SOVIET ATOMIC ENERGY VOL. 44, NO. 4

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• Document Creation Date: December 23, 2016
• Document Release Date: March 7, 2013
• Sequence Number: 3
• Publication Date: October 1, 1978
• Content Type: REPORT

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Russian Original Vol. 44, No. 4, April, 197.4 ?
SATktkZ'44-(4) 343-456 (1978)
SOVIET
TOM!
ENERGY
ATOMHAH 3HEP11411,,
(ATOMNAYA &ERMA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or`in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts; Engineering Indei, INSPEC?
Physics Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.-
Soviet Atomic Energy is a cover-to-cover translation of Atornnaya
Energiya, a publication of the Academy of Sciences of the USSR.
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Russian jOurnal.
?
Editorial Board of Atomnaya Energiya:
Editor: O. D. Kazachkovskii
Associate Editor: N: A. Vlasov
A. A. Bochvar V. V. Matveev
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Fursov V. B. Shevche,nko
I. N. Golo./in' V. I. Smirnov
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
October, 1978
Volume 44, Number 4
April, 1978
CONTENTS
ARTICLES
Introduction of Atomic Power Stations with the VVPR-440 Reactor
Engl./Russ.
- V. A. Voznesenskii
343
299
Evaluation of Plant-Location Strategies for the Nuclear-Power Fuel Cycle
- B. B. Baturov and V. M. Urezchenko .
350
306
Optimization of Energy Distribution in Active Region of Large Functional
Power Reactor - I. Ya. Emel'yanov, V. G. Nazaryan,
and V. V. Postnikov
355
310
Comprehensive Use of Transplutonium Elements - By-Products
of the Nuclear Power Industry- V. N. Kosyakov and I. K. Shvetsov
360
315
The Construction of Coordinate Functions in the Method of Imbedded
Elements for Boundary-Value Problems of Reactor Theory
-V. V. Kuz'minov, I. S. Slesarev, and A. A. Dudnikov
364
319
Subgroup Method for Taking Account of the Spatial Distribution
of Unscattered and Singly Scattered Neutrons in Multigroup
Shielding Calculations - V. F. Khokhlov, V. D. Tkachev, V. L. Reittlat,
and I. N. Sheino
370
324
Thermodynamic Stability of Uranium Mononitride - S. A. Balankin,
L. P. Loshmanov, D. M. Skorov, and V. S. Sokolov
374
327
Neutron Multiplication in Uranium Bombarded with 300-600-MeV Protons
-R. G. Vasil`kov, V. I. Gol'danskii, B. A. Pimenov,
Yu. N. Pokotilovskii, and L. V. Chistyakov
377
329
A Turbulent Plasma Blanket - N. N. Vasil'ev, A. V. Nedospasov,
V. G. Petrov, and M. Z. Tokar'
384
336
CAMAC Electronic Hardware for High-Energy Physics - I. F. Kolpakov
388
339
One Possible Way of Measuring Doses from Accidental Irradiation
- I. A. Alekhin, S. P. Babenko, I. B. Keirim-Markus, S. N. Kraiior,
and K. K. Kushnereva
396
347
DEPOSITED ARTICLES
Possibilities of Purifying the Products of Chemonuclear Synthesis,
with Estimates of the Cost of Such Operations - V. A. Bessonov
and E. A. Borisov
400
351
The Reconstruction of a Neutron Spectrumwith a Priori Information
- A. A. Shkurpelov, V. F. Zinchenko, and B. A. Levin
401
352
)'-Absorption Analysis of a Substance with Allowance for Effect of Heavy
Impurities - I. A. Vasil' ev, Ya. A. Musin, and P. I. Chalov
402
353
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CONTENTS
(continued)
Engl./Russ.
Estimation of the Steady-State Isotopic Composition of Plutonium in a Model
of an Exponentially Growing Nuclear Power Industry ? A. N. Shmelev,
L. N. Yurova, V. V. Kevrolev, and V. M. Murogov
403
353
Optimization of the Cyclical Operating Regime of an Atomic Power Plant
Reactor ? V. I. Pavlov and V. D. Simonov
404
354
LETTERS
Some Features of Nickel Blistering under Irradiation with Helium Ions
?V. I. Krotov and S. Ya. Lebedev .
405
355
Spatial fluctuations of Neutron and Power Distribution in Critical Reactor
? V. K. Goryunov
407
357
Improving the Characteristics of Liquid-Metal Fast Breeders
Using a Magnetic Field ? A. N. Shmelev, V. G. Ilyunin,
and V. M. Murogov
410
359
Surface Barrier Detector Based on Epitaxial Gallium Arsenide
?V. M. Zaletin, L I. Protasov, S. P. Golenetskii, and A. S. Mal'kovskii
412
360
Independent Control of Neutron Flux in Experimental Reactor Channels
? P. T. Potapenko
416
363
Thermokinetics of Hydrogen Generation from Metal?Hydrogen Compounds
Based on Transition Metals of Group V (V, Nb, Tal
? M. I. Eremina and E. V. Khodosov
417
365
Optimization of 238PU Production from 237Np ? A. I. Volovik
426
367
Apparatus for Remote Radiation Monitoring of Processes of Extractive
Separation of Transuranium Elements ? V. V. Pevtsov, V. I. Shipilov,
V. G. Korotkov, and A. N. Filippov
423
369
Flue Gas Scrubbing in Wire Cloth Filter in Combustion of Solid Waste
? N. S. Lokotanov and 0. A. Nosyrev
424
370
OBITUARY
In Memoriam of Artem Isaakovich Alikhan' yan
427
COMECON DIARY
Thirty-Third Meeting of the COMECON Standing Committee
on the Peaceful Uses of Atomic Energy ? Yu. I. Chikul
429
373
Seminar on the Development of Reactor Installations for Atomic Boiler Houses
? S. A. Skvortsov
430
373
Meeting of Specialists on Forecasting ? Yu. I. Koryakin
431
374
Fifteenth Meeting of the Interatominstrument Council
432
375
INFORMATION
The Baksan Neutrino Observatory of the Nuclear Research Institute
of the Academy of Sciences of the USSR ? A. A. Pomanskii
433
376
INTERNATIONAL COOPERATION
Session of Soviet?American Commission on Cooperation on Power Engineering
? M. B. Agranovich
438
380
CONFERENCES, MEETINGS, SYMPOSIA
Soviet?Italian Symposium "Present-Day Problems of Power Engineering"
? S. Lutsev and Yu. Klimov
439
381
The International Conference on Vibration Caused by Coolant Flow
in Fast Reactors ? V. F. Sinyavskii
441
382
The International Conference "Beryllium-77" ? G. F. Tikhinskii
443
384
European Conference on Plasma Physics and Controlled Thermonuclear
Fusion ? V. D. Shafranov
445
385
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CONTENTS
(continued)
Engl./Russ.
Seventh International Vacuum Congress ? G. L. Saksaganskii
447
386
Third International Seminar-School on Applied Dosimetry ? V. K. Mironov
450
388
Tenth Meeting of Group of Senior IAEA Advisers on Atomic Power
Plant Safety ? 0. M. Kovalevich and L. V. Konstantinov
451
389
SCIENTIFIC ? TE CHNICAL RELATIONS
Work on Channel-Type Reactors in Italy ? V. S. Romanenko
453
390
New Books from Atomizdat (First Quarter of 1978)
454
391
The Russian press date (podpisano k pechati) of this issue was 3/23/1978.
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
INTRODUCTION OF ATOMIC POWER STATIONS WITH
THE VVER-440 REACTOR
V. A. Voznesenskii UDC 621.039.566
At present, a number of the atomic power stations (APS) operational in COMECON member-countries
include units based on VVER (water-cooled?water-moderated) reactors of thermal power 1375 MW that yield
a power of 440 MW(electrical) at the design pressure (0.035 kgf/cm2) in the turbine condensers. These are
the third and fourth units of the Kolsk APS, the first and second units of the Kolsk APS, the Nord APS in the
German Democratic Republic, and the Kozlodui APS in Bulgaria.
In the late 1970s and early 1980s further APS with the VVER-440 reactor are to be built, bringing the
total number of units to more than twenty.
GENERAL INFORMATION ON ATOMIC POWER STATIONS
WITH THE VVER-440 REACTOR
The main design parameters of APS with the VVER-440 reactor, the parameters of the reactor and the
active region (AR), are given below [1-3].
Thermal power of reactor, MW
1375
Electrical power of unit (gross) with 0.035 kgf/cm2
pressure in turbine condensers, MW
440
Electrical-energy consumption for internal requirements
of APS for two-unit operation, %
7.15
Number of turbogenerators per block
2
Pressure in first loop at reactor outlet, kgf/cm2
125
Coolant flow rate in first loop, m3/h
39,000
Coolant temperature, ?C:
at reactor inlet
270
at reactor outlet
301
Pressure drop in first loop, kgf/cm2
5.5
Steam flow rate in steam generators, tons/h
2710
Steam pressure, kgf/cm2:
in steam generators
47
in steam collector
45
before turbines
44
Internal diameter of reactor body, mm
3560
Number of working modules and control and safety rods
(CSR) modules in AR
349,
Number of CSR modules
73; 37
Distance between centers of modules, mm
147
Module size (outer measurement), mm
143-144
Module wall thickness, mm
1.5; 2.1
Module wall material
Alloy (Zr +2.5% Nb)
Number of fuel elements in module
120, 126
Fuel-element diameter, mm
9.1
Thickness of fuel-element cladding, mm
0.65
Material of fuel-element cladding
Zr + 1% Nb
AR loading (in terms of metallic uranium), tons
41-42
Effective AR diameter and height, cm
312; 245
Mean bulk power of AR, kW/liter
86
Mean energy yield, kW/kg U
33.0-33.5
Fraction of fuel discharged on reloading
1/3
Design burnup depth in steady reloading conditions with
3.5% enrichment of fresh fuel, MW-day/ton U
28,600
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 299-305, April, 1978. Original article submitted
February 28, 1977.
0038-531X/ 78/4404-0343 $07.50 ?1978 Plenum Publishing Corporation 343
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The APS presently in operation are designed to work in baseload conditions and use two types of VVER-
440 differing in the basic number of control and safety rods (CSR) modules containing boron?steel absorber
in the upper part and nuclear fuel (UO2) in the lower part. The difference arose when in the course of pre-
paring the reactor bodies for the third and fourth units of the Novovoronezh APS it was decided to use boron
regulation, which allowed the number of CSR modules to be reduced in all subsequent units from 73 to 37,
without changing the interval between fuel reloadings (1 year).
Atomic power stations with the VVER-440 reactor characteristically have a two-unit structure in which
the turbine and reactor chambers are common to the two units, as are the systems for circulational and techni-
cal water, chemical water preparation, pure condensate, etc. The first APS loop, containing six circulational
subloops, consists of a hermetic chamber, designed for an excess pressure of 1 kgf/cm2, with automatic re-
lease of steam from the chamber to the atmosphere when the excess pressure reaches 0.8 kgf/cm2. In each
subloop there are two main stop valves (MSV), a sealed glandless main circulation pump (MCP), and a hori-
zontal steam generator. Access to the MSV and MCP chambers is possible in the course of reactor operation,
which permits maintenance of the equipment without reactor shutdown and ensures efficient use of the units.
In the reactor body (its size allows it to be transported as desired), an active region of 349 hexagonal working
modules and CSR modules is built. In operation at power, practically all the CSR modules are placed in an
extreme upper position, which ensures uniform filling of the active region by fuel and prevents additional
distortion of the energy-liberation field due to the presence of solid adsorbent or aqueous cavities. At the
inlet to the modules an additional hydraulic drag is provided (by disks for the working modules and by sets
of holes in the damper tubes for the CSR modules); this decreases the discrepancy in flow rate over the mod-
ules and provides the required interval before heat-transfer crisis in emergency situations with loss of flow
rate. The module walls and the cladding of the cylindrical fuel cells are of zirconium?niobium alloy; the
reactor body and the volume compensator are of high-strength thermostable steel without a noncorrosive sur-
face. To prevent corrosion of the reactor body and the volume compensator for the first loop of the APS,
a special ammonium?potassium water system has been developed. The supply to the MCP is provided from
several independent sources: internal-supply generators (ISG) and the main generators on the same axis as
the turbines.
The reactor-power regulator maintains a constant pressure in the steam collector (45 kgf/cm2), while
a special regulator ensures discharge of the turbine when the pressure in the steam collector decreases to
44 kgf/ cm2.
Atomic Power Station Characteristics in Startup and Running-in
Period and in Use
Thermal and Electrical Power of Units. The thermal power of the reactor is determined on the basis
of the heat balance in the first and second loops of the APS. Only using the correct prescribed instruments
may five independent balances be formulated. The appropriate tests are preceded by careful checking of the
measuring equipment. The discrepancy between the thermal-power values in different balances achieved in
practice is not more than ? 2%. (The margin for inaccuracy of the thermal-power value in the design calcu-
lations is 4%.) To obtain a measured value of the thermal power for the reactor, the data of the different
balances are averaged and the maximum value is taken for the most accurate measurements of the feedwater
balance in the steam generators. Special measurement programs are prescribed for the determination of the
turbine and electrical parameters in the course of testing. The deviation of the test conditions from the design
conditions is taken into account by the appropriate correction in the calculations.
As a result of measurements in different units soon after startup [4] it was established that when K-220-
44 turbines with nozzle regulation of the power are used the electrical power of the unit (gross) corresponding
to a thermal power of 1375 MW is about 445 MW. The margin in the transmission of the turbogenerators is
10% but its realization requires a corresponding increase in reactor power. The measured energy consump-
tion to meet the internal requirements of units with the VVER-440 reactor (except at the Novovoronezh APS)
was found to be 6.0-6.4%, which is significantly below the design value.
Hydraulic Characteristics of Reactor and First Loop. In the course of startup and use the hydraulic
characteristics of the first loop and reactor-are determined and on the basis of the correspondence between
these results and the design values it is possible to evaluate the prospects for reactor operation at the nomi-
nal thermal power and the safety of the unit. Relevant parameters are the coolant flow rate and pressure drop
in the first loop and the individual subloops; the coolant flow rate and pressure drop in the workirg modules
and the CSR modules; the coolant flow bypassing the AR modules. Direct measurement in use is possible only
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for the pressure drops in the reactor (AP reactor) and the MCP. The flow rate in the subloops of the first
loop is determined using the pressure characteristics (the dependence of the pressure drop at the pump on
the flow rate through the pump) obtained for each specific MCP on a factory test bed. The flow rate through
the reactor (G reactor) is determined initially as the sum of the flow rates over the subloops. Measurements
of the pressure drop in the reactor for different numbers of working subloops are used to construct the de-
pendenceA Pp = f(Gp), which is then usedto determine the flow rate. The pressure drop in the individual ele-
ments of the reactor (the active region, the working modules) is measured in one of the stages of the running-
in period, by leading out additional pressure-sampling tubes through the reactor roof. The hydraulic charac-
teristics of the VVER-440 reactor of the third unit at the Novovoronezh APS and others are given below.
Flow rate through reactor, m3/h
48,000, 43,500-46,000
Pressure drop, kgf/cm2
in first loop
4.1, 4.5-4.8
in reactor
2.2, 3.1-3.4
in AR
1.4, 2.3-2.6
in working module
0.9, 0.8-0.85
These differences are due to the individual properties of the equipment used, in particular, the pumps. For all
the units, the coolant flow rate significantly exceeds the design value; this is because the value of the resistance
of the first loop assumed in the design calculations was too high. As a result, there are good prospects for
an increase in the thermal power of the VVER-440 but at the same time additional investigations are necessary
to determine the performance of the equipment in the first loop, including the reactor and the active region,
in conditions of enhanced flow rate.
At reactor startup great care is taken to establish the correct value of the flow rate through the CSR
modules. If this flow rate is not to limit the thermal power of the reactor, it must be close to the flow rate
through the working modules. At the same time, increase in the flow rate through the CSR module (>140 ms/h)
is not permitted by the design, since it may lead to floating of the fuel component on separation of the pump
and, as shown by testbed trials, to increased vibration of the structural elements of the module. Measure-
ments on different units, using special attachments recording the weight loss of the CSR module under the
action of the flow, show that the real flow rate does not always correspond with sufficient accuracy to the de-
sired value. As a result, in some units additional correction of the flow rate through the CSR module is re-
quired. Steps are being taken to refine the calculations and to establish narrower tolerances in the prepara-
tion of structural components affecting the hydraulic drag at the inlet to the CSR module.
The coolant flow bypassing the AR modules (calculated value 5%) is determined from the balance equa-
tion between the thermal power of the reactor found from the flow rate and heating of the coolant in the re-
actor and the total thermal power of the working modules and the CSR modules (determinedby a special method
based on temperature measurements at the outlet from the working modules) and is 4%.
Physical and Thermophysical Characteristics of the Active Region. The main requirements in developing
the active region of the VVER-440 reactor include the following:
an operating period of 6000-7000 eff. h between reloadings; residence of fuel modules in reactor 3-4
years;
negative or near-zero temperature coefficient and reactivity and negative total power coefficient of
reactivity;
nonuniformity of energy liberation no more than 1.35 over the AR modules, and no more than 1.5 between
fuel elements;
sufficient CSR-module efficiency to compensate for rapidly appearing reactivity effects (power effects
and some temperature effects).
Table 1 gives the calculated physical characteristics of the primary AR of reactors at different APS
developed to meet these requirements; for comparison, the results of experimental measurements are also
given. As follows from Table 1, the primary AR at present in operation are of five different types, differing
in the mean initial enrichment and the use of consumable adsorbents. To a certain extent, this diversity re-
flects the gradual refinement of design concepts. Following measurements of the reactivity and the nonuni-
formity of energy liberation, the use of consumable absorbent in the active regions of VVER-440 has been
completely discontinued. It has been established that a working period of 7000 eff. h between reloadings is
achieved with 2.3% mean enrichment of the first charge and 3.3% enrichment of the feed fuel (instead of the
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TABLE 1. Basic Physical AR Characteristics of VVER-440 at Beginning of Service
Parameter
Novovoronezh
Kolsk and Nord
Kolsk
Nord, second
unit; Kolodui,
first and second
units
third unit
fourth unit
first unit
second unit
Composition of primary
AR (enrichment and
number of modules with
fuel)
Presence of consumable
absorbent
Mean enrichment, ?Jo
Total margin of reactiv-
ity, ilk/R.
Total eff. of CSR.
module at t= 20?C,
6,k/k
Temp. coeff. of reactiv-
ity at 260*C and zero
power, ,6k/k/eC
Power coeff. of reactiv-
ity in working state,
AkikPio
Critical concn. of boric
acid at 100?C for com-
pletely raised CSR
modules, g 11003/kg
H.,0
1%; 49
1,5%; 66
2,0%; 114
3,3%; 120
108 modules
with 3.3?
enrichment
each contain
6 BCA ?
2,2
0,147
0,18
?1,4?10-41.
1,6%; 138
2,4%; 127
3,6%; 84
?
2,37
0,177
0,15
?4?10-5
1,6%; 114
2,4%; 133
3,6%; 102
108 nodules with
2.470 enrichment
and 102 with
3.610 enrichment
contain 0.07?70
natural boron in
walls
2,5
0,168
0,095
?2.10-5
1,6%; 162
2,4%; 103
3,6%; 34
?
2,3
0,173
0,088
?5.10-5
1,6%; 114
2,4%; 133
3,6%; 102
?
2,5
0,188
0,088
?2,5.10-5
?1,8.10-4
?2,2.10-4
5,2/4,8
+3.10-5
?1,940-4
7,6/6,9
?1,5.10-5
?1,8.10-4
7,8/6,4
?3-10-5
?2.10-4
6,8/6,2
+1 ,4 ? 10-5
?1,85.10-4
8,8/8,0
*BCA ?Blocked consumable absorbent.
t The numerator gives the calculated value and the denominator the experimental value.
design values of 2.5 and 3.5%, respectively). The disagreement between the calculated and experimental
values of the physical characteristics (burnout depth, the efficiency of boric acid, etc.) indicates the need for
improvement in the methods of calculation currently in use.
Atomic Power Station Operation in the Case of Accident and Transient Conditions. The operating pro-
gram for the running in of VVER-440 power reactors involves complex checking of the APS performance in
the event of accident or transient conditions. Special tests are carried out to establish the conformity of the
operation of the regulation, blocking, and safety systems with the design requirements, and to investigate the
dynamics of APS-parameter variation under different perturbations and at different power levels. The most
important of these include tests of total APS shutdown and the investigation of module response to variation
and reduction in the electrical load and to MCP failure.
Complete APS shutdown (for safety reasons the tests are carried out with the reactor at 17=20% thermal
power) involves the combined operation of equipment and systems ensuring safe stoppage and adequate cooling
of the APS (even with sodium leakage in the first loop) in the event of disconnection from the energy system
and switching off (stop-valve closure) of the APS turbogenerators. The tests check APS shutdown by the
emergency-protection systems; the duration of MCP operation On the "rundown?, energy of the main generators
and the ISG; continuous supply of the most important electrical-energy requirements (initially from accumu-
lator batteries and then from diesel generators); connection to the diesel generators (after their startup) in
turn (in order of importance) of those electrical units that can tolerate a brief (up to 3 min) interruption of
supply; and the establishment of natural circulation in the first loop and shutdown cooling.
At startup, as a rule, one test is sufficient to demonstrate the satisfactory conformity of APS perfor-
mance in emergency conditions with the design specifications. It is found that the MCP operates for not less
than 180 sec (design time ? 100 sec) on the rundown energy of the ISG and the main generator; the diesel start-
up time is 70-90 sec; the length of connection of electrical units to the diesels is about 70 sec: the deviation
of the potential in the electrical supply system of the APS is not more than la. In the startup of APS with the
VVER-440 reactor, successful completion of the tests on total shutdown is a necessary preliminary to in-
crease in the reactor power (> 17-20%).
Tests of the response to reduction and variation in the electrical load are carried out at APS startup to
adjust the turbine control system and the main regulators of the unit and to determine their static and dynamic
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characteristics, to confirm the possibility of successful (while maintaining the APS at the power level appro-
priate to its internal requirements) reduction in electrical load, to investigate the dynamics of parameter
variation in the operation of the APS control systems, and to confirm the guaranteed indices with respect to
the rate of change of the load of the units.
Experience shows that after the necessary adjustment for any load reduction, up to a complete reduction
from 100% to the level of internal requirements, the fluctuation of the APS parameters does not trigger the
emergency protection systems of the turbine and reactor, or lead to the opening of the steam-generator safety
valves. For example, on complete reduction in load the maximum speed does not exceed 3200-3240 rpm and
after 20-30 sec the turbine rotation stabilizes. Rise in pressure in the steam collector for 5-8 sec triggers
the reduction valves, which release steam from the turbine condensers, and the maximum pressure does not
exceed 52 kgf/cm2. The brief increase in the first loop is 1.5-2.0 kgf/cm2. Trial loadings of the turbogenera-
tors at the guaranteed rates (2 and 5 MW/min from the cold and hot states, respectively) show that these rates
do not lead to any deviations from the required indices of the turbine heating.
The design allows for the disconnection of up to two MCPS (e.g., on short-circuiting in the supply section)
without the operation of the reactor emergency systems. In these circumstances the reactor power regulator
reduces the neutron flux in the active region by 50%. At the same time, the reduction in pressure in the steam
collector is accompanied by automatic reduction in turbine load. If, after stabilization of the parameters, the
thermal power of the reactor does not correspond to the number of MCP remaining in operation, the operator
makes an additional correction to the reactor power level. Tests of APS startup with one or two MCP dis-
connected have been carried out at 3-4 different power levels, including the nominal power. The control sys-
tems of the units successfully deal with transient processes when MCP are disconnected. The deviation of
the APS parameters does not trigger the emergency and blocking systems. Stabilization of the conditions at
the new power level takes f-=-: 300 sec.
Radiation Equipment
The state of the radiation equipment is determined continuously using specified measurement and moni-
toring systems. In addition, special programs of measurement must be carried out at APS startup and peri-
odically in the course of APS operation for the detailed verification of the conformity of the APS radiation
equipment with the design data. It is necessary to monitor the neutron and y-ray dose rate; the gas and aero-
sol activity in the APS structure; the release of radioactive gases, aerosols, iodine, and strontium to the
atmosphere; the activity of water in the first loop, the steam generator, the reloading tanks and the spent-fuel
stores, the tanks of the active-water retreatment system, etc.; the activity of the steam arriving at the tur-
bine; the gas and aerosol activity of the air; the radioactivity of water and soil in the area around the APS;
and the sealing of the heat-liberating modules on reloading.
Measurements on different units show that the dose rates from external fluxes of ionizing radiation in
APS structures established by the operating norms (1.4, 2.8, and 28 mrem/h for attended, semiattended, and
unattended chambers, respectively) are not exceeded on the average. Isolated deviations (by a factor of 5-10)
noted in semiattended chambers (at points of penetration through the walls and at the overlapping of the bio-
logical protection) must be easily localized, and additional measures are taken to this end.
The release of radioactivity to the atmosphere in normal operation is 5-100 (radioactive gases); 10-2-
10-4 (aerosols); 10-3-10-4 (1.31I); 10-4-10-8 Ci/day (88Sr +8?Sr) with norms of 3500, 0.5, 0.1, and 10-3 Ci/day,
respectively.
The activity of the coolant in the first loop is determined both using continuous-monitoring equipment
and by periodic analysis of samples. Under normal conditions, the analysis of the specific activity of dry
residues and iodine isotopes is carried out once a day and once every 2 days, respectively; for the total isotope
state the rate is once a month.
The reactor operation is regarded as satisfactory up to a total specific activity of the first-loop coolant
of 0.1 Ci/liter at the moment of sampling for 100% thermal power of the reactor (the specific activity of non-
gaseous fission products 2 h after sampling is 10-2 Ci/liter). The actual activity in operating units is con-
siderably below these limits. For example, in the first half of 1976 the figure for nongaseous fission products
(mainly iodine isotopes) was 10-4-2 .10-3 Ci/liter and for most units this corresponds to the end of the oper-
ating period. The corrosion products of the first-loop materials make an insignificant contribution (10-8-10-7
Ci/liter) to the total specific activity of the coolant.
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Analysis of the specific activity of the fission products by a special method allows the state of sealing
of the fuel elements to be evaluated. The specific modules with unsealed fuel elements are determined at the
time of reloading. To monitor the sealing of fuel-element shells on reloading, individual modules are placed
in a sealed can with subsequent holding in air (the method used at the Voronezh APS) or water and analysis
of samples.
On Sept. 1, 1976, 12 planned reloadings were carried out at reactors (three each in the third and fourth
units of the Novovoronezh APS, two in the first unit of the Kolsk APS, and one each in the other units). Practi-
cally at each reloading the sealing of the modules remaining in the reactor for the next term of operation was
checked 2/3 of the total number of modules with fuel). Between each reloading there are improvements in
the methods of detecting unsealed modules and developments in the quality standards.
According to the results of six reloadings in various units with a VVER-440 reactor in the summer and
autumn of 1968, one module on the average was removed from the reactor ahead of schedule.
No relation has been found between conditions of reactor use and the number of unsealed modules.
Work in Startup and Running-In Period
This work is carried out at the APS after the installation is complete and includes the following main
stages:
1) introduction into use of the electrical supply for the internal requirements of the unit and the chemical
water treatment;
2) washing and functional testing of the auxiliary APS systems;
3) hydraulic testing and circulational washing of first loop;
4) first inspection of first-loop equipment;
5) cold and hot running in of first-loop equipment;
6) second inspection of first-loop equipment;
7) loading of active region and physical startup of reactor;
8) operation of unit at 1-5% power as a preliminary to the introduction of the turbogenerators in circuit;
9) raising the unit to the design power, with successive operation at 17-20, 30-35, 75-80, 90, and 100%
power followed by 72-h continuous operation at the nominal power.
The mechanical purpose of the work at the stage of hydraulic testing and circulational washing is the
demonstration that the first loop is watertight and also washing of the loop after installation. Depending on the
conditions at each specific APS the sealing of the reactor at this stage is either by a temporary roof or by
the prescribed upper unit. The CSR drive is not fitted. The hydraulic drag of the missing active region is
simulated by a temporary throttling device. In the circulational washing the heat of the operating MCP raises
the coolant to 220-230?C, which facilitates the washing of the first-loop surface; the operation of the MCP and
the auxiliary systems of the reactor is checked, the specified technological operations are completed; and the
vibration and degree of expansion of the equipment and the turbine ducts are checked.
After the circulational washing the first loop is cooled, the reactor roof is removed, and the in-reactor
equipment is dismantled. The first inspection of the APS equipment and systems is then conducted; defects
observed in the hydraulic testing and circulational washing are eliminated; the state of the metal in the basic
equipment is monitored; the equipment and systems are prepared for hot and cold running in; and the specified
reactor pile is fitted with the CSR drive and the subcritical region. At the startup of the first units the region
was partially loaded with modules containing fuel for the hot running in. In conditions of imperfect adjustment
of the equipment, this led to difficulties in ensuring nuclear safety and the possibility of mechanical damage
of the regular modules.
The present practice at the time of running in is to load the region with stimulation modules that do
not contain fuel. One set of such modules is used successively in the startup of several different units. At
the stage of cold and hot running in, the electrical circuitry of the CSR system is adjusted and the CSR drive
is run in; the hydraulic characteristics of the reactor and the first loop are investigated; the stress?strain
dynamics of in-reactor instruments (for the principal units) is studied; and the blocking and safety systems
of the reactor are tested.
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The second inspection, following the cold and hot running in, must ensure that the equipment and sys-
tems of the power stations are in full readiness for the loading of the specified active region, physical startup,
and the buildup to full power. The main equipment is examined again and the state of the metal is monitored
by various methods. All defects appearing in the course of running in and the subsequent inspection are elim-
inated. The second inspection is concluded by the loading of the specified active region and the sealing of the
reactor. At stages 3-6, in parallel with the work on the first loop, the sealing of the hermetic chambers of
the reactor installations is checked and the ventilation and dosimetry systems are adjusted.
The beginning of physical startup concludes the multiple testing of the second-loop equipment, together
with the checking of the vibrational state of the turbogenerators and, if necessary, balancing and electrical
testing of the ISG and the main generators with a set of loads up to 20 MW. The source of the steam for this
work is either an energy train of temporarily installed steam boilers for the first units of an APS; for the
subsequent units, the units already operational are used.
The final check on the combined operation of all the systems in steady, transient, and emergency con-
ditions is made at physical startup and in the course of buildup to full power. The lengths of the main stages
of this work are as follows, days: hydraulic testing and circulational washing, 8-30; first inspection, 29-62;
cold and hot running in, 15-22; second inspection of equipment, 15-60; loading of active region and physical
startup, 15-34; total duration of buildup to design power (from the end of physical startup to the completion
of 72-h testing at 100% power), 75-211, including 6-85 for planned inspection.
Discrepancies in the length of the stages of this work for different APS may be due to a number of fac-
tors. For example, significantly more time was required for startup of the first units of each APS than for
the subsequent units, as a result of the broader test program, the larger number of defects discovered in the
equipment, the installation, and the design, and the lack of experience of the personnel involved. Some redis-
tribution of the work between the individual stages has been observed; different levels of APS reliability have
been noted by maintenance personnel; and different forms of operational organization of the work have been
developed.
LITERATURE CITED
1. V. P. Denisov et al., Paper at the Soviet?French Seminar on Steam Generators, Structural Materials,
and Production Technology of First-Loop Components of Water?Water Reactors [in Russian], Saclay
(Sept. 17-23, 1975).
2, V. P. Denisov et al., Fourth Geneva Conference, USSR Paper No. 639 [in Russian] (1971).
3. K. Gorski and M. Ivanov, Kernenergie, 7, 200 (1974).
4. G. M. Konovalov et al., Teploenergetika, No. 9, 52 (1975).
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EVALUATION OF PLANT-LOCATION STRATEGIES
FOR THE NUCLEAR-POWER FUEL CYCLE
B. B. Baturov and V. M. Urezchenko UDC 621.039.003
The development of nuclear power (NP) necessitates considerable increase in capacity of the components
of the fuel cycle. A wide range of predictive studies of different aspects of this problem have been under-
taken, with a view to evolving the optimal NP development strategy [1-5]. A question of considerable interest
concerns the options for the location and development of plants for fuel-element preparation and for the chemi-
cal reprocessing of spent fuel.
Various strategies are possible for the location of fuel-reprocessing plants. The first of these envisages
the construction of small plants close to a single atomic power station (APS) or a number of adjacent APS
(Fig. la). In the second, the development of the fuel-reprocessing industry occurs through the construction
of centralized large-capacity plants that serve many APS; these plants always have an unused, reserve capacity
in relation to demand (Fig. lb). The third strategy again involves centralized reprocessing plants but in this
case their capacity is calculated on the basis of the demand, without providing any unused reserve capacity
(Fig. lc).
An analysis using economic estimates is necessary if the optimal strategy is to be chosen for the loca-
tion of the components of the fuel cycle (FC). The three plant-location strategies differ in their capital and
current expenditures. The third strategy involves storage of the fuel, since the fuel is to be used in the future
and awaits subsequent use or subsequent reprocessing. This storage leads to the freezing of considerable
capital.
In [6] an economic functional was proposed for the analysis of the different NP development strategies,
taking into account the possible factors; the functional was constructed on the reduced-expenditure principle
but also taking into account the long-term working capital
F= K-1?T +Df ?Dst
(1)
T r
iI
where K is the total capital expenditure; T is the total current expenditure; Df and Dst are the long-term
working capital due to the prolonged residence of fuel in the cycle and the steplike growth in the FC capacity,
respectively; Nt is the estimated APS power introduced in year t; 0 is the number of hours of operation per
year; got is the use factor of the established power; Tpr is the time depth of the prediction; u is the norm in
taking into account the different time scales of the expenditures.
K and T are determined as the total values at all the FC plants over the whole period of prediction, taking
into account the different time scales of the expenditures. The long-term working capital is formed as a result
of the annual deduction of frozen capital and represents the sum over all the FC plants throughout the whole
period of prediction of these deductions, taking into account the different time scales; the deduction is only
taken from the moment of capital introduction until its recovery.
The various distribution strategies for the FC plants differ in the level of capacity of the plants intro-
duced. The values of the capital expenditure and costs of reprocessing at the plants depends on their capaci-
ties.
Analysis of the available data for the existing and projected FC plants shows that, for capital expenditure
in the range of capacity from 0.1 to a few tons per day, the following relation may be used [6]
K = K0 (G/G0), (2)
where K and Ko are the total capital expenditures in building plants of capacity G and Go, respectively; a < 1
is the index corresponding to the different FC plants.
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 306-310, April, 1978. Original article submitted
October 4, 1976; revision submitted December 14, 1977.
350 0038-531X/78/4404-0350 507.50 ?1978 Plenum Publishing Corporation
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10 20 t, yr
Fig. 1. Demand for fuel and strategies
for demand satisfaction for different ap-
proaches to increasing the total capacity
of fuel-reprocessing plants.
44
41 0,2 43
10 tons/yr
Fig. 2
41 42
G, 103 tons/yr
Fig. 3
43
Fig, 2. Dependence of specific capital expenditure on the capacity of plants for the
chemical reprocessing (1) and preparation (2) of fuel elements.
Fig. 3. Dependence of fuel-preparation costs at plants for fuel-element production on
the nominal (design) capacity GN and the actual capacity GA with a =0.4; 6const = 0.33.
In Fig. 2 the dependence of the specific capital expenditure on the capacity of plants for the preparation
and chemical reprocessing of fast-reactor fuel elements based on oxide fuels is shown.
The total expenditure (E) in reprocessing for a plant of capacity G may be written as the sum of constant
(Eemiat) and variable (Evan components
E =Econst_l_Evar
The constant component, determined mainly by the capital expenditure, also satisfies Eq. (2)
E const=EoconstG/Gx.
(3)
(4)
The variable component is determined by the expenditure of energy and materials, i.e., is directly pro-
portional to the actual plant capacity _
Evar =E_var G
Go ?
The values of EF?11st and Evar may be written as fractions of the total expenditure (Eo)
const A
E0 ?E0
06Var
Err ,=E
(5)
(6)
where 6 const and Ovar are the relative fractions of the constant and variable components of the total expendi-
ture.
Substituting Eqs. (4)-(6) in Eq. (3) and writing the total expenditure as the product of the reprocessing
costs and the plant capacity, an expression that takes into account the dependence of the reprocessing costs
on the plant capacity for operation with the total load is obtained,
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=c0 [6const(--g(7-)a + 6var (G/Go)] (7)
where c and co are the reprocessing costs* at plants of capacity G and Go, respectively.
In the operation of plants with an incomplete load, the constant expenditure corresponds to smaller pro-
duction and the specific reprocessing costs rise. Suppose that a plant of nominal capacity G operates at a
capacity g 0.8 MeV
through a layer of water 80 cm thick calculated in the one-group approximation is 103 times smaller than
the transmission calculated in the five-group approximation. In such cases it is particularly important to take
account of the correlation of cross sections of the same elements in separate layers of the shield.
LITERATURE CITED
1. L. P. Abagyan et al., USSR paper No. P/357, Third Geneva Conference (1964).
2. V. G. Ithokhlov et al., in: Nuclear Constants, No. 8, Part 4 [in Russian], TsNllatominform (1972), p. 154.
3. V. F. Khokhlov et al., ibid., Part 2, p. 119.
4. V. V. Filippov et al., Anglo?Soviet Seminar on Nuclear Constants for Reactor Calculations [in Russian],
Paper ASS-68/103, Dubna, June 18-22, 1968.
5. V. F. Ithokhlov and V. D. Tkachev, in: Abstracts of Papers on an All-Union Scientific Conference on
Shielding against Ionizing Radiation from Nuclear Engineering Installations [in Russian], MIR, Moscow
(1974), p. 7.
6. A. A. Dorofeev et al., Solution of the Transport Equation for a Slab (program 130Z-5), Part 1 [in Russian],
Inst. Prikl. Mat., Akad. Nauk SSSR (1972).
7. Yu. A. Kazanskii, Physics of Reactor Shielding, Israel Program for Scientific Translations, Jerusalem
(1969).
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THERMODYNAMIC STABILITY OF URANIUM MONONITRIDE
S. A. Balankin, L. P. Loshmanov, UDC 621.039.544.57
D. M. Skorov, and V. S. Sokolov
Thermodynamic stability may restrict the use of uranium mononitride as a nuclear fuel in high-tempera-
ture reactors, as a result of the change in the composition of the UN and the appearance of free uranium at
high temperatures. A change in the composition of the UN is indicated by the reduction in the rate of vaporiza-
tion when the material is held isothermally at temperatures of 1878 and 1983?K [1]. There are also reports
of observed changes in the partial pressures of nitrogen and uranium in the vaporization of UN [2, 3]; however,
the reasons for these changes are not discussed in detail. Data on the temperature at which free uranium
appears in the UN vary widely: 1773?K according to [4], 1973?K according to [5], and 2073?K according to [1].
To investigate this phenomenon, we measured the rate of vaporization in the 1758-2168?K temperature
range. The temperature at which the free uranium appeared was determined by x-ray phase analysis of the
specimens after vaporization experiments. The original uranium nitride had the following chemical composi-
tion (in % by mass): U, 94.3; N, 5.15; C (total), 0.1; C (free), 0.018; 0, 0.25; this corresponds to the formula
composition U(N0.NC0.0200.04)0.99 ? 0.0i. The x-ray analysis of the original specimens did not ipdicate the
presence of any phases other than uranium mononitride with a lattice period of 4.890 ? 0.001 A. The rate of
vaporization was investigated in a vacuum of 1 '10-5 mm Hg by the Langmuir method in the variant using con-
tinuous weighing in a high-temperature apparatus with automatic recording of the measurement results [6].
The measurement error in the vaporization rate was 15%. A specimen having the shape of a plate measuring
7 x 7x 1 mm, weighed on a quartz microbalance with a tungsten filament, after establishing the necessary
temperature, was left in the heating zone, and the changes in the mass of the specimen were then automatically
recorded. It follows from Fig. 1 that for isothermal holding, the rate of vaporization decreases, reaching a
constant time-independent value. The results of x-ray phase analysis indicate the presence of free uranium
in the uranium mononitride specimens held at 1970?K and higher, which is in good agreement with the data
of [5].
In order to explain the results on the basis of statistical-thermodynamic theory [7], which was success-
fully used for UC [8], we calculated the variation of the partial pressures of uranium and nitrogen as functions
of the temperature and the composition of the uranium mononitride. According to [7], the expressions for the
partial pressures of the components of the phase Ai_xBx have the form
In PA PA?(F1 -F2RT ln 2 a)i2RT ? ? In (1)
in = ln F13 I2RT In i-;;, (2)
where Pi and Pt are the pressure values above the pure components A and B; FIA and Ft are the free energies
of formation of the structural vacancies of the components A and B; a is the concentration of thermal vacancies
in the metallic or nonmetallic sublattices.
Knowing the partial pressures of the components above a compound of Imown composition and the pres-
sures above the pure components, we can determine from Eqs. (1) and (2) the values of 43-, F-IA- + 2RT1n2a and
then obtain expressions for the partial pressures in the region of homogeneity of the compound.
Substituting the experimentally determined partial pressures of uranium and nitrogen over UN0.99 into
Eqs. (1) and (2), using the most reliable values of the pressure above pure uranium [9], we can determine the
desired values:
Fu, 2RT In 2a= 60400-80.07', I/mole ;
FN+= 583000-99.47' J/mole,
(3)
(4)
Translated from Atoranaya Energiya, Vol. 44, No. 4, pp. 327-329, April, 1978. Original article submitted
February 17, 1977.
374 0038-531X/ 78/ 4404- 0374 $07.50 ? 1978 Plenum Publishing Corporation
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10-
10"
7
t?10;
sec
Fig. 1. Rate of vaporization as a func-
tion of holding time at various tempera-
tures, ?K; 1) 1758; 2) 1873; 3) 1938; 4)
1970; 5) 2020; 6) 2073; 7) 2133; 8) 2168.
.r 10-5
0,48 449
Fig. 2. Variation with composition
Ui_xNx at 1970?K: a) partial pressures
of nitrogen (0) and uranium (?, A) [2, 81;
b) rate of vaporization of original (0) and
congruent (8) compositions.
A
and find the variation with temperature of the partial pressures of uranium and nitrogen above uranium mono-
nitride specimens of various compositions:
ig pu = 26850 1 ? 2x (5)
f2.9?+1g N/m2;
10.2-6? +21g 2x N /m2. (6)
Making use of the vaporization congruence condition and expressions (5) and (6), we can represent the
temperature variation of the compositions of congruent vaporization (xk) of the UN in the form
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Xk
A =1.03-4.22.10-5T. (7)
- Xh
Figure 2 shows the calculated variations of the partial pressures of uranium and nitrogen and also of
the total rate of vaporization as functions of the composition Ui_xNx at 1970?K. At compositions close_to
stoichiometric the partial pressure of nitrogen is considerably higher than the partial pressure of uranium
(see Fig. 2), which must lead to nitrogen depletion of the uranium mononitride, as shown by (7). The partial
pressure of the nitrogen and the rate of vaporization decrease, while the partial pressure of uranium increases
until congruent vaporization is achieved. The foregoing explains the experimentally observed changes [1-3]
in the rate of vaporization and the partial pressures of uranium and nitrogen when UN vaporizes.
In accordance with Eq. (7), the higher the temperature the closer the composition of congruent vaporiza-
tion will be to the lower limit of the region of homogeneity of the UN. At a certain temperature (1970?K) the
composition of the congruent vaporization reaches the lower limit of the homogeneity region.
For comparison with the calculations, we show in Fig. 2 the published data on partial pressures of nitro-
gen and uranium, as well as the experimental results on the rate of vaporization. Since in [8] the UN speci-
mens, before the investigation, were subjected to prolonged annealing at the maximum experimental tempera-
ture, the composition of the specimens varied. Therefore we applied a correction obtained from [8] to the
composition which, according to Eq. (7), corresponds to the annealing temperature. Fig. 2b shows the experi-
mental data on the rate of vaporization of the original composition and the composition of congruent vaporiza-
tion of the UN. The data for the original composition corresponds to the rate of vaporization at the initial
instant of time at 1970?K (see Fig. 1). The final, time-independent value of the rate of vaporization relates
to the composition of the congruent vaporization, calculated from Eq. (7). The calculated, experimental, and
published data are in good agreement.
Thus, we have established that the experimentally observed decrease in the rate of vaporization in the
process of isothermal holding is due to nitrogen depletion of the uranium mononitride and also to the appear-
ance of free uranium as a second phase at 1970?K.
LITERATURE CITED
1. C. Alexander, J. Ogden, and W. Pardue, J. Nucl. Mater., 31 13 (1969).
2. K. Gingerich, J. Chem. Phys., 51 No. 10, 4433 (1969).
3. Y. Ikeda, M. Tamaki, and G. Matsumoto, J. Nucl. Mater., 59 No. 2, 103 (1976).
4. H. Inouye and J. Leitnaker, J. Am. Ceram. Soc., 51 No. 1, 6 (1968).
5. P. Evans and T. Davies, J. Nucl. Mater., 10, No. 1, 43 (1963).
6. D. M. Skorov, S. A. Balankin, and V. S. Sokolov, in: Physicochemical Analysis of Alloys of Uranium,
Thorium, and Zirconium [in Russian], Nauka, Moscow (1974), p. 164.
7. L. Kaufman and E. Clougherty, in: Metallurgy at High Pressures and High Temperatures, AIME, New
York (1964), p. 322.
8. R. A. Andrievskii et al., At. Energ., 26 No. 6, 494 (1969).
9. E. K. Storms, Refractory Carbides, Academic Press (1967).
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NEUTRON MULTIPLICATION IN URANIUM BOMBARDED
. ,
WITH 300-660-MeV PROTONS
R. G. Vasilikov, V. I. Goltdanskii,
B. A. Pimenov, Yu. N. Pokotilovskii,
and L. V. Chistyakov
UDC 621.039.54
Research on neutron multiplication in massive (quasi-infinite) blocks of heavy elements, such as Pb,
Bi, Th, and U, bombarded with particles accelerated to hundreds and thousands of mega-electron-volts is of
interest for the solution of various scientific and applied problems. For example, high-current beams of
accelerated protons, deuterons, and possibly helium nuclei, may offer a convenient method, frequently called
electronuclear, of producing free neutrons which may turn out to be a useful supplement to the self-sustaining
chain process of nuclear fission and controlled thermonuclear fusion for the large-scale production of neu-
trons in general, and for nuclear power engineering in particular. The idea of producing free neutrons by
using proton or deuteron accelerators was suggested in the late 1940s by N. N. Semenov in the USSR and in-
dependently by E. 0. Lawrence in the U. S., and was subsequently developed in the U. S. and Canada to the
level of technical designs of electronuclear devices [1, 2]. The possible role of such devices was discussed
in [2-9].
To aid the development of these plans, and also for other reasons, many calculations and measurements
of neutron yields from targets of various geometries and compositions were performed in several laboratories
[10-15]. In particular, in 1963-1969 the authors studied neutron multiplication in massive targets of uranium
metal bombarded with 300-, 400-, 500-, and 660-MeV protons at the synchrocyclotron of the Nuclear Problems
Laboratory at Dubna.
Method of Measurement. The absorption of protons in a uranium target leads to the production of fast
cascade and evaporation neutrons and also fission neutrons with energies ,-1-100 MeV which are scattered
by uranium nuclei and degraded to energies in the range where their radiative capture occurs:
238u (n, ,ozzau 239N p 239pu.
During slowing down, the neutrons are further multiplied as a result of uranium fission. By measuring the
(n, y) capture-density distribution over the volume of the target A(z, r, (p) and integrating this distribution,
normalized to one absorbed accelerated proton and one gram of target material, we obtain the total number
of captures (the 239Pu yield) per high-energy proton:
A (z, r, (p)dv,
where z is in the direction of the proton beam and p is the density of the uranium metal. A cylindrical co-
ordinate system (r, p, z) is used since the neutron-density distribution must be axisymmetric in a homogene-
ous target. Since the fast-neutron source is axisymmetric, the measured distributions do not depend on cp,
and therefore it is sufficient to measure them in any half-plane of the target passing through the axis of the
proton beam. Then the expression for the total yield takes the form
2ztp A' (z, r)dS.
The number of fissions is determined in a similar way. The (n, y) capture-density distribution was
measured by the yield of 239Np separated radiochemically from uranium samples irradiated at various points
in the target, and the uranium fission-density distribution was found by using miniature silicon surface-bar-
rier counters covered with a layer of uranium. The uranium samples in the radiochemical experiments and
the fissionable layers for the counters were made of the target material.
Primary Proton Beam. The experiments were performed with a 660-MeV extracted proton beam. For
experiments with 300-, 400-, and 500-MeV bombarding particles the primary protons were slowed down in
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 329-335, April, 1978. Original article submittild
April 6, 1977.
0038-531X/78/4404- 0377 07. 50 1978 Plenum Publishing Corporation 377
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378
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Fig. 1. Schematic diagram of target
arrangement in JINR synchrocyclo-
tron research room: 1) accelerator;
2) trajectory of extracted proton
beam; 3) polyethylene attenuator; 4)
magnetic lens; 5) bending magnet;
6) iron shielding wall with collima-
tors; 7) ionization chamber; 8) sup-
plementary shielding wall (60 cm of
concrete and 40 cm of iron); 9) lead
casing; 10) uranium.
Fig. 2. General view of a portion of
the uranium target in its lead shield
showing the location of charnels for
detectors and the opening for introduc-
ing the proton beam into the target.
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60
50
40
30 X
20
TO 30 40 50
Fig. 3
60 Z,cm
3
2
1
5
10
15 20
Fig. 4
25
30 r;cm
Fig. 3. Distribution of activity of various detectors irradiated in channel 2 of a natu-
ral uranium target: 0) 2391j; 0) Al; x) Cu; A) In; A) In in cadmium cover.
Fig. 4. Radial dependence of the activity of various detectors irradiated in a natural
uranium target at points corresponding to"the maximum of the longitudinal distribu-
tions: A) 23913; *) Cu; C) Al.
polyethylene attenuators placed in the beam before it entered the magnetic quadrupole lens. The required
thicknesses of the attenuators and the energy dispersion of the slowed-down protons were determined from
data in [16].
By using magnetic probes, a focusing quadrupole, and a bending magnet, the proton beam was brought
through a 2-cm steel collimator in a 4-m iron shielding wall onto the target locatedP-2, 5 m behind this wall.
The diamater of the proton beam at the target entrance was 4-5 cm (Fig. 1).
In the work with semiconductor fission-fragment counters the intensity of the proton beam at the target
entrance was measured with a helium-filled ionization chamber calibrated by the 27A1(p, 3pn)24Na reaction.
Its cross section was taken from [17]. In experiments on the measurement of the 239Pu yields when the uranium
detectors were irradiated for several hours, the total number of protons incident on the target during the time
of exposure was determined directly from the activity of the aluminum foil induced during this same time.
The absolute 24Na activity of the irradiated foil was measured with a spectrometer using a NaI(T1)
crystal. The error in determining the number of protons absorbed by the target was 7%.
Target. The targets were built up of rectangular bars of natural (2 x 4 x 8 cm) and depleted (8 x 8 x 16
cm) uranium. The total mass of each target was 3.5 tons, and its linear dimensions were 56 x 56 x 64 cm.
The background of high-energy scattered neutrons was reduced by surrounding the targets on all sides by a
10-cm-thick layer of lead. This lead casing also decreased the neutron leakage from the target somewhat.
The proton beam was introduced into the central part of the target through an opening 8 x 8 cm in cross
section and 16 cm deep. As a result the neutron source was, so to speak, displaced into the interior of the
target, and this decreased the neutron leakage through its front face.
The detectors and silicon counters could be moved along a system of channels 2 x 0.3 cm in cross sec-
tion and 60 cm long made in a diagonal plane of the target passing through the axis of the proton beam. The
channels were about 3 cm apart, parallel to the proton beam, and from 6 to 45 cm from it. A portion of the
target is shown in Fig. 2.
The background was measured by removing the part of the target in which the protons were slowed down,
so that the beam passed freely through the 8 X 8-cm channel in the target to a concrete shielding wall about
13-14 m away.
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25
20
10 20 30 40 50 zpm 0 10 20 30 40 50 Z, cm
Fig. 5
Fig. 6
Fig. 5. Distribution of (n, y) capture density (i.e., of 239Np nuclei) measured in channels 1,
3, 5, and 7 in a natural uranium target. The distribution is normalized to 1. g of natural
uranium and one primary proton. Curve a is the background in a channel.
Fig. 6. Distribution of 235U fission density measured in channels 1, 2, 4, 7, and 11 in a de-
pleted uranium target. The distribution is normalized to 1 g of 235U and one primary proton.
Detectors. The 238U(n, y) capture-density distribution in the target was measured with small uranium
samples of the same isotopic composition as the target. These samples were 1 x 1 x 0.1 cm in size and had
masses of 1.5-2 g. The samples were irradiated in the target channels for several hours and then allowed
to cool a day or two before the 433Np was separated from them radiochemically. The absolute activity of the
239Np was then measured with a proportional-flux counter every 2 or 3 days for 16-25 days. After the 239Np
had decayed there remained an activity with a half-life of about 70 days, which contributed from 1-20% de-
pending on the length of the irradiation of the uranium sample and the cooling time before the measurements
of the 239Np activity were begun. The chemical yield of neptunium was at least 99.5%.
In addition, in the initial phase of the research the spatial distribution of the various groups of neutrons
was studied by recording them with aluminum, copper, natural uranium, and indium detectors with and without
cadmium covers. Figures 3 and 4 show how the activities of such detectors as 24Na, 64Cu, 238U, and 116mIn
vary along a channel. In experiments with the depleted uranium target the number of time-consuming radio-
chemical operations was reduced by using the fact that the relative distributions measured with 239U and 84Cu
detectors are very nearly the same (cf. Figs. 3 and 4), and therefore in determining the total 239PU yield the
relative (n, y) capture-density distributions were established from the absolute yield of 239Np measured in
the first six target channels. Similar capture-density distributions were obtained directly in natural uranium
from the 239Np yield in the first 12 target channels.
The uranium fission-density distribution in the target was measured with miniature fission chambers ?
n-type silicon surface-barrier fission-fragment counters covered with aluminum foils with layers of uranium
deposited on them. In each series of experiments with natural or depleted uranium targets a set of 10 counters
was used. Five counters recorded fission fragments from a uranium layer of the same isotopic composition
as the target, and the other five "looked through" a layer of uranium of a different isotopic composition. Two
counters with uranium layers of different isotopic composition were located simultaneously at the same point
in each channel. For a known concentration of 235U and 239U nuclei in the detector layers and in the target, an
inspection of the two fission-density distributions obtained with a pair of counters calibrated in a standard
thermal-neutron flux permitted the determination not only of the sum of the 235U and 23911 fissions, but also
their partial contributions to this sum.
380
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1,5
/go
2,5
0
16 24 JZ 40 48 56
Fig. 7
70
60
50
20
?.48
30
20
10
0
ZOO
400
600
Ep,MeV
Fig. 8
Fig. 7. Fission-density distribution measured in channel 2 of a natural uranium
target at various energies of the primary protons: V) 300; 0) 400; 0) 500; >0 660
MeV.
Fig. 8. Dependence of total 239PU yield in a natural uranium target on the energy
of the bombarding protons: ---) [18]; xl [20]; 0) our results.
In the experiments with a uranium target irradiated at the synchrocyclotron the counting rate of a frag-
ment detector is
Ny =nape,
where II is the proton flux, a is the number of fissions in the counter layer per gram per absorbed proton, p
is the mass of the uranium layer, and e is the efficiency of counting fission fragments. The counting rate
of this same detector in a neutron flux with a Maxwellian spectrum at the normal temperature of the moderator
is given by the expression
NA ?
N qj A
L35 ? pc ?
2
The combination of these two expressions gives a value for the interesting quantity a which does not contain
the product pc:
= Vi NY NA (PTCrit35
CC
2 Np A n
Here T35 is the relative concentration of 2351j hi the counter layer, c9T is the neutron flux in the thermal column
of the reactor, o-T is the cross section for the fission of 235U by thermal neutrons, NA is Avogadro's number,
and A is the mass number of the fissioning nucleus.
The values of Np for all counters were measured in the thermal column of the F-1 reactor at the I. V.
Kurchatov Institute of Atomic Energy, and the isotopic composition of the fissionable enriched and depleted
uranium counter layers was checked with an alpha spectrometer. As a rule the thickness of the layers was
250-300 /A g/cm2 and the area was 0.5 cm2.
Results and Discussion. Figures 5 and 6 show typical distributions of 239Np yields and 235U fission densi-
ties obtained for 660-MeV protons. The distribution in natural uranium is similar to that in depleted uranium
and differs only slightly in ordinate. Such distributions were observed in almost all the 15 channels (in some
of them several times) under various operating conditions of the accelerator which significantly changed the
intensity of the proton beam, and thus the constants cited below are averages over the data of 10 separate
381
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TABLE 1. Yield of 239Pu and Number of
Fissions of Uranium Nuclei in Targets of
Natural and Depleted Uranium
Con-
stant
EP
300 .400 5" I 660
138
135
14,7+1,8
(12,2+1,4)
5,9+0,8
(4,4+0,6)
4,7+0,6
(3,9+0,5)
1,2+0,2
0,48+0,06)
22,1+2,4
(18,2+0,2)
8,9+1,1
(6,6+0,8)
7,0+0,8
(5,8+0,7)
1,9+0,2
0,72+0,09)
32,6+3,3
(27,0+2,7)
13,1+1,4
(9,7+1,1)
10,4+1,1
(8,7+1,0)
2,8+0,3
(1,06+0,12)
46+4
(38+4)
18,5+1,7
(13,7+1,2)
14,6+1,3
(12,2+1,1)
3,9+0,4
(1,5+0,1)
Note: Numbers in parentheses refer to de-
pleted uranium.
experiments. The 239Pu yield yield per 660-MeV proton, found by integrating the 239Np distributions over the
volume of the target, is 46 ? 4 in natural uranium and 38 ? 4 in depleted uranium. Extrapolation of the measured
distributions beyond the limits of the target shows that the neutron leakage from targets of the dimensions
used does not exceed 10-12%, but this leakage is not included in our values of the plutonium yields and the
number of fissions.
Integration of the fission-density distributions obtained for the same proton energy gives the following
values of the total number of uranium fissions n in the target and the numbers of 235U and 238U fissions:
in natural uranium n =18.5 ? 1.7; 77 35 = 3.9? 0.4; ri 38= 14.6 ? 1.3;
in depleted uranium n =13.7 ? 1.2; 7135=1.5 ? 0.1; n 38= 12.2 ? 1.1 fissions per proton.
These values do not take account of nuclear fissions in the part of the target where the bombarding pro-
tons are slowed down and a cascade of nuclear reactions is initiated by high-energy nucleons, i.e., in the
fast-neutron source. For 660-MeV primary protons the number of inelastic interactions in the cascade can
reach five to six [18], and taking 0.75-0.8 for the fissionability of uranium by nucleons with energies of hun-
dreds of mega-electron-volts [19], these lead to approximately three of four fissions in the source [18].
The dependence of the quantities cited above on'the energy of the bombarding protons was also established
in the experiments. To do this the distribution (Fig. 7) similar to that shown in Fig. 6 was observed in the
second and third target channels at proton energies of 300, 400, and 500 MeV by using counters. The ratio
of the areas under these curves to the area under the curve measured at 660 MeV is a measure of the change
in the neutron source strength which occurs as the energy of the primary protons is varied. It was assumed
that the neutron-source spectrum varies slowly with the energy of the bombarding particles in the region
where the detectors were located. The relative values 6 of the neutron-source strengths measured in this
way for Ep = 300, 400, 500, and 660 MeV were 0.33 ? 0.03, 0.48 ? 0.04, 0.71 ? 0.04, and 1, respectively.
Table 1 lists the values of the 239Pu yields and the fission yields for natural and depleted uranium targets
at proton energies of 300, 400, and 500 MeV, obtained by multiplying the corresponding values measured at
660 MeV by 6. The errors given take account of the errors at 660 MeV. The mean-square error of the values
of the 239Pu yields is ? 8% at Ep = 660 MeV, and increases to ? 12% at Ep= 300 MeV. The loss of statistical
accuracy at lower energies is due to the sharp decrease in the intensity of the proton beam which results from
its scattering in the attenuators.
The error in the measurements of the number of fissions is ? 9% at Ep= 660 MeV, and increases to ? 13%
at Ep = 300 MeV. The largest contributions to the total error come from errors in determining the proton flux,
or the total number of them, (? 7%) and in determining the thermal-neutron flux in the reactor for calibrating
the counters (? 3%). The statistical accuracy of the measurement of the fission-density distributions (captures)
reached ? 2% and ? 8% at E =660 and 300 MeV, respectively, and the error in determining the absolute number
of 239Np nuclei did not exceed ? 2%.
In addition, the decrease in neutron yields for 660-MeV protons was measured in several target channels
by replacing the uranium in the central part of the target, where the protons are slowed down, by a lead block
of the same size (8 x 8 x 48 cm). The ratio of neutron yields for lead?uranium and natural uranium targets
was 0.48? 0.2.
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Except for the results of [18, 201 the authors know of no calculated or experimental data on neutron
yields and the number of fissions for infinite (quasi-infinite) uranium targets bombarded with accelerated pro-
tons with energies in the interesting range 300-700 MeV. Figure 8 compares data from [18], the present work,
and [20] obtained at the Chicago synchrocyclotron for 340-MeV protons. The calculations in [18] were per-
formed for quasi-infinite uranium targets 120 cm in diameter and 90 cm thick; the results in [20] were ob-
tained in experiments with a depleted uranium target. To within ? 5% such a target (30x 30 x 20 cm) emits
approximately nine neutrons per absorbed proton into the manganese sulfate solution surrounding it. This
number represents the outside value of the yield and does not include neutrons absorbed in the target itself.
It is difficult to compare other experimental data [2, 11, 15] with our results since there are large dif-
ferences in target sizes. Our experiments used uranium cylinders 10-15 cm in diameter and 30-60 cm long.
Therefore it is proposed that a joint analysis of all the known results be performed later. In conclusion we
note that the measured numbers of fissions enable us to set up an energy balance in quasi-infinite uranium
targets, since the energy release in them is determined essentially by the fission energy of uranium nuclei.
LITERATURE CITED
1. LRL-102 (1954).
2. AECL-2600 (1966); AECL-2750 (1967).
3. A. Weinberg, in; Proceedings of the International Conference on Isochronous Cyclotrons, Gatlinburg
(1966).
4. AECL-2177 (1965).
5. A. P. Aleksandrov, At. Energ., 25, No. 5, 356 (1968).
6. W. Lewis, AECL-3190 (1968).
7. V. A. Kirillin and M. A. Styrikovich, Nauka Zhizn, No. 4, 12 (1970).
8. V. A. Davidenko, At. Energ., 29, No. 3, 158 (1970).
9. R. G. Vasilikov et al., At. Energ., 29, No. 3, 151 (1970).
10. D. West and E. Wood, Canad. J. Phys., 49 2061 (1971).
11. R. Fullwood et al., LA-4789 (1972).
12. L. Veeser et al., Nucl. Instrum. Methods, 117 509 (1974).
13. R. Madey and F. Waterman, Phys. Rev. C, 8, 2412 (1973).
14. V. S. Barashenkov, V. D. Toneev, and S. E. Chigrinov, At. Energ, 37 No. 6, 475 (1974).
15. V. S. Bychenkov et al., Preprint RIAN K-859 (1973).
16. V. V. Vasilevskii and Yu. D. Prokoshkin, At. Energ., 7, No. 3, 225 (1959).
17. J. Cumming, Ann. Rev. Nucl. Sci., 13, 261 (1963).
18. V. S. Barashenkov and V. D. Toneev, At. Energ., 35, No. 3, 163 (1973).
19. N. A. Perfilov, 0. V. Lozhicin, and V. M. Ostroumov, Nuclear Reactions Initiated by High-Energy Parti-
cles [in Russian], Izd. Akad. Nauk SSSR, Moscow-Leningrad (1962), p. 228.
20. W. Crandall and G. Millburn, J. Appl. Phys., 29 698 (1958).
383
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A TURBULENT PLASMA BLANKET
N. N. Vasil'ev, A. V. Nedospasov, UDC 533.9: 621.039.61
V. G. Petrov, and M. Z. Tokart
In future D?T tokamak power reactors the thermal fluxes from the plasma to the wall will be 0.4-1
MW/m2. With a plasma temperature of 10-20 keV at the axis of the reactor, a density n 1020 in-3, and a
small fraction of multiply charged impurity ions, radiation may play only a second-order role in the removal
of energy from the reactor. The required thermal fluxes may occur if turbulence develops in the plasma vol-
ume due, e.g., to the trapped particle instability which is characterized at high temperatures by large trans-
port coefficients [1]. The reactor walls would then be in contact with a hot plasma (T "=, 3 keV) and be bombarded
by particles with energies greatly in excess of the sputtering threshold of the wall material. Thus, power re-
actor designs include the use of divertors which attenuate the flux of particles and energy to the first wall by
two orders of magnitude.
Another means of protecting the first wall that has been discussed previously [2] is to artificially induce
turbulence in the plasma near the wall to ensure that the required thermal fluxes are transported at relatively
low plasma temperatures. Here we consider a model of a turbulent plasma blanket assuming that Bohm dif-
fusion, with D= 1/16(cT/eB) and thermal diffusivity xi= xe= 3D/2 is produced in some fashion in a layer
10 cm thick. It is shown that such a blanket can replace a divertor and remove helium and unburnt fuel from
the reactor to ensure a low impurity content in the plasma.
? Derivation of Equations. The model used here for the physical processes in the region near the wall is
as follows. Electrons and ions diffusing perpendicular to the magnetic field strike the wall where they re-
combine and are thermalized. Because of desorption from the wall a flux of neutral atoms with a temperature
TM =1 eV enters the plasma [3]. It is assumed that their concentration is low and their mutual collisions may
be neglected. The following basic physical processes take place: ionization and excitation of the atoms by
electron impact, and charge exchange of atoms with ions. Since the probabilities of charge exchange and ioni-
zation are comparable, a substantial fraction of the atoms return to the wall.
Part of the neutrals escape through apertures or windows in the walls and are absorbed, e.g., by cryo-
panels. Thus, it is possible to remove the helium that is formed along with unburnt fuel for regeneration in
a steady-state reactor. It seems that the area of these apertures must be small.
The thickness of the region with the neutrals is small compared to the radius of the vessel and the be-
havior of the neutral atoms may be described by the one-dimensional kinetic equation
afa
k--1= ? (kion+ k) nia ?kiina, (1)
where x is the distance from the wall; n and na are the plasma and atomic density; fi and fa are the velocity
distributions of the ions and neutral atoms; kion= (aion I ve I); kex = ( CreX I ye I ) = (creel va vi I) ; ?Ion is
the ionization cross section; aex is the excitation cross section; ace is the charge exchange cross section;
and, ( ) denotes averaging over a Maxwellian distribution. In the definitions of kica and kex it is assumed
that ve ?va; k is taken to be a constant equal to the average value for the region being considered herb.
The boundary conditions for Eq. (1) are the distribution function fm of the atoms desorbed from the wall
(x=0) and the absence of neutral atoms as x fm and fi are assumed to correspond to a single velocity in
the x direction and to Maxwellian distributions in the other directions; i.e.,
2
r 2T m) ? m
f. rm
V ( V, 1/ en. f r"-1- 1
mn 2nTmt 1 2T r f
2Tmlnm
2
2T f 2T1 mmu_
fi=7[6 (Vx-17 7,Ti)?6(vx+-1/ jT ?
iT)j
2nTt exP 1 - 2T f '
(2)
(3)
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 336-339, April, 1978. Original article submitted
March 30, 1977.
384 0038-531X/78/4404-0384807.50 01978 Plenum Publishing Corporation
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where m is the deuteron mass; T is the plasma temperature; t= 3/2 ?1/ ir is a coefficient chosen because
the average energy equals 3T/2; and Fm is the flux of neutral atoms from the wall.
Equation (1) can be transformed into the integral equation [4]
fa _ M exp (x') dx, f f
VX
0
Here, f_, the distribution function of the charge exchange neutrals moving toward the wall (vx 0), are given by
(4)
and
x?
kna (x') (x',v)exp{
vx [kion(x")-- )
n (x"
vx ? dx") dx' (5)
x?
f _xf kna(e) (x, v)exp{ f Ikion(x")+k] n (x") ?}
vx dx' . (6)
Jo vx
Integrating Eq. (4) with respect to the velocities, we obtain an integral equation for the density na and average
energy Ca of the atoms.
The plasma is treated in the hydrodynamic approximation and the magnetic field is directly parallel to
the wall surface. It is assumed that the collision frequency is large, the ion and electron temperatures are
equal, and the plasma diffusion is ambipolar.
The particle balance equation including ionization has the form
d (, dxn )
k ? 0 nn
? ? n -a?
dx dx .d
(7)
In the energy balance equation for the plasma we include the energy loss due to ionization and excitation of
atoms, the exchange of energy between ions and atoms due to charge exchange, and the passing of the energy
of the ionized atoms into the plasma:
dQ3
dx = r ?(Ik0? iexicex k (E.? T)? eakion]nna, (8)
where I and lex are the ionization and excitation energies of the atoms (13.6 and 11 eV, respectively); Q=q+
(3T +I)1' is the total thermal flux transported by the plasma; and, q = ( Xi+ Xe)n(dTicbc) is the thermal conduc-
tivity flux.
Boundary Conditions. We now describe the choice of boundary conditions for Eqs. (7) and (8). For
x-0 (x max {ni(v)). and the coefficients Xp are subject to determination from the integrated experiments (1).
.-I.. .. L
Writing the errors Aj and dk as ej=i).0, and 6:L=0)0 (Pi= max 6(;')I AO; 'o= max
'
A(,v);6= min 6h)
v=1 L; i=1 N ,
It=1, ..., M
we can find the sought solution ill and Xp by minimizing the functional
,cm, 1 i (ah. i? oh, i-l) (I j +1) Or 2 N
62 x--1 I Q
? 2 (/)
11=1 h j
1 3-1 AA +-Er .2? k fi ? 2 XplIp. j) //); ii= oto) ?1.
(o
If the solution ell, i =1, . . N obtained by minimizing functional (4) is to satisfy the system of measure-
ments (1) within the limits of exp:erimental error, the error A of the expansion is varied from the value A =A0
with a gradual increase. As soon as the solution begins to satisfy the system (1), the corresponding value of
A is taken to be the optimal and the matrix of errors for the sought solution is found by minimizing functional
?(4)
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(4). The matrix can be used to evaluate the error in various functionals from the sought spectrum, including
those characterizing the efficiency of radiation damage of materials. The paper gives the results of processing
of the data from actual experiments which testify to the efficacy of the proposed method. As A ?0 or
the method is in agreement with methods published earlier [3, 41.
LITERATURE CITED
1. D. J. Hughes, Pile Neutron Research, Addison-Wesley, Cambridge, Mass. (1953).
2. V. A. Daugavet, Zh. Vychisl. Mat. Mat. Fiz., 11 No. 2, 289 (1971).
3. G. Cola and A. Rota, Nucl. Sci. Eng., 23, 344 (1965).
4. V. A. Dulin, At. Energ., 9, No. 4, 318 (1960).
y-ADSORPTION ANALYSIS OF A SUBSTANCE WITH ALLOWANCE
FOR EFFECT OF HEAVY IMPURITIES
I. A. Vasil'ev, Ya. A. Musin, UDC 539.106
and P. I. Chalov
The modification of the 'y-absorption method of analysis presented in the paper enables the concentration
of an element or a group of elements in samples to be determined in the presence of impurities with higher
atomic numbers than those of the elements being determined. The 7-ray source is chosen with an energy
such that; 1) the lower energy (Et) lies between the values of the K-absorption edge of the heaviest element
determined and the lightest of the heavy impurity elements; and 2) the highest energy (E TM) lies beyond the
K-absorption edge of the heaviest impurity element.
The concentration of the sum of the sought elements is found from the simple relation
,
C = P --m)1111,
I ' I"
where I is the intensity of y-ray beam after passage through a layer of the sample of thickness x; 10 is the
initial intensity; and M and m are determined during calibration of the setup or by calculation from the formu-
las
M=x2 (11, PK);
n
m = x E ci(pt?PK)..
Here Ci and are, respectively, the concentration of the i-th element in the sample and the coefficient of
7-ray attenuation in the i-th element; and Ci/C is the relative concentration of the i-th element being de-
termined in the sum. (All of the quantities refer to a 7-ray energy of E/ or Eft, respectively.)
The coefficient C is chosen from the condition of minimum variation
n Tt
P = E (AC1)2 (AC1)2
i=h+1
where AC1 is the real variation of the concentration of the i-th impurity element in the sample.
The method has been introduced in a plant producing rare-earths, where it is used for operative mon-
itoring of the technological process.
402
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ESTIMATION OF THE STEADY-STATE ISOTOPIC COMPOSITION
OF PLUTONIUM IN A MODEL OF AN EXPONENTIALLY GROWING
NUCLEAR POWER INDUSTRY
A. N. Shmelev, L. N. Yurova, UDC 621.039.5
V. V. Kevrolev, and V. M. Murogov
The paper considers a three-component model of a developing nuclear power industry (including fast
breeders, thermal reactors, and hybrid thermonuclear reactors as auxiliary producers of plutonium) as well
as steady-state conditions of exponential development of the nuclear power industry with a close uranium?
plutonium cycle. The approach proposed by A. I. Leipunskii et al. (Third Geneva Conference, 1964, USSR,
Rep. No. 369) was used to formulate equations for the variations in the contents of higher plutonium isotopes
with allowance for losses and delays in the external fuel cycle. The relations obtained make it possible to
calculate the steady-state isotopic composition of plutonium as a function of the structure, the growth rate
of the nuclear power industry, the losses and delays in the external fuel cycle, and the critical charge of the
fast breeders. The isotopic composition obtained can be used to get more precise physical characteristics
for the reactors. The following conclusions were reached.
1. In the one-component model of the nuclear power industry, containing fast breeders, with allowance
for an increase in its growth rate the steady-state content of the higher plutonium isotopes in the fuel may
drop appreciably in comparison with the asymptotic content. For example, for a BN-600 fast breeder operating
on oxide fuel (the estimated asymptotic content of 239-242PU was 64.1, 26.4, 5.8, and 3.7%, respectively) with
allowance for the development of the nuclear power industry at a rate such that it doubles in size in 5 years,
the steady-state composition of 239-242PU is 79.3, 17.1, 2.9, and 0.7%, respectively.
2. The two-component model of the nuclear power industry contains fast breeders and thermal reactors,
with the proviso that the fuel from the fast breeder cores and shields can be charged into the thermal reactors
and then returned to the fast breeders. With a small proportion of fast breeders in the industry, the tendency
to use the "cleanest" possible plutonium in the thermal reactors makes it preferable to choose the layout of
the fast breeders so that to an appreciable extent the charged fuel would burn out and new fuel would accumu-
late in various areas of the fast breeder cores. In this case the fast breeder cores will be provided with
"dirtier" plutonium since the plutonium burned up in them will be made up to a great extent by plutonium from
thermal reactors and not by their own production of 239PU.
3. In the two-component model of the nuclear power industry, containing hybrid thermonuclear reactors
and thermal reactors, the steady-state composition of the plutonium in the thermal reactors will be determined
by their own repeatedly regenerated plutonium and supplementary charges from the thermonuclear reactors.
Such plutonium will be found to contain a noticeable quantity of higher isotopes. The inclusion of fast breeders
in the nuclear power industry can make the plutonium used in the thermal reactors "cleaner."
403
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OPTIMIZATION OF THE CYCLICAL OPERATING REGIME
OF AN ATOMIC POWER PLANT REACTOR
V. I. Pavlov and V. D. Simonov UDC 621.039.516:139.566
The maximum principle* is used to optimize the operating regime of an atomic power plant reactor
whose power is periodically reduced for several hours according to the load chart of the energy system. The
problem is solved for maximum operating time at nominal power Unom in a cycle of period T for a reactor
with an operational reactivity margin smaller than the non-steady-state poisoning with xenon which accumu-
lates during the fuel discharging time T,
Since the operating regime of the reactor in the interval T ? T consists of a phase at nominal power and
a preparatory phase which makes it possible for nominal power to be attained after the discharging time, the
problem reduces to one of minimizing the duration of the second phase. When the allowable values of the
power and concentration of 135Xe nuclei are limited from above, a reactor operating cycle satisfying the indi-
cated criterion is guaranteed by a three-stage sequence of change in power during the preparatory phase:
U(t) --- 0, U(t) = var, and U(t)=Unom?
The general character of the optimal operating regime and the quantitative characteristics of its indi-
vidual phases and stages are considered by examining the example of a one-group zero-dimensional model
of a water-moderated?water-cooled (VVER) power reactor.
Calculations are made for a number of 24-h cyclic regimes, differing as to the extent and duration of
the fuel discharging. Relations are obtained for the operating times at nominal power as a function of the
operative reactivity margin and minimum reactivity values are determined, in which case the regime need
not be optimized since cyclicity is ensured by operation at nominal power in the interval T ? T and by direct
discharging in the time T. The length of reactor operation at variable power U(t)= var is also calculated -
as a function of the operative reactivity margin and the reactivity values for which a preparatory phase in
this stage ceases to be necessary are calculated.
The method developed and the results calculated can be used to optimize cyclic regimes of reactor
operation with partial rechargings of fuel at the end of the run. For reactors with continuous fuel recharging
and a constant reactivity margin, in addition to optimizing the cyclic regime with a known reactivity margin,
the method makes it possible to calculate the minimum reactivity margin for a 24-h cyclic regime for an
atomic power plant in an energy system with an acceptable length of the phase of preparation for a decrease
in power.
*L. S. Pontryagin, The Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1965).
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LETTERS
SOME FEATURES OF NICKEL BLISTERING UNDER IRRADIATION
WITH HELIUM IONS
V. I, Krotov and S. IVA. Lebedev UDC 621.039.51
The process by which blisters (swellings) are formed on the surface of various 'heals and alloys tinder
irradiation with helium and hydrogen ions has been studied in a considerable number of works, especially
[1-5].
The present paper gives the results of studies of the surface of polycrystalline specimens of nickel after
irradiation with helium ions at various temperatures. Nickel foil 0.2 mm thick was annealed at 800?C for 1 h
in a vacuum of 10-6 mm Hg and, after electropolishing, specimens with a diameter of 3 mm were ctit from the
foil. The specimens were then again electropolished to reveal the grain boundaries, placed in a cassette, and
irradiated in the ELU-100 accelerator with 20-keV helium ions according to the method described in [6]. The
radiation temperatures was varied within the limits 400-700?C, the ion current was 40 pA/cm2, and the total
dose was 8.1017 ions/cm2. The irradiated specimens were studied by means of optical microscopy and inter-
ferometry.
The outer annular segment of each specimen was shaded from the ion beam by a shielding ring which
made possible a direct comparison of the state of the relief and level of the irradiated and unirradiated sur-
face. In all specimens there is a general rise in the level of the irradiated surface in comparison with the
adjacent unirradiated segment; this rise depends on the radiation temperature (Fig. 1). With a rise in the
radiation temperature, the height of the step gradually decreases, the uniformity of the distribution of blisters
over the surface and the area they occupy decrease, and so does the mean size of the bligters. After irradia-
tion at 700?C the blisters are practically indistinguishable under the optical microscope.
Figure 2 gives the plots of the relative area occupied by blisters, their concentration, and their mean
size as a function of the temperature. At 400?C practically the entire area is covered comparatively uniformly
with blisters (Fig. 3a), at 500?C there is a noticeable difference in the covering of various grains (Fig. 3b), and
at 650?C the entire area of the specimen is free and only several grains have blisters (Fig. 3c). In the range
400-450?C traces of completely and partially destroyed blisters can be seen on the surface (Figs. 3a, 4a, and
4b). Thus, in addition to whole blisters in Fig. 4a we can clearly see round unshadowed contours, "bases"
which had held the cupolas of the blisters. Figure 4b shows a microkraph of the same segment, taken with the
500 600
Fig. 1
Fig. 1. Rise Ah in level of irradiated part of specimen as function of radiation
temperature.
Fig. 2. A) Concentration p, 0) mean size d, and 0) relative area S occupied by
blisters as function of temperature.
re-
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 355-357, April, 1978. Original article submitted
January 25, 1977; revision submitted August 22, 1977.
0038-531X/78/4404-0405807.50 01978 Plenum Publishing Corporation 405
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Fig. 3 Fig. 4
Fig. 3. Photomicrographs of obliquely illuminated surfaces of nickel specimens irradi-
ated with 20-keV helium ions with a dose of 8.1017 ions/cm2 (x1350) at: a) 400?C, b) 500?C,
and c) 650?C.
Fig. 4. Photomicrographs of obliquely illuminated surfaces of nickel specimens irradiated
with 20-keV helium ions at 450?C with a dose of 8 ? 1017 ions/cm2 (x1350) removed at different
focusing objectives: a) on sample surface; b) on cupola blisters.
objective focused on a plane somewhat above the plane of the specimen; this makes it possible to notice cupolas
which are beginning to tear away. The dark elongated formations in the micrograph are such cupolas, but
already turned almost vertically, which is why the "bases" from which they have partially torn away are visible
in Fig. 4a.
The observed pronounced anisotropy which arises in the distribution of blisters between the surfaces
of the various grains of the polycrystal with a decrease in temperature is probably related to the anisotropy
of the coefficient of helium diffusion in the crystal lattice. The effect of this anisotropy does not manifest
itself at low temperatures when the helium diffusion is insignificant.
Note should also be taken of the character of the destruction of the blisters. Thus, on the basis of the
expressions obtained for estimating the stresses in the center and along the periphery of the blister cupolas
in the process of the lifting of the cupola (proceeding from the model of an edge-clamped round plates) it was
concluded [7] that at the instant the cupola begins to la, when the deflection is smaller than the cupola wall
thickness, the stress along the periphery is greater than the stress at the center of the cupola, i.e., in mate-
rials with low elastic deformation strain to failure the blister tear should occur along the contour (e.g., for
niobium). If the lift of the cupola is commensurate with its thickness, then the inverse relation is observed
and more convex blisters (i.e., in more plastic materials) should break at the center of the cupola (e.g., for
1Kh18N9T steel). In the case of nickel, which is a material with a quite high plasticity, judging by the con-
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siderations above, one would expect the blisters to break at the cupola center, whereas in Fig. 4 it is seen that
the bream occurs along the cupola periphery (as in niobium).
This disparity with calculation can be explained by the fact that the side walls of a quite high cupola will
become thinner when the central part sputters more quickly since with oblique incidence the sputtering ratio
is high.
It may be that the cupola contour loses strength as the result of its side walls becoming saturated with
helium under oblique incidence and whereas the top of the cupola is "shot right through" by ions.
Undoubtedly there should also be a "dimensional" effect due to the fact that the cupola wall thickness
is comparable to the distances of the interactions of defects and structural components of the material with
the cupola surfaces. Thus, dislocations come out on the surface, phase transformations occur on the surface,
etc. [8]. The strength of the material in the zone of cupola-base contact may, therefore, differ from the
strength of the material of the cupola itself.
In conclusion, the authors are pleased to thank G. G. Gunin and L. A. Zhdamirov for preparing and
irradiating the specimens as well as L. P. Naumov and G. P. Fokin for processing the experimental results.
LITERATURE CITED
1. S. Das and M. Kaminsky, J. Appl. Phys., 44, No. 1, 25 (1973).
2. S. Erents and G. McCracken, Rad. Effects, 18, 191 (1973).
3. S. Das and M. Kaminsky, J. Nucl. Mater., 53 115 (1974).
4. B. A. Kahn et al., At. Energ., 39 No. 2, 126 (1975).
5. J. Roth, R. Behrish, and B. Scherzer, J. Nucl. Mater., 57_365 (1975).
6. V. I. Krotov, S. Ya. Lebedev, and S. D. Panin, Preprint FEI-652 (FE.I ? Physics and Power Engineering
Institute), Moscow (1976).
7. B. A. Kalin, D. M. Skorov, and V. T. Fedotov, in: Proceedings of the Fourth All-Union Conference
"Interactions of Atomic Particles with Solids," Part I [in Russian], Kharkov. State Univ. (1976).
8. P. Hirsch et al., Electron Microscopy of Thin Crystals [Russian translation], Mir, Moscow (1968).
SPATIAL FLUCTUATIONS OF NEUTRON AND POWER
DISTRIBUTION IN CRITICAL REACTOR
V. K. Goryunov UDC 621.039.564.2
In most cases, errors in physical reactor calculations may be attributed to real or hypothetical spatial '
fluctuations of the macroscopic cross sections. There is a broad class of problems in which the fluctuations
of the cross section may be regarded, formally at least, as a random function of the coordinate (e.g., fluctua-
tions due to neglected variations in the fuel enrichment or temperature oscillations). The present work con-
siders the statistical characteristics of spatial fluctuations of the neutron flux in a single-velocity diffusion
model of a reactor.
Assume that in a homogeneous initially critical reactor with mass parameter 1;ti there is a small varia-
tion in the physical properties of the active region (e.g., the macroscopic cross sections) according to the
law e (r) which does not affect the diffusion coefficient. The reactor is restored to an accurately critical state
by imposing some (constant over the volume) variation in the property 0, so as to satisfy the equation
? (1)
with the boundary condition nVc13(r)+,343(r) =0 and the condition that the flux 43(r) is not negative in a reactor
of volume V.
In the approximation linear with respect to the perturbation e(r)+ U it is simple to obtain expressions
for the fluctuation of the neutron flux
Translated from Atomnaya Energiya, Vol. 44, No. 4, pp. 357-359, April, 1978. Original article submitted
January 25, 1977.
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cr, (0_ (DA (r) (r') e (r') (Do (r') dr' (pm (r)
(r) nit (4,, xa) (r") 12 dr" cDo (r)
and for the first correction to the eigenvalue (which, in the same approximation, is 0)
(Do (r) 28 (r) dr
0?
S I (Do (e) 12 dr' ?
Here it m and 1,tm are the eigenfunctions and eigenvalues of the unperturbed problem. The subscript m=0
corresponds to the eigenfunction describing the neutron distribution in a homogeneous reactor: (?) (r) =a cDo(r).
Consider first of all perturbations of the cross section that have the properties of white noise with zero
mean; ( e(r)) = 0. The correlation of these perturbations maybe represented by a Dirac 6 function
Ke (r, r') _= (8* (r) s (rT=c6 (r?r'). (4)
It follows from Eqs. (2) and (3) that in a linear approximation (it (r)) = ( 0) = 0. It may be shown that the
mean over the realizations of the second correction to the eigenvalue is always negative. This was discussed
in detail in [1] for a Markov form of correlation of the perturbations; Ke (r, r') = olexp(?a I r ? rT I).
Taking into account Eqs. (2) and (4) the self-correlation function (SCF) of the relative fluctuations of the
neutron flux 0* (r1)c1;(r2)) is
(2)
(3)
(ri, r2)= 2 jx, c041'
(0,) el?ox(;) la dr
)
X
m, n
1 (rt) (r2)
X . (5)
S Om (e) 12 I On (e) 12 dr' dr" (Do (rt) (1)0 (r2) ?
The relative fluctuations of the power distribution N(r), considered in the same single-velocity diffusional
model of the reactor, are due to variation both of the neutron flux and of the fission cross section.
Accordingly, the SCF of the power distribution is represented as the sum of the SCF of the neutron flux,
the SCF of the cross-sectional perturbations, and an interference term taking into account the correlation of
the fluctuations in the flux and the cross section., In fact, taking the same approximation for N(r) as in Eq.
(2), the SCF of the power distribution ?