mining
process itself and during primary processing of the ore enables us to 'increase the uranium
content of the commercial ore that is passed on for chemical refining. This leads to a con-
siderable'reduction in the cost of the raw material for nuclear fuel.
LITERATURE CITED
I. A. I. Gorshkov et al., Proceedings of the MAGATE International Conference on Nuclear
Power Engineering and Its Fuel Cycle, Salzburg, May 2-13, 1977, IAEA-CN-36/321.
2. V. A. Mokrousovet al., Theoretical Fundamentals of the Radiometric Enrichment of
Radioactive Ores [in Russian], Nedra, Moscow (1968).
3. L. N. Posik et al., Radiometric Rapid Analysis of Extracted Ores [in Russian], Atomiz-
dat, Moscow (1960).
4.' M. I. Prutkina and V. L. Shashkin,'Manual of Radiometric Surveying and Radiometric
Analysis [in Russian],, Atomizdat, Moscow (1975)-.
5.. I. M. Tenenbaum, Fundamentals of Ore Radiometry [in Russian'],'Gosatomizdat,Moscow
'(1961).
6. V.-L?..Shashkin, Analyzing Radioactive Ores by Gamma 'Radiation.{'in Russian]., Atomizdat,
Moscow -(1972).
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USING DETERMINATIONS OF PROTACTINIUM WHEN ASSESSING
URANIUM SHOWINGS AT THE PROSPECTING STAGE*
G. N. Kotel'nikov and I. P. Shumilin UDC 550.8.835
A group of uranium ores known to prospectors is formed by the leaching of uranium and
radium from ore deposits and the subsequent deposition of these elements near to the surface.
Showings of this type are often highly radioactive and conditioned at the outcrop, but tend
to die away rapidly at depth. Such showings are known as "rootless," "insolated," "false,"
etc., and are difficult to diagnose at the surface. A great deal of time and material can
go into the mining of such deposits before they are found to'be commercially useless.
In certain geochemical settings connected with processes of hypergenesis, we observe
intensive transport of uranium and radium in the outcrops of conditioned ore bodies. In
such cases, weak anomalies only are maintained at the surface, while analysis shows a balanced
concentration of uranium, which does not correspond to the real content in the primary
ores. This group of showings is most often passed over or classed as noncommercial, parti-
cularly during small-scale surveys. At best, they tend to be mined as a last resort.
The features of prospecting and methods of assessing anomalies in which there is a
loss of equilibrium between uranium and radium have been described in [1], but these methods
are not always suitable for the showing that presently concerns us. An efficient method of
primary assessment of showings, based on the complex determination of protactinium, uranium,
and radium in samples taken over the anomalies is recommended.
The nuclide 231Pa is a product of the decay of 235U and is found in company with it in
a definite ratio. The half life of 231Pa is 3.248.10? yr. Protactinium has a considerably
lower migration capacity than uranium or radium and is retained better at the outcrop of the
ore body, even under intense conditions of hypergenesis. This allows us to use it as a
"datum" and employ it to determine the intensity and direction of the transport of uranium
and radium. The directivity of the migration processes (acquisition and transport) is an
important factor when assessing showings and deciding whether or not to mine a particular
deposit.
All the variety of features of the various uranium showings reduce in the final analysis
to three types. of uranium-protactinium ratios (see Table 1), which characterize the direc-
tion and intensity of the migratory processes and also govern their preliminary assessment.
In showings of the first type, where U/Pa is equal to or close to unity, we see a weak
transport of uranium and radium. Surveys of this type of showing have indicated that the
uranium contents at the surface and at deep horizons are roughly the same, and that the
mineralization represents the primary minerals of uranium: pitchblende, coffinite, etc.
The second type of showing is characterized by the prevalence of uranium over protactinium
(U/Pa >1), which indicates an intensive acquisition of uranium. In this case, the content
of uranium at deeper horizons is lower than at the surface, and frequently approximates to
a Clarke distribution. The uranium mineralization is represented'by colored secondary mine-
rals. In showings of the third type, the content of protactinium is considerably higher
than the uranium content (U/Pa < 1), which indicates an intensive transport of uranium into
the surface parts of the showing and a high content of uranium in the primary ores. The
content of uranium in boreholes and workings at deep horizons is several times greater than
at the surface. The uranium mineralization is either absent altogether in the hypergenesis
zone or takes the form of traces of secondary minerals.
*A version adapted for this journal of a paper read at the MAGATE symposium on assessing
uranium resources and mining techniques, Buenos Aires, October 1-4, 1979.
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 144-145, March, 1980. Original
article submitted June 4, 1978.
0038-531X/80/4803-0159$07.50 ? 1980 Plenum Publishing Corporation 159
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TABLE 1. Radiological Features of Show-
ings in Relation to the Direction of
Migration of Radioactive Elements
Type of
Content of radio-al.
active elements,
showing
U
I Pa
I Ra
0,070
0,075
0,060
0,93
0,80
0,86
II
0,07
0,05
0,08
1,40
1,60
1,15
III.
0,05
0,17
0,08
0,29
0,47
1,6
Note. The contents of protactinum and radium are given
inupits of equilibrium with uranium.
The results we have obtained give us reason to recommend the determination of protac-
tinium in all anomalies observed during prospecting, in order to assess the uranium content
in the primary ores up to the point at which they are disrupted at the outcrop. The proposed
method of assessing uranium showings during the prospecting stage has been made possible by
the development by I. P. Shumilin of a radiometric method and the necessary transducers for
rapid analysis of samples of uranium, radium, radon, protactinium, and thorium (the deter-
mination of potassium is'also possible) [2, 3].
The analyses can be carried. out on standard commercially available apparatus., The
transducer takes the form of a crystal of NaI(Tl) measuring 100 x 100 or 80 x 60 mm on which
six a counters type STS-6 are arranged in two or three rows, with additional removable fil-
ters 0.2 g/cm2 in density. The milled samples, weighing from 20 to 150 g, are measured in
one cuvette (or alteratively several cuvettes, to increase the accuracy of the (i measurements),
120 cm2in area, in layers that are intermediate or saturated for S-radiation. The measure-
ments are conducted simultaneously through six channels.
The uranium is determined from the high energy (3-radiation, while the radon is deter-
mined by means of the total y-radiation with.a discrimination threshold of 300 keV. The
protactinium is determined in two parts of the spectrum: in the energy ranges 82 and 270
keV, which enables us to duplicate the protactinium analyses. The radiation of Ra is deter-
mined in the energy region 186 keV, while that of thorium is determined in the 2620 keV
region. On the basis of such measurements, we have compiled a system of six equations.and
determined U, Ra, Rn, Pa (two results), and Th. To increase the accuracy of the analyses,
we can raise the temperature of the samples to 800-1000?C. Under these conditions, the sam-
ples lose about 90% of their radon, and the intensity of the radiation from the radon, whose
presence has an adverse effect on the analysis, is reduced by an order of magnitude. The
analysis as a whole occupies a period of 10-15 min.
LITERATURE CITED
1.
G.
N.
Kotel'nikov, At. Energ.,.24, No. 6, 154 (1968).
2.
I.
P.
Shumilin, At. Energ.., 37, No. 5, 384 (1974).
3.
I.
P.
Shumilin, Second All-Union Conference on the Chemistry of Uranium [in Russian],.
Nauka, Moscow (1978), p. 130.
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP1O-02196ROO0800030003-1
PROBLEMS OF DIAGNOSTICS OF PHYSICAL CHARACTERISTICS
OF RBMK REACTORS ACCORDING TO NEUTRON NOISE
B.
A.
Vorontsov, I. Ya. Emel'yanov,
L.
N.
Podlazov, V.. D. Rogova,
V.
I.
Ryabov, and B. M. Svecharevskii
The operation of high-capacity atomic power plants requires that the physical and
dynamic characteristics of the reactor be monitored not only in the stage of start-up and
entry into steady-state recharging conditions but also throughout the entire period of
operation. The latter is due in particular to the fact that rapid advances in the fabrica-
tion of fuel elements make it possible to improve the technical and economic characteristics
of reactors already in service. The final assessment of the effect of such measures on the
characteristics of an atomic power plant should be made through full-scale tests.
In experimental studies of power reactors the principal of minimal changes in their
operating conditions is most important. It is therefore advisable and promising to intro-
duce into the practice of operational tests statistical methods excluding interference in
the operating conditions of the atomic power plant. One such method is based on analysis
of the neutron power, whose noise contains information about practically all processes and
properties of the reactor [1]. The literature contains information about the use of analy-
sis of neutron noise from power reactors to predict resonant instability [2], to diagnose
vibrations and displacements of elements of the reactor construction [3, 4], etc.
In the present paper on the basis of experimental and computational-theoretical inves-
tigations we substantiate the possibility and the promise of using statistical methods for
operational monitoring and diagnosis of changes in the steam coefficient of reactivity of
reactors of the RBMK type under the conditions of commercial operation.
Formulation of the Problem. In a qualitative examination of the oscillograms of the
neutron power (Fig. 1) of the RBMK-1000 reactor of the first unit of the Leningrad Atomic
Power Plant it was found that the character of these fluctuations changed with entry into
the steady-state recharging conditions along with the change in the reactivity coefficients
and some dynamic characteristics of the reactor. This was the basis for studies on the per-
tinent quantitative relations. The method of solving this problem was refined after prelimin-
ary analysis of the autocorrelation functions (ACF) of the neutron noise, which were obtained
in special experiments.
Description of the Experiment. From the measuring part of the regular control and
safety system (CSS) the neutron-noise signal, being the relative deviation of the neutron
power from the prescribed value, was fed into two recorders: a sensitive electronic record-
ing potentiometer and a magnetograph. The use of a multichannel magnetograph enhanced the
quality of the record and simplified the processing of the experimental information; at the
same time, the noise of some other thermohydraulic parameters of the reactor installation
was recorded in parallel. The experiments were performed with steady-state operation of the
reactor at 85% nominal power. A study was made of the effect of the operation of the auto-
matic pressure (APR) and level (ALR) regulators in drum separators (DS) on the spectrum of
neutron noise. As a result, we obtained a series of realizations for the following modes
of operation: all regulators switched on,(nominal mode of operation); only the APR switched
off; only the ALR switched off.
Fig. 1. Fluctuations of neutron
power of RBMK-1000.
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 145-148, March, 1980. Original
article submitted July 24, 1978.
0038-531X/80/4803-0161$07.50 ? 1980 Plenum Publishing Corporation 161
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
50 75
.Fig. 2
4010 4015 4010
Fig. 3
Fig. 2. ACF of neutron noise: 1) all
respectively, switched off.
regulators switched on; 2, 3) APR and ALR,
Fig. 1. Spectral density S of neutron noise (same notation).
Computational and Theoretical Analysis and Discussion of Results. The mathematical .
processing of the data was carried out on a electronic computer according to a special pro-
gram for calculating the ACF, the spectral densities (SD), and other statistical character-
istics-
Figures 2 and 3 show the experimental ACF and SD of the neutron power for the three
operating modes indicated. The ACF is in a form similar to the exponential-sinusoidal rela-
tion which is characteristic of processes excited by a wideband input signal when the object
has resonant properties [1]. The cosine component implies periodicity in the signal of the
neutron-power noise. The form of the ACF depends weakly on the conditions of the experiment.
These features are traced in the resonance peak of spectral characteristics in the frequency
region 0.021-0.022 Hz. It can also be concluded from the data of Fig. 3 that the resonance
at 0.021-0.022 Hz reflects the internal resonance properties of the reactor plant.
Fig. 4. Block diagram of transfer func-
tions of RBMK-1000.
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Fig. 5. AFC of reactor plant for a(p/aFE = -6.4 (1) , -12.8 (2) ,
and -19.2 (3). (app is the change in reactivity per percent
steam content; aFE, the change in reactivity per degree change
in fuel-element temperature.)
Fig. 6. Change in characteristic resonance during operating
run of first reactor of Leningrad Atomic Power Plant (0 -
experiment).
To confirm these conclusions we studied the amplitude-frequency characteristics (AFC)
of a model of the reactor plant (Fig. 4). The system of automatic thermal controls of the
APR and the ALR was not taken into account in the model. The following notation has been
adopted in Fig. 4:
6
aft,; ll_1
The symbol n is the deviation of the neutron power; WK the transfer
t=~
function of the reactor kinetics with the assumption that Zdn/dt = 0; WAPR = -q(A)/s, the
transfer function of the automatic power regulator (APR); q(A), the coefficient of harmonic
linearization; WT = XT/ (S + AT), the transfer function of the change in the temperature gradient
from the fuel elements to the coolant; AT, the inverse time constant, of the change in the
thermal power of the reactor; PAPR, the relative reactivity of the APR; TFE, the dimension-
less deviation of the thermal flux from the fuel elements to the coolant; K1, K2, K3, coef-
ficients determining the change in the steam flow rate under a change in the pressure, ini-
tial enthalpy, and thermal power of the reactor; Kc, Kam, Kam, coefficients determining
the change in the steam content as the result of a change in the thermal power of the reac-
tor, the pressure in the DS, and the initial enthalpy; MWp, M(Pp, A(Pi, the changes in the
steam content as the result of, a change in the thermal power, pressure in the DS, and the
initial enthalpy; K, the gain of the pressure-change transfer function; TM, the time con-
stant of the smearing of the temperature front in the circulation loop; T, the transport
delay in the circulation loop; aFE, a'p, the reactivity according to the fuel-element tempera-
ture and the steam content; PDC, the deviation of the pressure in the DS; and i, the devia-
tion of the initial enthalpy.
It is seen from the block diagram of Fig. 4 that in the range of frequencies studied
a change in the reactor reactivity occurs primarily because of a change in the fuel temper-
ature and the steam content, the change in the latter being associated with a change in the
thermal power (positive relation*), a change in the pressure in the DS.(negative relation*)
and a change in the initial enthalpy with a corresponding transport delay (positive relation*).
Each process has its phase shifts and gains, and this is why resonance peaks appear in the
AFC of the reactor.
*With positive a'p.
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Periodic measurements during an operating run of the RBMK indicated a small change in
aFE and a substantial change in a(p. Therefore, in order to ascertain the effect of the phy-
sical characteristics of the reactor core on the AFC it was sufficient to change app in the
calculations. From Fig. 5, which presents some of the results of the calculations, it is
seen that at 0.023 Hz there is a resonance, which is in good agreement with experimental data.
It is also seen that the amplitude of the resonance increases as alp grows. It thus follows
that in the real spectral densities of neutron noise, recorded at various times during the
RBMK operating run, the resonance at these frequencies should also increase as a(p grows.
Figure 6 shows the change in the amplitude of the resonance as found by processing
neutron noise recorded at various times during the operating run of the reactor. The maxi-
mum in this plot corresponds to the state of the reactor with the highest value of acp. The
subsequent decrease in the amplitude of the resonance corresponds to a new state of the reac-
tor core after modernization of .the charge.
Thus, experimental (see Fig. 6) and computational and theoretical (see Fig. 5) data
indicate that the parameters of the resonance of the spectral characteristic of the neutron
noise of the RBMK-1000 at frequencies-of 0.021-0.022 Hz can be conveniently used to diagnose
changes in the physical and dynamic characteristics of a reactor. And on the basis of the
well known relation Si/So = IWi12/IWoI2, with the assumption that the perturbing action is
of an unchanged character, it.is possible to make a quantitative estimate of the change in
app at any i-th moment in the operating run if at some moment, labeled by a zero subscript,
a neutron-noise spectral density So was measured with known properties of the reactor core,
i.e., in fact, with a known reactor transfer function Wo.
Conclusion. Studies of the neutron noise of the RBMK-1000 can be made on the basis of
the existing regular CSS equipment. In studying the neutron noise it was revealed that in
the frequency range 0.021-0.022 Hz the spectral characteristic displays a resonance whose
amplitude depends essentially on the steam coefficient of reactivity; this makes it possible
to use analysis of neutron noise to monitor and diagnose changes in the steam coefficient
of reactivity of reactors of the RBMK type during normal operation. At the same time, it
was established that for analysis of neutron noise in the RBMK-1000 in the frequency range
indicated one'can use a simplified model of the dynamics of the reactor plant.
LITERATURE CITED
1.
R. E. Uhrig, Statistical Methods in Nuclear Reactor Physics [Russian translation],
Atomizdat, Moscow (1974).
2.
V.
A. Afanas'ev et al., At. Energ., 24, No. 4, 363 (1968).
3.
J.
Robinson and R. Kryter, Trans. Am. Nucl. Soc., 24, 413
(1976).
4.
M.
Mathis et al., Trans. Am. Nucl. Soc., 23, 466 (1976).
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
Yu. P. Elagin, A. S. Il'yashenko,
V. A. Lyul'ka, T. S. Poveshchenko,
and N. V. Sultanov
The complex of programs being developed for the detailed calculation of RBMK reactors
must provide for the rapid and sufficiently accurate calculation of the neutron flux aver-
aged over a cell of a fuel channel (FC). This problem can be solved in various ways. In
the present article we investigate the surface pseudosources method (SPM) in the GN approxi-
mation with the reduction of the channel to cylindrical geometry, the SPM in the GNP approxi-
mation, the first collision probability method (FCPM), and the generalized first collision
probability method (GFCPM).
These methods are compared with the Monte-Carlo method. In addition to accuracy the
machine time necessary in the various methods is also taken into account. With this in
mind the following problems were treated in the one-group approximation;
1. The problem of a unit unidirectional flux of neutrons incident on the outer boun-
dary of a FC with no internal sources; neutrons emerging from the channel are not returned.
2. Problems of a source of specified constant strength inside the FC; neutrons emerg-
ing from the channel are not returned;
3. Problems of a source of specified constant strength inside the FC; neutrons are
specularly reflected inward from the outer boundary of the channel.
In these variants it is required to determine the average neutron fluxes in zones into
which the FC is divided. By a FC we mean the reactor channel itself plus an adjoining layer
of graphite a few centimeters thick (Fig. 1). The FC is divided into several zones with
P2 =0-9 cm, p3 =2.3 cm, and p,,= 3.78 cm; the numbers 2, 3, and 4 refer to circles counting
from the center of the channel. The graphite is also divided into two or four regions by
concentric circles..
Surface Pseudosources Method in the CN Approximation. In this method a calculation is
first made for a two-zone cylindrical microcell consisting of the fuel element and a sur-
rounding layer of water with an outside radius determined in the Wigner-Seitz approximation
by the expression
TABLE 1. Comparison of Average Neutron Fluxes in a RBMK FC with External Sources
Zone
No
Material
pout or
p
' cm
E cm-1
t'
E cm-1
a '
; -mMC
_ ?too%
' MC
_
' MC
Mc
?too%
mMC
?MC
.
c
MGG3
G{
(anisotropic source)
CPM
GFCPM
(isotropic source)
1
Zr
0,75
0,3485
0,0085
-7,5
-3.
1,34 (1?1,3.10-2)
+0,8
-3,4
1,32 (1?1,3.10-2)
2
H2O
{
2,3
2,1318
0,0075
-4,5
-0,6
1,52 (1?0,6.10-2)
+0,7
-2,0
1,51 (1?0,6.10-2)
U02
1,6
0,6114
0,2455
-2,5
-0,8
1,34 (1?0,7.10-2)
+3,5
-0,9
1,33 (1?0,7.10-2)
3
H2O
{
4,0
2,1318
0,0075
+1,3
+0,3
3,08 (1?0,3.10-2)
+0,3
-1,0
3,06 (1?0,3.10-2)
U02
3,09
0,6114
0,2455
+0,42
+0,2
2,36 (1?0,3.10-2)
-1,7
+0,3
2,35 (1?0,3.10-2)
4
Zr
4,4
0,3485
0,0085
?0,43
+0,2
4,64 (1?0,3.10-2)
-3,5
-1,0
4,59 (1?0,3.10-2)
5
C
5,4
0,3809
0,0002
+0,39
+1,2
5,10 (1?0,2.10-2)
-3,7
-1,2
5,07 (1?0,2.10-2)
6
C
6,4
0,3809
0,0002
+0,70
+1,2
5,60 (1?0,2.10-2)
-3,2
-1,2
5,68 (1?0,1.10-2)
7
C
7,7
0,3809
0,0002
+0,33
+0,30
6,09 (1?0,2.10-2)
-3,1
-1,3
6,06 (1?0,2.10-2)
8
C
9,0
. 0,3809
0,0002
+0,80
+1,1
6,47(1?0,1.10-2)
-3,0
-0,8
6,49(1?0,2.10-2)
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 148-151, March, 1980. Original
article submitted March 26, 1979.
0038-531X/80/4803-0165$07.50 ? 1980 Plenum Publishing Corporation 165
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
Fig. 1. One sixth of a RBMK fuel
channel; 1) zirconium rod; 2) water
or steam-water mixture;.3) fuel ele-
ment; 4) zirconium tube; 5) graphite;
---) radii of centers of fuel slugs
of first and second rows.
RM_ P -Pa ii-P
6 12,
where P2 and p3 are respectively the inside and outside radii of the homogenized zone (Fig.
1), and the superscript ,M characterizes quantities referring to the microcell.
The choice of neutron source in the calculation.of a microcell depends on the model -
problem. For problem 1 a unit difference current of incoming neutrons is specified on the
outer boundary of the.microcell for the "sink at infinity" boundary condition [1]. For
problem 2 uniform volume sources of unit strength are specified in water with diffuse reflec-
tion at the outer boundary of the microcell. Diffuse reflection is achieved by introducing
an additional zone with a large total cross section and a small absorption-cross section.
From microcell calculations performed by the PRAKTINETs 3F program [2], the disadvantage
factor d = 4)MH2O/OcUO2 and the macroscopic cross section of the homogenized annular zone
containing the fuel elements are determined by the expression*
5 Ea SPAt (r) dr
gam =V 5 a)M(r) dr ? (2)
V
Here superscript g indicates the homogenized value. A macrocell is also calculated by the
PRAKTINETs 3F program.
Average neutron fluxes over the microcell in the homogenized region were determined by
using the disadvantage factors d and the balance condition
Z6 J02 " UO2'0O2 + E H2O ' H2O i1 0 = FavgED-
Surface Pseudosources Method in the GNP Approximation. The development of the surface
pseudosources method for determining neutron distributions in complex two-dimensional cells
was reported in [3]. Using the algorithm obtained, N. V. Sultanov wrote a PRAKTINEK program
[3] for calculating neutron fluxes averaged over zones of a FC in the GNP approximation; N
is the number of spherical harmonics; and P, the number of axial harmonics.
First-Collision-Probability Method. It.has frequently been pointed out in the litera-
ture [4, 5] that the FCPM is a fruitful method of calculating the spatial and angular dis-
tributions of neutrons in a lattice of a heterogeneous reactor. The calculation of Pik, the
*This method of averaging can lead to an appreciable error for Esg, but this does not have
a large effect on the final result.
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
TABLE 2. Comparison'of Average Neutron Fluxes in a FC of a RBMK Reactor with Inter-
nal Sources
Zone
Material
Port
E1.
1
Ea
1
4, cm-3
m-0 MC
?1oo%.
mMC
-
MC
m- mMC
?1oo%
AMC
m
MC
No.
P ,
cm-
cm-
Gj I
FCPM.I
GFCPM
MGG3
I G
1
Zr
0,75
0,3475
0,0075
0,00755
0,4
-10,2
-1,4
0,137 (1?1,9.10-2)
-0,1
-1,0
0,103 (1?2,8.10-2)
2
J H2O
2,3
1,434
0,0102
0,8196
0,2
-3,4
-1,4
0,144 (1?0,8.10-2)
-1,8
-0,6
0,112 (1+12 . 10-2)
,
2
UO2
1,6
0,6708
0,3233
0
0,0
-0,8
-0,6
0,114 (1?0,8.10-2)
-0,8
0,4
0,0905 (1?1,2.10
)
3
H2O
{
4,0
1,434
0,0102
0,8196
-0,7
0,0
-0,7
0,140 (1?0,5.10-2)
1,9
0,0
0,157 (1?0,8.10-2)
-
UO2
3,09
0,6708
0,3233
0
0,0
0,0
0,0
0,112 (1?0,6.10-2)
0,7
-0,2
0,1210 (1?0,7. 10
2)
4
Zr
4,4
0,3475
0,0075
0,0075
1,1
0,0
0,8
0,125 (1?0,7.10-2)
-0,0
-0,2
0,197 (1?1,0.10-2)
5
C
6,4
0,4
0,0003
0,0636
0,9
-1,8
0,0
0,109 (1?0,6.10-2)
0,4
1,4
0,214 (1?0,8.10-2)
6
C
9,0 '
0,4
0,0003
0,0636
0,75
-1,2
-1,5
0,0665 (1?0,5.10-2)
0,9
0,4
0,233 (1?1,0.10-2)
probability of a neutron created in.zone i from a uniform isotropic source experiencing its
first collision in zone j, plays a fundamental role in this method. Unfortunately, the
approximate version of the FCPM, the so-called method of geometrical characteristics, cannot
be applied directly to an actual FC since it was developed only for two-component (moderator-
fuel) media, and a FC has a more complex structure involving at least three components.
Therefore, Pij must be calculated by the exact method using double integrals,* and this
increases the computation time. The calculations were performed by V. A. Lyu'lka and Yu. P.
Elagin.
Generalized First-Collision-Probability Method. In this method the flux is expanded
in a set of orthogonal polynomials in Cartesian coordinates. We present the results of cal-
culations performed by T. S. Poveshchenko using the generalized first-collision-probability
method in the linear approximation; the neutron flux in a zone is represented by a linear
function of the x and y coordinates.
Monte-Carlo Method. In principle, high accuracy can be achieved with this method (e.)g.
[4]). Therefore, we take the results obtained by A. S. Il'yashenko using the results of the
Monte-Carlo method as bench marks.
Results of Calculations. The accuracy of neutron flux averages over zones of a FC cal-
culated by various methods was determined by comparison. with the same averages calculated
by the Monte-Carlo method. The first calculation' was for a channel with-neutrons entering
from the outside. In calculations by the surface pseudosources method in the GNP approxima-
tion and the GN approximation with the reduction of the FC to cylindrical geometry, the neu-
trons entering the cell through the outer boundary had a linearly anisotropic angular dis-
tribution with an anisotropic fraction of 7.25%.. In calculations with the ordinary and
generalized first collision probability methods the angular distribution of the; neutrons
entering the cell was isotropic. The calculations with the Monte-Carlo method were made
with both angular distributions of, the entering neutrons.
The input data and. calculated results are listed in Table 1, where AMC is the average
neutron flux calculated by the Monte-Carlo method. In order to compare results the calcula-
tions were normalized to-the same number of neutrons. absorbed in the channel per unit time.
This variant of the calculation is the most complicated because of the large gradient of the
neutron flux toward the center. Therefore, we discuss it in more detail.
In the calculation by the surface pseudosources method in the G3 approximation with the
reduction of the FC to cylindrical geometry (we denote it as the MGG3 approximation) the.
channel was divided into zones as shown in Fig. 1. The fluxes were averaged over the zones
by the expression
_ M dV/i V. (4)
*The integral is triple, but the inner integral is tabulated beforehand..
I
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In all zones the approximate neutron fluxes differ from the bench mark values by ''l%
except in the central rod (-7.5%) and the water zone adjoining the first row of fuel slugs
(-4.5%).
The division into zones for calculations by the surface pseudosources method in the.G3
approximation is shown in Table 1. The error of the calculation is 'l% (3% in the central
zone). In the FCPM the FC is divided into zones as shown in Fig. 1, but each fuel element
and. the water surrounding it are further divided into two parts (dashed curves). Thus, the
channel is divided into 16 zones. The maximum error of the calculation is ti3%. In the
GFCPM the FC is divided into zones as shown in Fig. 1, i.e. into 12 zones. The accuracy
of.the calculation of the neutron flux in the fuel elements is somewhat better than in the
FCPM with division into 16 zones.
In the second stage of comparison of the accuracy of the approximate methods a calcula-
tion was made of a channel with internal neutron sources. The calculations were normalized
to one neutron absorbed in the channel. The input data and results of the calculations are
listed in Table 2.
In order to compare the results of the SPM calculation in the GNP approximation, the
FCPM, and GFCPM with bench-mark values, a channel was chosen with a vacuum outside it.
These boundary conditions were established exactly in all the methods considered except in
the SPM where at the outer boundary of the channel the integrated current of incoming neu-
trons from the FCPM calculation was specified.. The neutron source density in zones of the
channel was assumed proportional to the slowing-down power of the medium iES. The error of
the SPM calculation in the G3 approximation and the GFCPM was 1%; the FCPM has the same
error except in the average neutron flux in the first and second zones where there is a
systematic underestimation of the flux by tilO%.
SPM calculations with the reduction of the FC to cylindrical geometry and in the GNP
approximation were compared with the bench mark value by calculating a "closed" channel,
i.e. a channel with internal neutron sources and zero neutron current at the outer boundary
of the channel.
The results of calculations in the G9 approximation differ from the accurate values
by 1%; the calculations in the G3 approximation also differ by 1% except for water zones
where the flux differs by 1.9%.
The values presented show that the SPM with the reduction of the channel to cylindrical
geometry requires considerably less machine time and is not far inferior inaccuracy to the
SPM in the G3. approximation and to the GFCPM.
The computation times of a FC of a RBMK on a BESM-6 computer by the MGG3, G9i FCPM,
and GFCPM are 3., 30, and 90 sec, and 4 min; by the Monte-Carlo method the times are 2 h for
variant a and 15 min for variant b.
1. N. I.. Laletin, in: Methods of Calculating Thermal Neutron Distributions in Reactor
Lattices [in Russian], Atomizdat, Moscow (1974),,p,. 238.
Z. N. V. Sultanov, Preprint IAE-2143, IAE-2144, Moscow (1971).
3. N. I.. Laletin and N. V. Sultanov,'At. Energ.,? 46-, 148 (1979); N.'V. Sultanov, Preprint
IAE-3005., Moscow (1978)..
4. I.'M.Sobol, The Monte Carlo Method, Univ. of Chicago Press (1975):.
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CALCULATION OF EFFECTIVE BOUNDARY CONDITION AT THE
SURFACE OF A MULTIREGION CYLINDRICAL SLUG
B. P. Kochurov UDC 5.39.125.52:621.039.51.12
In heterogeneous reactor theory [1] the effective boundary condition at the surface of
a slug is specified in terms of the thermal constant
2nDp [aN (p) lap]/N (p), (1)
where D is the neutron diffusion coefficient in the moderator, p is the radius of the slug,
and N(p) is the asymptotic neutron flux in the moderator extrapolated at the surface of the
slug. Many papers have been devoted to the calculation of y or the related quantity r:
r = N (p) ll [ON (p) lap] = 2nDp/ly (2)
based on various methods of neutron transport theory and applying mainly to one-region slugs
in an infinite moderator, generally assumed not to absorb neutrons [2, 3]. A more detailed
bibliography can be found in [4].
We consider the calculation of r for a multiregion cylindrical slug, based on a numeri-
cal solution of the integral neutron transport equation.[5], specifically in a finite cell.
Suppose the slug is located in an infinite moderator. Assuming isotropic scattering,
or in the transport approximation, the neutron flux in the one-velocity theory satisfies the
integral equation
HN=O; H=1-L;
LN = K (r, r') X. (r') N (r') dr'.
Fig. 1. Distribution of neutron
flux N (r), the source Q (r), and
the weight function W (r). The
moderator is 8.4 cm thick.
(3)
Translated from Atomnaya Energiya,, Vol. 48, No. 3, pp. 151-153, March, 1980. Original
article submitted April 2, 1979.
0038-531X/80/4803-0169$07.50 ? 1980 Plenum Publishing Corporation 169
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TABLE 1. Effective Boundary Condition r of
Black Slugs, Obtained by Using a Numerical
Method and from Data in [4]
c=0,99
r I
r [41 1
or, %
r [4] t
or; %
I
r[4]. I
or,%.
0.1
1,2010
1,2058
-0.40
1.2207
1-,2216
-0.07
1,3979
1,3856
0,89
0,2
1.1300
1.1362
-0.55
1,1480
1,1502
-0,19
1,3046
1,2951
0.74
0,3
1,0802
1.0858
-0.52
1,0969
1,0985
-0,15
1.2368
1.2284
0,68
0.5
1.0103
1;0149
-0.46
1,0249
1,0255
-0.06
1,1395
1,1336
0,52
0,7
0,9622
0.9662
-0.42
0,9753
0.9755
-0,02
1,0720
1,06851
0.33
1,0
0,9122
0.9159
-0,41
0,9239
0,9237
+0.02
1.0025
1,0016
0.09
2.0
0,8286
0.8318
-0,39
0,8384
0,8374
+0,12
0,8479
0.8459
0,15.
5.0
0,7632
0,7623
+0.12
0,7715
0,7664
+0,67
0.8082
0.8062
0,36
8.0
0,7521
0,7429
+1,24
0,7540
0,7466
+0,99
0.7876
0,7836
0.52
Here K (r, r') =exp (-ER)/4TrR2; R = lr - r'I, ER is the optical path between r and r'.
Let Ho and Lo be the corresponding operators for an infinite moderator:
LON = K. (r, r') EsN (r,')dr';
Ko (r, r') = exp (- ER)/4nR2,
where Es and.E are the scattering and total cross sections of the moderator.
The regular solution No and the Green's function G0'(r, ro) for the operator Ho are
H0N0 = 0; N0 .= I-o, (xr);
HoG0(r,ro) _$(r, -ro)+
where'Yt is a root of the equation (the asymptotic parameter)
(2,/2x), In [(1 + x/E)/(1: -.x/E)1 = 1;
and the.Green's function for large jr, ro.l has the asymptotic representation
Go.ac (r, ro)= g (c,.,1) KO (x j r--ro ~.);. c
:(1- -
1=1%E; g(C., l) X2 XV)
= n(X212_1+C)
At. large distances, from the surface of the slug (more: than one, td two neutron mean free
paths in: the moderator) the azimuthally symmetric solution of Eq. (3) has the form
Nac (r) = A[I0 (xr) + uKa (xr)1,
where the parameter u.is uniquely related to y or r;
a/I'= z[I1(z)-uKi (z)1
jo (z)-1-uKo (z).
a = pl; z - xp.
A closed functional expression can be obtained for the parameter u. Rewriting Eq.. (3).
in-_ the form,
HN=H0N?(H-H0)N=0.
(10)
and using the Green"s function we find
Nac (r) = g (c, 1) Ko (xr).S Io (Nro) (L-Lo)Ndr0,
(11)
where the addition theorem for Bessel functions [1] has been . applied. to Ko ('.tlr - rol).
Comparing Eqs. (8) and (11), we obtain.
(12)
u = [g (c, l)/I IIo (xro) (L - Lo) N = [k (c, l)/I (L+ - Lo) ION (ii) di,
Thus, u isfound as a functional for the solution,'. determined by the weight
W (r) [g (c, 1)/I S [E (r) K (r, ro) -EK0 (r, ro)11o (xro) dro, (13)
in.which the integration in Eq. (12) is extended over the slug and part of its neighborhood.
The function W (r) is damped out exponentially at distances from the slug of the order of
the neutron mean-free path in the moderator.
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TABLE 2. Parameters u-and T of Two Four-
Region Cylindrical Slugs (Di is the.layer
thickness in cm)
c[0
0
N%
A
E '0
Ai
5,0
0,1
0,3
0,04
Yi
0,20
0,09
3.10-5
0,09
0,4001
7'3i
0,14
0,08
3.10-5
0,08
0,4030
Ai
2,5
0,4
0,3
0,3
Ii
0,50
0,01
2,0
0,01
0,4001
Esi
0,25
0,01
1,98
0,01
0,4000
Equation (3) can be solved by transforming the regular part of the solution into a
certain source. Let
No (r) = AIo (xr) (14)
be the regular solution, continued into the slug. We find the complete solution in the form
We rewrite Eq. (3) in the form
N (r) = No (r) + N1 (r).
HN=HN1+(H-H0)N0=0
(15)
N1 = LN1 + Q; Q = (L - Lo) No, (16)
where the source function Q is damped out exponentially in the moderator at distances from
the slug of the order of a mean free path. How do we find u or r from the solution of the
integral equation in a cell of finite dimensions? We surround the slug with a sufficiently
thick layer of moderator, and seek the solution in the form (15), where
No (r) = 10 (xr) (17)
is the fixed regular part of the solution continued into the slug, and the operators in Eq.
(16) are defined for a finite cell. Sufficiently far from the slug 1
Ni,ao (r) = uKo (xr) + B [Io (xr) + uKo (xr)] = B [Io (xr) +K1((xR) Ko (xr)J , (18)
where the first term comes from the fixed regular part of the solution No (17), and the
term tiB is related to the finite size of the cell. The latter part of Eq. (18) follows
from the vanishing of the diffusion current at the cell boundary R. The coefficient B can
be found by requiring the least deviation of (18) from the numerical solution in a certain
asymptotic region of the moderator. Then it follows from Eq. (18) that
B11(xR)1K1(xR)
Equation (12) can also be used for u with A =1 +B representing the total amplitude of
the regular'solution in the present case.
Table 1 lists the calculated values of F for black slugs surrounded by a moderator which
absorbs neutrons, obtained with a program for solving an integral equation in a finite cell
[5]. The condition at the cell boundary indicated above is realized as a result of the
location of an infinite scattering moderator in the region r > R. The highly accurate data
of [4] presented here serve essentially as tests. In the calculations it was assumed that
Es1 = 100 cm 1 , Essl = 0.001 cm-', E =1, c = Es/E, a = pE. The moderator layer was 4-5 mfp
thick.
Table 1 shows that the divergences from [4] are generally within ?0.5%. Table 2 lists
the calculated values of u and r for two four-region slugs which can serve as tests, with
an error of no more than ?1%.
171
3 I 4 QO c0
N
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Figure 1 shows the neutron flux N (r), the source Q (r), and the weight function W (r)
for variant 2 of Table 2. The functions Q (r) and W (r) are exponentially damped out in
the moderator at distances of the order of a neutron mean free path.
The author thanks A. D. Galanin for helpful comments.
1. A. D. Galanin, Thermal Reactor Theory, Pergamon, New York (1960).
2. B. Davison, Proc. Phys. Soc., 64A, 881 (1951).
3. D. F. Zaretskii and D. D. Odintsov, in: Reactor Engineering and Reactor Theory [in
Russian], Vol. 5, Izd. Akad. Nauk SSSR (1955), p. 279.
4. A..Kavenoky, Nucl. Sci. Eng., 65, 514 (1978).
5. A. Ya. Burmistrov and B. P. Kochurov, Preprint ITEF-49, Moscow (1976).
NEUTRON IMPORTANCE AND SENSITIVITY COEFFICIENTS
IN ITERATION SYNTHESIS METHODS
A. M. Kuz'min, K. S. Rafaev, UDC 539.125.52:621.039.51.12
and V. V. Khromov
In the practice of neutron-physical calculations of reactors extensive use has been
made of iteration synthesis methods in which the. space-energy distribution of neutrons is
presented as a product of functions, each of which depends on one variable. These methods
include methods of conditional separation of variables [1] and methods of synthesis in the
class of continuous functions [2]. These methods served as the basis for high-speed pro-
grams (18-4RZ-15 [3] and its up-to-date modification SINVAR, SYNHAX [4], etc.) which make
it possible, with sufficient accuracy for optimization studies, to calculate the neutron
distribution and to determine the physical characteristics in reactors of complex form.
However, the application of these methods in calculations from the formulas of perturba-
tion theory and with automation of the search for the optimal reactor parameters (e.g., by
the method of successive linearization [5]) was hindered by the lack of algorithms for the
solution of the pertinent equations for the neutron importance. In the present paper within
the framework of the methods mentioned we formulate equations for the neutron importance,
describe an iteration scheme for solving these equations, and give the results of calcula-
tions of the sensitivity coefficients for a typical fast sodium reactor with oxide fuel.
For simplicity, we confine ourselves to consideration of problems in which the neutron flux
density t(x, y) depends on two variables (extension of the discussion to the case of a large
number of variables does not entail any major difficulties). As follows from [1, 2], to
find the distribution (D(x, y) it is necessary to solve the system of nonlinear equations
L(t)iV+)~Q()(F =d; (1)
+ ) (~1) = 0
for the auxiliary vector functions cp(x) and ii(y), whose boundary values cps and *s satisfy
the conditions r1(cps) =0 and P2(*s) =0- In the course of the solution there are the non-
linear transformations
= P w; ~1 = S (T) (2)
.to the vector functions ~(y) and n(x), on the basis of which the operators of Eq. (1) are
constructed: L(C) and L(C), operators "kindred" to operator t of the neutron transport
equation describing the spatial displacement, absorption, and scattering of neutrons, as
well as Q(c) and Q(n), operators "kindred" to operator Q of the transport equation char-
acterizing the creation of secondary neutrons. In this case A is the leading eigenvalue of
the problem and is proportional to the neutron-multiplication factor keff while the opera-
tors L(C), L(n)Q(E), and Q(n) depend in a known way on the perturbation parameter u (the
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 154-157, March, 1980. Original
article submitted July 13, 1979.
172 0038-531X/80/4803-0172$07.50 ? 1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
. AX, I AX2 AX3
Fig. 1. Scheme of reactor:
AX1 = 109,0; AX2 = 43,3; AX3 = 50,0;
AY1=52.0; and AY2=50.0 cm.
concentration of any element, e.g., can be taken for such a parameter). The concrete form
of these operators and the mappings P(s) and S(c) were described in detail in the papers
indicated above.
We shall assume that:
with a fixed value u = uo the eigenvalue ao and the corresponding solutions Qo and 4,
are obtained;
in the proximity of the solution the products kg (to); 1c1 (i1o); J PV (to); Sc ((Po); MLL (to); and
Mu(no) are definite and continuous, so that
aL (to) (Po aQ (to) To .
Mg (to) (Po = - at at
aP (+Vo) ;
Pp ($o = M 010) to aL (no) *o +2,o aQ (*Io) lho
app - an al
aL ($o) qo aQ (to) To.
'ST (4po) - aq) , Mu (to) To = 8u + o au
8L ~~) o + -0 a_ __ +ho ;
Ru (,lo) to
there exist ad joint operators L+(Co) , Q+(Co) and L+(flo) , Q+(no) Q+ (no) in the class of func-
tions fi(x) and $+(y), respectively, which satisfy the adjoint boundary conditions 1'i(tps+) _
0 and I 2 (*S) = 0.
The orthogonality conditions
{ST(WO) To}x = 0; {Rp(' I'0) 'V'o}o = 0
(3)
are satisfied; here, { }x and,{ }y denote the integration of the expression in braces
over the range of variables x and y, respectively. The latter condition is easily verified
with due account for the properties of transformation (2), as described in [1, 21.
Suppose that uo has changed by du. A new eigenvalue a = ao +Sa and new distributions
(p = cpo + &p and J =>J, o + dp correspond to the value u = uo + Su. As a result, any physical char-
acteristic F, which is a functional of the neutron flux, experiences an increment SF. To
obtain the perturbation theory relations associating SF and Su, we employ discussions simi-
lar to those in [6]. In this case it is easily shown that to estimate the variation Sa it
is necessary to successively solve the adjoint equations
- L+ (~lo) k F ~oQ+ (110) ~k - P, (qo) {q - 1, 1ti14 (So) TO).;
1 + (b0).~k + a OQ+ (40) Tk = - `s+ (To) {' l' M71 ('10) *0}t/,
where k =1, 2,....
As the first approximation we can take the distribution (Po which satisfies the homo-
geneous equation
- L+ (4o) qPo + ?oQ+ (to) 1Fo = 0.
Solutions tpk and ik. (k =1, 2, ...)YY exist since by conditions (3) the equations
(to PV (h0) (W -1, Mg (to) APO}x }U = {APO, S,p ((P,) { Y k-1, M11 (~10) Y 0}U}x.- 0
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TABLE 1. Properties of Reactor Zones
Cross section,
cm 1
Etr
102E
102VE f
1,1 11,2and2,21 2,1 3,1 ajfd3,2
- 1
0,2353
0,5286
0,5610
0,2548
0,4123
0,1090
0,2354
0,5690
0,6781
0,3119
0,5555
0,1518
are satisfied and can be obtained by-well-known methods [7].. It is of interest to use an
iterationless scheme, described in [8], since the eigenvalue ao is known.
If the iteration process (4) is truncated at the step of number k = n, we get
- 6XW = {~+, Mu ( o) gosu}x +{,V+, Mu (tlo) gho8u}b + An,
where
n-i n
W = WO, Q (to) To).; w+ _ tPn + aqn; '$+ = E, '$n;
k=0 k=1
nn = a {S*, PTV (*o) {fin, M (o) q)o}x}Y+(1-a) {sgp,Sq) ((po) {*n, M,, (no) *o}b}x;
where __J0 if the n-th iteration ended in the determination of tin;
1 if the n-th iteration ended in the determination of (Prl+.
The value of An characterizing the error of calculation of 8a in,the n-th approximation will
be smaller the weaker the nonlinearity of the initial equations (1) and (2). It is also
obvious that the final result (as n-}u) for da should not change if the iteration process
is begun by finding the solution iyo of the homogeneous equation
- G+ (' io) '1 Vu + 2,ot+ (1 o) '$o = 0,
having simultaneously changed the sequence in which the functions 4k+ (Pk+ are found in
each k-th step in the system (4) and in Eq. (6a).
To estimate the variation F of any linear-fractional functional F((p, 4,) of the neutron
flux it is necessary to obtain the sequential solution of equations of the form of Eqs. (4),
taking for the initial distributions the solutions of the inhomogeneous equations
- L+ (rho) % + ),0Q+ (tlo)1Ft = - FV, (To, '$o);
- L+ ( o) qpo } ),oQ+ ( o) To = -Fqp'(qpo, -Vo) - ST (Wo) {' I,o, M1 1(' o) *o}u, (7)
where F*((po, *0) and F(p((P0, 4'o) are the functional products in ,y(y) and (p(x), respectively,
calculated for u = uo ; (p= (Po and dr = t~ o.
For simplicity we shall assume that the functional F((p, *) does not depend explicitly
on the parameter u. Then for the variation 6F we get an expression of the same form as in
the right-hand member of Eq. (6). In this case
n-1 - nn.11
IF+ wk + aun; *+ = LJ 1pk.
k=0 k=0
By way of illustration of the efficacy. of the schemes described for solving adjoint
equations, we give some results obtained for a two-dimensional, cylindrical, multiple-zone
reactor, symmetric about a central axis (x =0) and the diametral plane (y =0). The scheme
TABLE 2. Sensitivity Coefficients of Functionals Keff and Fo
Sensitivity
coefficient,
104 cm
L
L,
174
Calculation by perturbation-theory formulas (with cn = 0)
n=o n=i
l n=2
a=1 a=0 l a=i I a=0 a=1
-0,9727
0,6667
-0,9786
3,8763
-0,9804
3,9601
-0,9806
3,9688
-0,9809.
3,9816
-0,9811.
3,9864
Calculation
from Eq. ( 8)
-0,9817
3,9869
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of the reactor is given in Fig. 1 and the properties of the zones are given in Table 1. It
is assumed that each zone of thickness .Xi (i =1, 2, 3) and height AYj (j =1, 2) is labeled
by two subscripts (i, j) denoting, respectively, the number of the i-th radial layer and
the j-th height layer of the reactor. For macroscopic cross sections of neutron interaction
.we introduced the following notation: E, absorption cross section; Etr, transport cross
section; vEf, product of number v of secondary neutrons and the fission cross section.Ef.
The distribution of the density of neutron fluxes was calculated in the one-group
diffusion approximation by the method of conditional separation of variables [1]. Within
the framework of the modification of this method used, the components of the vector func-
tions (p(x) and $(y) had the sense of neutron-flux distributions integrated over the thick-
nesses of the respective layers of the reactor. The components of the vector functions in
(or ), defined only on the boundaries of the zones with coordinates x = Xi (or y = Yj), are
numerically equal to the ratio of one-sided neutron currents, obtained in the distributions
cp(x) [or *(y)], to the neutron fluxes integrated over the volumes of the adjacent reactor
zones. In constructing the adjoint operators, for the initial equations (1) we took the
finite-difference analogs of the respective equations of the method of conditional separa-
tion of variables.
Let us examine the convergence of the iteration schemes and the values of the variations
for two functions F: Keff, the effective coefficient of neutron multiplication, and Fo, the
ratio of the integral neutron flux density in zone (2, 1) to the integral flux density in
zone (1, 1). As the perturbation parameter u we take the absorption cross section E for
zone (1, 1). Calculations showed that iteration schemes of the form of Eq. (4) converge
quite rapidly. For example, no more than 7 iterations were required (n =7 and in each
iteration two corrections *k+ and (pk+) in order that, with an accuracy of e =10', there
be simultaneous satisfaction of the inequalities
nn',
kI)x3IId{1*n1}t~ (2Eb/m) 1/2 (m is the neutron
mass) pass through the energy barrier and are recorded by the detector; neutrons with vz <
(2Eb/m) 1/2 are reflected. Ultracold neutrons with oppositely oriented spin (against the
Fig. l.. Schematic diagram of magnetic-
integrating UCN spectrometer. 1) Reac-
tor core; 2) UCN converter; 3) trans-
porting neutron guide; 4) aluminum
membrane; 5) rotatable knee; 6) neutron
guide of spectrometer; 7) electromagnet
yoke; 8) poles; 9) exciting coils; 10)
diaphragm; 11) UCN detector.
Translated from Atomnaya Energiya, Vol. 48, No. 3, pp. 166-169, March, 1980. Original
article submitted April 23, 1979.
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
L b
3,e
sec-1
q1L
0
b
100 Eb, neV
Fig. 2. Dependence of UCN count rate on height of energy barrier of magnetic
spectrometer operating in the (a) accumulative, (b) streaming mode. The solid
curves correspond to calculation, the circles to experiment, and the dashed
lines to the count rate for neutrons with spin oriented against the field.
Fig. 3. a) Experimental arrangement; b) plot of dependence of UCN count rate vs
barrier height for spectrometer operating with collimator. 1) Spectrometer
neutron guide; 2) collimator; 3) electromagnet; circles correspond to experi-
mental points; dashed line corresponds to count rate for neutrons with spin
oriented against the field.
field) pass through the space between the poles for any value of the magnetic field and are
accelerated, acquiring an additional kinetic energy, equal to Eb in the region with maximum
magnetic induction. If the maximum energy of the investigated spectrum Emax > Eby/2, where
Eby is the boundary energy of the guide wall material (for copper Eby =172 neV), neutrons
that have gathered an energy E > Eby can leave the confines of the neutron guide as a result
of a diffuse collision and fail to enter the detector. Neutrons with an oppositely directed
spin can be lost only within the magnet gap, where E > Eby, since after they have traversed
the gap the ultracold neutrons are again decelerated to the previous energy.
The probability of UCN being lost from the confines of the guide is reduced greatly by
placing a collimator in front of the pole tips; the collimator selects neutrons from the
incident flux whose velocity lies in a narrow solid angle along the axis of the neutron
guide. If Emax `-Eby/2, all neutrons with spin against the field pass through the neutron
guide of the spectrometer, and the need for a collimator disappears. In this case the spec-
trometer was used in the accumulative or streaming modes of operation.
In the accumulative mode of operation, neutrons which have passed through the barrier
are gathered in the region between the detector and the poles of the magnet. For this pur-
pose, the area of the detector input window is made much less than cross-sectional area of
the neutron guide in the region of the poles. The UCN count rate depends on the height of
the barrier produced by the magnetic field in the following manner:
Emax
J (Eb) =const J q (E) dE+Jo, (1)
Eb
where cp(E) is the investigated spectrum of the UCN flux; Jo = J(0)/2 is the count rate for
neutrons with spin against the field, where J(O) is the UCN count rate for Eb =0.
It can be seen from (1) that, in the accumulative mode, the spectrum of the flux can be
found by differentiating J(Eb):
q (Eb) = const [dJ (Eb)[ IdEb. (2)
When the spectrometer is operated in the streaming mode, neutrons which have passed
through the energy barrier are immediately recorded by the detector. In this case, the area
of the input window of the UCN detector is made much greater than the cross-sectional area
of the neutron guide. In this case, the UCN count rate as a function of barrier height
aquires the form:
E ax
J.(Eb) = const (E) (1- Eb'E) dE+ Jo,
188
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
100 Eb, neV
50
0 50 700 h, cm 0
Fig. 4. Experimental arrangement and re-
sults.of linewidth investigations using
gravitational differential spectrometer.
a) Gravitational differential spectrometer
[1) knee, 2) rectangular channel, 3) UCN
absorber, 4) UCN detector]. b) UCN count
rate vs h, height to which knee is raised.
c) Experimental arrangement for analyzing
linewidth by magnetic integrating spectro-
meter [1) knee, 2) rectangular channel, 3)
UCN absorber, 4) UCN detector, 5) magnetic
spectrometer]., d) Dependence of UCN count
.rate on height of energy barrier of magnet-
ic spectrometer connected at exit of rec-
tangular channel with absorber.
where the factor (1 - Eb/E) has the significance of the transmission coefficient for neutrons
of energy E through a barrier of height Eb averaged over angles of incidence for a UCN flux
with an isotropic angular distribution.
It follows from (3) that the spectrum of the flux can be found utilizing the relation-
d2d2
q (Eb) = const Ebdda E b)
magnetic integrating spectrometer was used in the accumulative and streaming modes
of operation to measure the spectrum of the UCN flux at the outlet from the rotatable knee,
lifted to a height HM= 104 cm. The UCN count rate directly at the exit from the knee amoun-
ted to 10 neutrons/sec. The accumulative mode was implemented by placing a copper diaphragm
with an aperture of area 2.5 cm2 in front of the detector. In the streaming regime, the
diaphragm was removed.
In the experiment we investigated the dependence of the count rate for UCN which tra-
versed the neutron guide of the spectrometer as a function of the height of the energy bar-
rier produced by the magnetic field. The results of the measurements are shown in Fig. 2.
The solid curves correspond to calculation via (1) and (3). on the assumption that the UCN
spectrum corresponds to the initial part of a Maxwellian flux distribution with Emax =91
neV. This choice for the maximum energy of the spectrum was made-because the upper boundary
of the spectrum of ultracold neutrons taken from the transporting neutron guide amounts to
197 neV [5].
As can be seen from Fig. 2, the obtained experimental plots for the accumulative and
streaming modes differ considerably, but are in satisfactory agreement with the theoretical
calculations obtained on the assumption that the spectrum of the flux is Maxwellian. This
demonstrates that the accumulative and streaming modes are indeed realized. The slight
discrepancy between the results of experiment and calculation probably comes about because
the ultracold neutrons removed from the transporting guide contain a small proportion of
energy greater 197 neV.
sec"' --1
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 Declassified and Approved For Release 2013/02/01 : CIA-RDP10-02196R000800030003-1
Figure 3 shows the experimental dependence J(Eb) obtained using the magnetic spectro-
meter to investigate the spectrum of the UCN flux directly at the exit from the transporting
neutron guide. In this case Emax >Eby/2, and accordingly a collimator (Fig. 3a) made from
polyethylene in the form of a rectangular channel of cross section 1 x l cm is placed in front
of the poles. In the collimation mode of operation of the spectrometer, the spectrum of the
UCN flux is connected with the UCN count rate by relationships (1) and (2), as in the accumu-
lative mode. As can be seen from Fig. 3b, the obtained dependence coincides in its basic
features with the expected form of the spectrum. The lower boundary of the spectrum, deter-
mined by the presence of the aluminum membrane (Eby =55 neV) in the transporting guide,
amounts to 50-60 neV, and the upper boundary to 160-170 neV, which differs slightly from the
value obtained in the previous experiment. The discrepancy in the upper region of the spec-
trum is probably due to insufficient collimation of neutrons with spin oriented against the
field.
The magnetic spectrometer was also used-to analyze the linewidth obtained from the
gravitational differential spectrometer described in [6, 7-], which incorporates a 11-shaped
knee in the upper horizontal part of which is introduced 'a rectangular channel with an UCN
absorber (Fig. 4a). A construction of this sort should transmit neutrons with an energy in
the range mgh