SOVIET ATOMIC ENERGY VOL. 47, NO. 2

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• Document Page Count: 107
• Document Creation Date: December 23, 2016
• Document Release Date: February 15, 2013
• Sequence Number: 2
• Publication Date: August 1, 1979
• Content Type: REPORT

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Russian Original Vol. 47, No. 2, August, 1979
February, 1980
SATEAZ 47(2) 591-690 (1979)
SOVIET
ATOMIC
ENERGY
ATOMHA} 3HEPIIIH
(ATOMNAYA ,ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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N ? wvfer f+romic energy is a cover-to-cover translation of Atomnaya
Energiya,-a publication of the Academy of Sciences of the USSR.
ATOMIC
ENERGY
An agreement with'the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
.original glossy photographs and artwork.' This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first? issue of the
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
I. N. Golovin
V. 1. I l'ichev
V. E. lvanov
V. F. Kalinin
P. L. Kirillov
Yu., 1. Koryakin
A. K. Krasin
E. V. Kulov
B. N. Laskorin
Associate Editors: N. A. Vlasov and N. N.'Ponomarev-Stepnoi
,Secretary: A. I. Artemov -
V. V: Matveev -
I. D. Morokhov
A. A. Naumov
A. S. Nikiforov
A. S. Shtan
B. A. Sidorenko
M. F. Troyanbv
E. I. Vorob'ev
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
February, 1980
Volume 47, Number 2 August, 1979
ARTICLES
Choice of Organic Diliuents for the Extractive Regeneration of the Spent Fuel
of Nuclear Power Plants - G. F. Egorov, A. P. Ilozhev, A. S. Nikiforov,
CONTENTS
Engl./Russ.
V. S. Smelov, V. B. Shevchenko, and V. S. Shmidt ? ? .
591
75
Possible Core Designs for the VG-400 Nuclear Power Plant - E. V. Komarov,
F. V. Laptev, A. G. Lyubivyi, F. M. Mitenkov, O. B. Samoilov,
and Yu. B. Sukhachevskii.......................................
597
79
Analysis of Neutron Yield Produced by High-Energy Proton - Y. Nakahara
and H. Takahashi ............................. ......
602
83
Calculation of the Pressure Change Caused by Saturated Steam Entering a Vessel
- A. K. Zvonarev, V. N. Maidanik, A. P.. Proshutinskii, A. G. Tolmachev,
and V. K. Shanin . ....
614
91
Method of Calculating the Functionals of Cross Sections in the Regionof Forbidden
Resonances - V. N. Koshcheev and V. V. Sinitsa .......... ...... .
618
94
Principles of Construction of Crystal Coordinate Detectors for Nuclear Radiation
-B.M.Lebed'andI.I.Marchik ...............
622
97
Production of 109Cd by Irradiating 107Ag with Reactor Neutrons - A. G. Beda,
A. V. Davydov, A. V. Lyakhov, and K. I. Shchekin . . . . , . , . . , .
626
101.
Calculation of Radiation Burden from Secondary Neutrons during Proton Irradiation
of Tumors - V. I. Kostyuchenko, B. I. Reznik, and A. P. Shchitov...... , . . ,
630
104
LETTERS
Vacuum Fission Chambers for Neutron Monitoring - A. B. Dmitriev, E. K. Malyshev,
41
and O. I. Shchetinin .:...... .`
?
?
?
636
108
Phase Diagrams of Systems of Uranium
Trifluoride
with Fluoride of Alkali-
Metal.
- V. A. Volkov, I. G. Suglobova, and D. E. Chirkst, ,
638,
110
Calculation of Parameters of Scintillation Detectors for Low-Activity)' Rays
- I. F. Lukashin. ; ? ?
641
112
Release of Hydrogen from 0Kh16N15M3B Steel on Heating - A. G. Zaluzhnvi,
D. M. Skorov; A. G. Zholnin, V. D. Onufriev, I. N. Afrikanov, V. S. Tsyplenkov,
V. G. Vladimirov, and V. P. Kopytin .....................
644
113
Backscattering Coefficients of Electrons - G. B. Radzievskii . .. . ... . . . . . . . . . . .
646
114
Measurement of Water and Steam Flows in a Sealed Vessel - V. N. Maidanik,
L. N. Mitrakov, A. P. proshutinskii, A. G. Tolmachev, Yu. A. Favorin,
and V. K. Shanin ................... . .........................
649
117
Nondestructive Method of Measuring the Activity Distributions of Sources
- V. N. Groznov, V. M. Kotov, V. V. Paramonov, B. V. Sorokin,
and Yu. S. Cherepnin ................. .............. .........,.
652
118
Radial Motion of Plasma Filament in Tokamak Thermonuclear Machine
- V. S. Manuilov . ....... . .
654
119
Optimal Flattening of Two-Dimensional Energy Distribution - R. A. Peskov .. . . . ... . .
659
122
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CONTENTS
X Ray Fluorescence Analysis of Uranium in Water with Radioisotopic a Sources
- S. M. Brodskii, S. V. Mamikonyan, and V. I. Filatov .... .............. . . .
Comparison of Incomplete Factorization with Variable Directions in. Solving a One-Group
Two-Dimensional Reactor Equation - P. N. Alekseev, N. I. Buleev, S. M. Zaritskii,
V. A. Stukalov, and L. N. Usachev ...................................
Experimental Investigation of Effect of Lead and Bismuth Multiplication Zones on Neutron
Parameters of Model of Liquid-Salt Blanket of Thermonuclear Reactor
- V. M. Novikov, S. B. Shikhov, V. L. Romodanov, V.. A. Zagryadskii,
and D. Yu. Chuvilin ...............................................
ANNIVERSARIES
Seventieth Birthday of Nikolai Nikolaevich Bogolyubov ........: . . ? ? ? ? . . . . ? . . ? . ?
COMECON CHRONICLES - INFORMATION
Journal of Collaboration .............................. ? . ? ? . ? , . ? , ? ? ? . ? .
Socialist Integration of Nuclear Science and Technology ...........:.............
CONFERENCES, MEETINGS, AND SEMINARS
Seminar on Procedural Problems for Investigating the Reliability of Large
Power-Generating Systems - T. A. Golubeva . , ....... ................
Fourth. All-Union Seminar on High-Temperature Power Generation.
- A. Ya. Stolyarevskii ..............................................
International Symposium on the Thermodynamics of Nuclear Materials
- V. V. Akhachinskii and A. S. Panov .. ... ................. ..... .
Conference on Controlled Thermonuclear Fusion - E. I. Kuznetsov .................
Conference on Materials for Thermonuclear RoaGtors - N. A. Makhlin ..............
International IAEA Symposium on the Biological Consequences of the Discharge
of Radionuclides by Nuclear Installations - Yu. I. Moskalev ...................
Urgent Problems of Radiation Protection - R. M. Aleksakhin . . ................
Seventh Seminar on Computer Simulation of Radiation and Other Defects
in Solids - Yu. V. Trushin .........................................
The Russian press date (podpisano k pechati) of this issue was 7/24/1979.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
(continued)
Engl./Russ.
661
123
664
125
666
127
669
,129
672
131
673
133
675
133
676
134
679
136
681
138
684
139
686
141
688
142
689
143
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ARTICLES
CHOICE OF ORGANIC DILUENTS FOR THE EXTRACTIVE REGENERATION
OF THE SPENT FUEL OF NUCLEAR POWER PLANTS
G. F. Egorov, A. P. Ilozhev,
A. S. Nikiforov, V. S. Smelov, V. B. Shevchenko,
and V. S. Shmidt
At the present time the extraction of tributyl phosphate dissolved in hydrocarbon diluents is the basis for
a number of engineering methods for regenerating spent fuel from nuclear power plants in the USSR [1-3],
France [4], Great Britain [5], Japan [6], and the Federal Republic of Germany (FRG) [7]. The development of
work in this area over a period of many years has determined the evolution of the technical requirements
placed on the diluents. It is known that previous plans for using technical products with involved composition,
such,as Solvesso 100, "odorless" kerosene, Shell Sol, p-aminobenzine, etc., have gradually been replaced in
favor of the application of individual hydrocarbons or mixtures of hydrocarbons of fairly narrow fractions
(mainly synthetic products), which has limited the spectrum of possible admixtures to be controlled. The pur-
pose of this article is to unify the physicochemical data which determine the choice of hydrocarbon diluents
in extractive technology.
The main indicators which characterize the hydrocarbon diluents of the aliphate series (n-alkanes) are
the length of the hydrocarbon chain and the content of admixtures of different chemical nature - olefin and
aromatic hydrocarbons, alcohols, carboxylic acids, and also other admixtures which enter the diluent from the
original raw material or which are formed in the synthesis. For hydrocarbon diluents in the extractive cycle,
it is important to take into account the content of the products of nitrating, oxidation, and radiative-chemical
interaction with the dissociation products of the extracting agent [8]. Our main attention in this article is di-
rected to those admixtures which are found in a fresh extracting agent, having regard for their consequences
as products which initiate the formation of the above technologically harmful substances as the extracting
agent and diluent are used.
Effect of the Length of the n-Alkane Chain on the Properties of the
Diluent and the Extractive System as a Whole
The properties that determine the applicability of a diluent for practical use are the boiling point, freez-
ing point, flash point, viscosity, density, surface tension, and solubility in the liquid phase. Also very important
are the properties of the diluent which are responsible for' its interaction with the extracting agent and extract-
ing compound, those which affect the distribution of the extracting agent (tributyl phosphate - TBP) between the
liquid and organic phases, those which affect the distribution of the system components being extracted, those
which affect the compatibility of the diluent with the solvates of the compounds being extracted and the disso-
ciation products of the extracting agent. We will consider below the effect of the length of the hydrocarbon
chain of the diluent on these properties.
Boiling Point, Freezing Point, and Flash Point. The dependence of these characteristics on the length
of the hydrocarbon chain of the n-alkanes (C) is shown in Fig. 1. It is seen that the freezing point of the n-
alkanes becomes comparable with the lowest likely temperature of the operating area only when the number of
carbon atoms in the chain is higher than 15. On the other hand, reducing C to 10 puts the diluent in the flam-
mable category (B): the flash point becomes less than 25? higher than the maximum temperature of the sur-
rounding medium (^- 35?).
The boiling point of the n-alkanes Cii-Cis falls within the limits which are tolerable in case vacuum distil-
lation is necessary. The addition of TBP leads only to a certain increase in the flash point and a reduction in
the freezing point of the extractive mixture as compared with the individual diluent. According to the indicators
shown in Fig. 1, it is thus permissible to use the n-alkane diluents Cii-Cis.
Viscosity, Density, and Surface Tension. The dependence of these characteristics is shown in Fig. 2,
Translated from Atomnaya 19nergiya, Vol. 47, No. 2, pp. 75-79, August, 1979. Original article submitted
January 30, 1979.
0038-531X/79/4702- 0591$07.50 ?1980 Plenum, Publishing Corporation 591
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where it is seen that lengthening the hydrocarbon chain causes a certain increase in the values of these char-
acteristics. For C less than 15, however, they remain at an acceptable (as far as the rate of phase stratification
in the extractive apparatus is concerned) level. The variation of the specific gravity and surface tension is
quite small (in the interval C11-C15 it is "Z35%). The viscosity of the diluent in the same interval increases by
almost a factor of two, but this does not affect the rate of stratification of the emulsions and only can have
.some effect on the kinetics of the mass exchange process in the organic phase. Since the kinetics of the ex-
traction processes with TBP solutions in n-alkanes are on the whole rather satisfactory (extraction equilib-
rium is attained in at most 1-2 sec [9]), this variation does not play a significant role in estimating the quality
of the diluents.
Solubility of the Hydrocarbons in the Liquid Phase. Hydrocarbons dissolve in the liquid phase to a very
small extent, with a severalfold reduction in the solubility associated with each successive carbon atom added
to the n-alkane chain. Using the available data [10] for the solubility of n-alkanes in water (n-hexane, - 120
mg/liter; n-heptane, - 50 mg/liter; and n-octane, 25 mg/liter), we derive a dependence of the form log S =
4.4 - 0.4 n,* from which we find by extrapolation that for n = 10 and n = 11 the solubility of alkanes in water is
expected to equal, respectively, " 4 and - 1 mg/liter, and should decrease at higher values of C (n is the num-
ber of carbon atoms). Because of this characteristic, the physical distribution of n-alkanes with chain lengths
greater than Cio-C11 does not introduce any appreciable content of organic substances to the aqueous solutions
in contact with the extracting agent (refinates, reextractates, and washing solutions).
Distribution of TBP between the n-Alkane Diluent and the Liquid Phase. The distribution of TBP be-
tween the n-alkane diluent and the liquid phase depends on the chain length of the alkane, since changes in
the latter are associated with a change in the activity coefficient of the TBP in the organic solution. The effect
of the nature of the diluent on the activity of the TBP in the extracting agent can be approximately predicted by
using the theory of regular solutions [12, 13]. An increase in the chain length of the alkane and its correspond-
ing molar volume causes an increase in solubility of the TBP in the equilibrium liquid phase as one passes to
diluents with large molecular weights. Data on the concentration of TBP in the equilibrium liquid solution are
shown in Fig. 3 (using the data of [14] for alkanes up to C12,-and calculated data for C13 and higher). As one
passes from C12 to C151 the content of TBP in the liquid phase increases by 2070, which should be taken into
account in estimating the possible losses of extracting agent on contact with the large volumes of the liquid
phase.
Distribution Coefficients of the Valuable Components While Extracting TBP in n-Alkanes. The length
of alkyl chains of hydrocarbon diluents has practically no effect on the distribution coefficients of uranium (VI),
plutonium (IV), and nitric acid during extraction by means of TBP solutions from aqueous solutions of nitric
acid (Figs. 4-6). As a result, this factor has little effect on the choice of the length of the hydrocarbon chain
of an n-alkane diluent. From this point of view, any n-alkane with chain length C11-C14 or a mixture of them can
be used as a diluent.
Compatibility of the Solvates Being Extracted and the Diluents. The nitrate solvates of hexavalent ac-
tinides are quite compatible with hydrocarbon diluents. It is therefore useful to consider the compatibility of
nitrate solvates with tetravalent actinides. This is determined by the maximum content of extracted element
or compound (in the organic solution) for which demixing of the organic phase does not occur. Figure 7 shows
the corresponding maximum concentrations of thorium extracted by a 30% solution of TBP in the form of a
nitrate. As is seen, the lengthening of the n-alkane chain causes the compatibility to become worse, which
agrees with theoretical conjectures [13]. When the number of carbon atoms in the n-alkane chain is around
15, however, the permissible concentrations of tetravalent actinides (^-20 g/liter) far exceed those which
usually occur in the reprocessing of thermal neutron reactor fuel elements [2].
Effect of the Length of an n-Alkane Hydrocarbon Chain on the Radiative-Chemical Stability. The forma-
tion of oxidation and nitrating products during the irradiation of a system consisting of a hydrocarbon with an
aqueous solution of nitric acid takes place as a result of the interaction of the hydrocarbon radicals with the
oxygen and the nitrating agents (NO2, NO, and HNO2), i.e., with the dissociation products of the nitric acid [8].
It is known [15] that the overall yield of hydrocarbon radicals is a slowly varying function of C (from 6 to
16) in the radiolysis of n-alkanes. It should therefore be expected that their yields of oxidation and nitrating
products, which are used as the principal criteria of radiative-chemical stability, will be similar. However,
the experimentally observed accumulations of nitrating and oxidation products on irradiation of n-octane, a
C1o-C12'hydrocarbon mixture, and also n-dodecane in contact with a 2 M solution of nitric acid indicate that the
..; r, *The solubility of aliphatic alcohols in water shows a similar dependence [11].
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t,?c
260
220
180
140
100
60
20
6 8 10 12 14 16
No. of carbon atoms
of
6 8 10 12 M16
No. of carbon atoms
6 8 10 12 ;4
No. of carbon atoms
Fig. 3
Fig. 1. Dependence on the number of carbon atoms in the hydrocarbon chain
of the melting point (-?-), flash point (---), and boiling point (-) of n-
alkanes.
Fig. 2. Dependence of the density (a), surface tension (b), and viscosity (c)
of n-alkanes on the number of atoms in the hydrocarbon chain.
Fig. 3. Content of TBP in the liquid phase in equilibrium at 25?C with 30 vol.%
solutions of TBP in n-alkanes with a different length of hydrocarbon chain.
TABLE 1. Initial Radiative-Chemical Forma-
tion Yields of Products of Hydrocarbon Nitrat-
ing and Oxidation of Various Molecular Weights
in Two-Phase Systems
Hydrocarbon -
G. molecule/100 eV
2 M HNO3
nitro
organic
I
carbonyl
dissoci-
system
com-
pounds
nitrites
I compounds
I ation of
HNQ
n-octane
1,2?0,2
0,8?0,2
0.64--0,1
,
2,0?0,5
CIO-C12 n-
alkane mix
0,5?0,1
0,3?0,1
0,1?0,02
0,8?0,2
n-dodecane
0,2?0,04
0,1?0,0^-
0,07?0,005
0,3=0,1
C14-rc15 n-
alkkane mix-
0,2
0,08
0,1
-
initial radiative-chemical yield of products that is calculated from their accumulation curves for dosages of
up to 5.1020 eV/ml becomes smaller with increasing C (Table 1). The five- to tenfold difference observed
in the initial yields of the products of nitrating and oxidation on irradiation of n-octane and n-dodecane in con-
tact with aqueous solutions of nitric acid is caused by the variation of the dissociation yield of the latter. The
hydrocarbons dissolved in an aqueous solution react with OH radicals, which reduces the rate of reverse oxi-
dation of nitrous acid to nitric acid and in this way increases the dissociation yield to an extent which depends on
the hydrocarbon concentration in the aqueous phase. In addition, the hydrocarbon radicals formed in the aque-
ous solution by the reactions
RH+OH-H+HZO;
RH+H-->R+HZ
interact with the nitric acid by the reaction
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0,4
15 0,3
14
z0,2
a 0,3
13
42
12
ni
6 8 10 12 14
No. of carbon atoms
Fig. 4 Fig. 5
Fig. 4. Coefficient of the distribution of uranium (VI) between aqueous nitrate
solutions and 30 vol.% solutions of TBP in n-alkane, as a function of carbon
atoms in the diluent. Initial concentration of uranium in the liquid phase - 1
g/liter, Vorg:Vliq = 1: 1, concentration of nitric acid in the liquid phase: 3 M
(1); 1 M (2); 0.1 M (3).
Fig. 5. Distribution coefficient of microconcentrations of plutonium (IV) between
30% solution of TBP in n-alkane and 3 M HNO3, as a function of the number of
atoms in the n-alkane.
Fig. 6. Distribution coefficient of nitric acid between a 30% solution of TBP in
n-alkane and the aqueous solutions, as a function of the number of carbon atoms
in the hydrocarbon chain. Acid concentration'in the liquid phase: 0.8 M (a) and
1.7M (b).
and contribute to the total yield of nitrating products.
In the case of n-alkanes, it is worth noting that the transition from C12 to C14_15 makes no significant
difference in the initial yields of the nitrating and oxidation products of these hydrocarbons (see Table 1). It
should also be noted that accumulation in the irradiated system of destruction products from hydrocarbons of
high molecular weight causes the rates of formation of oxidation and nitrating products in two-phase systems
containing n-octane and n-dodecane to become comparable for dosages >1021 eV/ml (>50 Wh/liter).
This behavior is due to the equalization of the rate of decomposition of nitric acid between these systems.
It is seen from the data given for the radiative-chemical stablity that the quantity C12-14 should also be
considered as optimal for hydrocarbon diluents. Difficulties may arise for greater lengths of the hydrocarbon
chain because of worsened removal of the high-molecular-weight products of the hydrocarbon radiolysis when
they are regenerated.
Any n-alkanes with chain lengths from C11 to C15 or a mixture of them can be used in this way as a di-
luent for the extractive regeneration of spent fuel elements from nuclear power plants with thermal neutron
reactors.. The lengthening of the chain, while reducing the flammability of the diluent, does not affect the dis-
tribution coefficients of the valuable components. It also improves somewhat the radiative-chemical stability
with practically no change in the hydrodynamic properties of the extracting agent and the solubility of the TBP
in the liquid phase, but it worsens (though within allowable limits) the compatibility of the diluent with the sol-
vates of the actinide nitrates.
Effect of Additives on the Properties of the Diluent
and the Extractive System as a Whole
The possible additives whose presence must be taken into account in order to estimate the properties of
the hydrocarbon diluents are unsaturated compounds, aromatic hydrocarbons, aliphatic alcohols, and acids.
The content of these additives is limited, since they worsen the properties of the extractive system. Aliphatic
alcohols and acids reduce the distribution coefficients because of solvation of the functional groups of the nu-
cleophilic extracting agents [16] (Fig. 8). Carboxylic acids have a similar effect. Branched aliphatic hydro-
carbons and olefins are considerably inferior to hydrocarbons with a straight chain (n-alkanes) with respect
to chemical [17] and radiative [18] resistance to the action of nitric acid, so their presence in aliphatic diluents
is required to be minimal.
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0U(VO
6 6 10 12 14
No. of carbon atoms
Fig. 7
Fig. 7. Maximum concentration of thorium (in nitrate
form) in 30% TBP for which the organic phase is still
homogeneous, as a function of the number of carbon
atoms in the n-alkane chain.
Fig. 8. Coefficient of the distribution of uranium (VI)
between a 10% solution of TBP in a mixture of dode-
cane-octanol and an aqueous solution of nitric acid, as
a function of the octanol concentration in the diluent.
Initial concentration of U ^' 10 g/liter; Vorg: Vliq = 1: 1.
Concentration of HNO3: 2.9 M (1); 0.23 M (2).
Certain aromatic compounds inhibit the decomposition of the extracting agent and the diluent by the
transfer of energy in one or another way from molecules of the latter to molecules of the aromatic substances.
The addition of 0.1 M monoisopropyldiphenyl to a solution of TBP in n-dodecane reduces by a factor of two
the yield of the formation of acid products of the radiolysis of the extracting agent - DBP and MBP. However,
for large contents of aromatic compounds in the extracting agents, significant unfavorable phenomena are also
observed: a rapid increase in the products of nitrating and an inhibition of the fission fragment elements (zir-
conium) of the organic phase even for small irradiation dosages. From modeling experiments with diluents
containing additions of aromatic nitro compounds, alkylphenols, and radiolysis products of TBP it can be as-
sumed that the cause of the inhibition of zirconium may be the formation of complexes of the type Zrx(DBP)y
(PhOH). Evidently it can therefore be assumed that since the time of contact of the extracting agent with the
HNO3 in the apparatus amounts to 10-20 min, the presence of no more than 1% concentrations of aromatic com-
pounds in n-alkane diluents does not cause significant impairment of the extractive characteristics and at the
same time to a certain extent maintains the protective properties of the aromatic. Some simple aromatic
compounds of the alkylbenzol type can be used successfully either as a diluent (e.g., for ternary amines) or
as a polar additive to the aliphatic diluents. In both cases, a higher degree of purification of the plutonium
from the fission fragment elements over a wide range of dosages is attained compared with systems based on
aliphatic diluents [191.
The effect of the other admixtures is considered using as an illustration the radiative stability of three
samples of the mixture C10-C12. The contents of the admixtures of unsaturated compounds and of alcohols were,
respectively, 0.2 and 0.12 in sample 1, 0.02 and 0.12 in sample 2, and 0.004 and 0.012 M in sample 3. Table
2 gives the results of the investigation of the radiative-chemical stability of these samples and also of spec-
trally pure n-dodecane in two-phase systems containing a 2 M solution of nitric acid. The rates of formation
TABLE 2. Radiative-Chemical Stability of
Samples of the Mixture C10-C12 at a Dose of
30 W ? h/liter
G, molecules/100 eV
Diluent
RNO2
RONO I
RONOz I
RCOO-
Kp Zr
Sample 1
0,98
1,57
0,13
0,27
0,5
Sample 2
0,50
0,78
0,08
0,40
0,3
Sample 3
0,20
0,15
0,02
0,05
0,04
n-Dodecane
0,2
0,1
-
0,07
0,06
0 2 4 6 8 10
Alcohol content, vol.
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
of. nitrating products of the hydrocarbon mixture used increase as, the additive concentration increases. The
content of olefins and alcohols in aliphatic diluents evidently should not exceed the values indicated for sample
3, which approaches that of n-dodecane with respect to its radiative-chemical stability.
CONCLUSIONS
The length of the n-alkane chain which provides a-basis for the diluent can lie within the interval C11-C15.
Within this interval, the ratio of the separate n-alkanes in the diluent can be regulated. It is better, however,
to use the hydrocarbons C11-C15; their rather high flash point gives them.a slight edge over the higher members
of the group in regard to their compatibility withthe extracting solvates of the actinide nitrates and also with
regard to their hydrodynamic characteristics. The content.of aliphatic acids and alcohols 0.01 M; of
unsaturated compounds < 0.005 M; of aromatic hydrocarbons I vol.%. These requirements may change in
the future as more investigations are made and a deeper study is made of the factors which affect the behavior
of the diluent in the extractive cycle.
LITERATURE CITED
1. I. D. Morokhov (editor), Nuclear Science and Technology in the USSR [in ]Russian], Atomizdat, Moscow
(1977), p. 153,
2. V. B. Shevchenko et al., Fourth Geneva Conference (1977), Report of the USSR No. 435.
3. V. V. Fomin et al., At. Energ., 43, No. 6, 481 (1977).
4. J. Souteron et al., in: P roc. Intern. Conf. on Nuclear Power andlts FuelCycle. Salzburg, May 2-13, 1977,
IAEA-CN-36/567.
5. R. Allardice et al., ibid., IAEA-CN-36/66.
6. K. Hasimoto et al., ibid., IAEA-CN-36/167.
7. W. Schuller et al., ibid., IAEA-CN-36/571.
8. G. F. Egorov and V. A. Medvedovskii, Khim. Vys. Energ., 5, 78 (1971).
9. V. V. Fomin, Extraction Kinetics [in Russian], Atomizdat, Moscow (1978).
10. A., M. Rozen (editor), A Handbook of Extraction [in Russian], Vol. 1; Z. I. Nikolotova and N. A. Kart-
asheva, Extraction by Means of Neutral Organic Compounds [in Russian], Atomizdat, Moscow (1976).
11. F. Krause and W. Lange, J. Phys. Chem., 69, 3171 (1966).
12. J. Siekiersky, J. Inorg. Nucl. Chem., 16, 205 (1962).
13. J. Hildebrand and R. Scott, Regular Solutions, New York (1950).
14. L. Burger, Nucl. Sci. Eng., 16, 428 (1963).
15.. R. Hoiroyd, in: Aspects of Hydrocarbon Radiolysis. L., Academic Press, New York (1968), p. 14.
16.. V. S. Shmidt, V. N. Shesterikov, and E. A. Mezhov, Usp. Khim., 36, 2167 (1967). '
17. C. Black, W. Davis, and J. Schmitt, Nucl..Sci. Eng., 17, 626 (1963).
18. Reactor Fuel Proc., Vol. 4, No. 4 (1961).
19. V. A. Medvedovskii.et al., in: Proceedings of the Third COMECON Symposium on. Spent Fuel Repro-
cessing (Vol. 2),. Czechoslovak Socialist Republic Atomic Energy Commission, Prague (1974), p. 302.
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
POSSIBLE CORE DESIGNS FOR THE VG-400 NUCLEAR
POWER PLANT
E. V. Komarov, F. V. Laptev,
A. G. Lyubivyi, F. M. Mitenkov,
O. B. Samoilov, and Yu. B. Sukhachevskii
UDC 621.039.524.2.034.3
Research in high-temperature nuclear power is designed to provide high-potential heat for various in-
dustrial purposes, including the large-scale manufacture of hydrogen, which can be used in metallurgy for the
direct reduction of iron, in the chemical industry for the synthesis of hydrocarbon fuels, and also directly in
engines [1, 2]. It is economically desirable to combine the production of high-potential heat with that of elec-
trical energy [3].
Various complicated problems have to be solved in the routine production of such heat from high-
temperature gas-cooled reactors (type VTGR), particularly in the production, transportation, and the use of
heat at very high temperatures, which may involve helium technology, new forms of equipment, and new ma-
terials. An important step in this area is the creation of the VG-400 prototype system, as experience with this
will be used in constructing commercial systems.
The VG-400 (Fig. 1) is intended to provide high-potential heat for the production of hydrogen, as well as.
for the production of electricity in a steam-turbine cycle. The basic characteristics are as follows:
Reactor power, MW
thermal.
1100
electrical
300
Hydrogen output., normal m3/h
1-101
Helium pressure, kgf/cmZ
50
Helium temperature, ?C
at outlet from reactor
950(750)
at inlet to reactor
350
Number of loops
4
Steam pressure, kgf/cm2
175
Steam temperature, ?C
535
Diameter and height of core, m
6.4 and 4
Number of spherical fuel elements
8.5
The mean time for passage of fuel elements
through core, years
3-4
Standard fuel-element sizes, mm
sphere (diameter)
60
six-faced prism
distance between lateral bases
400
height
840
In the reactor unit, the first4oop coolant circulates through four loops, which pass in turn through the
core, the high-temperature heat exchanger, where some of the heat is given up to an intermediate helium loop,
and the steam generator. The high-temperature heat exchanger and the steam generator work in countercurrent
mode, while the steam superheater works in direct-flow.
The system with the coolant working at 950?C involves the development of new heat-resistant materials,
which will delay the construction; therefore, the general scheme, the layout, and the design of the equipment
have been defined for implementation in stages, with appropriate upgrading and operation.
Translated from Atomnaya Energiya, Vol. 47, No. 2, pp. 79-83, August, 1979. Original article submitted
June 20, 1978.
0038-531X/79/4702-0597$07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
J
0
13 14
2
503j I
;S02
02 H2O
650?C
ftl-i
0
2 H2O
H2504
H2
J__E7
16
H2 504
-25 MW
(elect.)
[42
Fig. 1. General scheme of the VG-400: 1) reactor; 2) high-temperature inter-
mediate exchanger; 3) bypass; 4) steam generator; 5) main blower; 6) feed pump;
7) condenser; 8) generator; 9) turbine; 10) thermalizer;11) gas blower; 12) steam
separator; 13) evaporator; 14) intermediate vessel; 15) electrolyzer; 16) separator;
17) compressor; 18) drum separator.
A-A
Fig. 2. The VG-400 reactor with spherical fuel elements: 1) pressure vessel;
2) core; 3) heat exchanger; 4) gas blower; 5) steam generator; 6) intermediate
steam superheater; - 7) ionization-chamber support; 8) control and safety rod
effector mechanism; 9) charging holes; 10) graphite reflector; 11) discharge
channel.
In the first stage, the system can be operated to produce only electrical power with the coolant at 'the
exit from. the reactor at 750?C, which is passed directly to the-steam generator via bypass devices that replace
the high-temperature heat exchangers. -The design of these bypass devices allows the system to be operated
without the intermediate sections for use with the core at an elevated temperature.
'It is envisaged that- the production of hydrogen and other substances will take place in'the second stage
when experience has been accumulated with the reactor equipment.
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9
M
it `: jl ! I ~I
Fig. 3. The VG-400 with prismatic fuel elements: 1)
core; 2 and 3) start-up and working ionization chambers;
4) control and safety rods; 5) pressure vessel; 6) ther-
mocouple.
The reactor unit in the VG-400 has the first loop enclosed in a prestressed reinforced-concrete body.
The core, the high-temperature heat exchanger, the steam generator, and the gas blowers are placed in par-
ticular parts of the body, which are linked by horizontal pipes (Fig. 2). Thermal insulation is also fitted to the
inside of the pressure vessel. The use of a concrete vessel and integrated enclosure of the main equipment
improves the reliability and safety, while also giving means of evaluating future assemblies for the VTGR
high-power reactors. The main circulation-pumps are designed to cool the system on total pressure loss and
disconnection of the external electrical supplies.
A solid moderator of interchangeable type is used, which requires the movement of considerable bodies
of graphite in the core. This operation has to be performed in the absence of a common removable cover in
the reinforced-concrete pressure vessel, while the first loop has to remain sealed, which has imposed some
specific design features on the reactor and charging unit.
The reactor is used as a source of high-potential technological heat, so the core must heat the coolant
to 950?C while maintaining the fuel at the minimum temperature. The fuel cycle must be reasonably economical
and the system generally must meet rigid specifications for reliability and repairability, while the fuel should
be exchangeable in a minimum time or while the reactor is running. Also, the main requirements imposed
on the design of the core must be formulated on the basis that the unit will be employed in devices of high unit
power. These,specifications define the choice of fuel-element units, the schemes for the coolant distribution,
the mode of energy distribution, and the techniques for fuel recharge.
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Two types of core are currently used in high-temperature gas-cooled reactors: with prismatic and
spherical fuel elements [4]. Both of these have been- considered for the core of the VG-400.
The core may be formed by columns of hexagonal graphite blocks containing holes for the ring fuel
elements (Fig. 3). The height of a block is 840 mm, distance between faces 400 mm. Seven columns of such
blocks form a modular group, which contains a central.column under the control and safety rods, which is
surrounded by six columns containing the fuel blocks. The end reflector and the first lateral reflector are
formed by graphite blocks of analogous dimensions, while the second lateral reflector consists of stationary
blocks of interlocking shape.
The physical parameters of the core are optimized along with the scope for recharging by the use of four
recharge cycles during a single running cycle. In each recharge cycle one quarter of the fuel modules will be
replaced. In that case, fuel blocks differing in age will be present together in the core, and these will differ
in power output, so it is necessary to adjust the coolant flow rate by a regulator installed on each module.
The attainment of very high helium temperatures (950?C) subject to restrictions on the fuel temperature
means that the energy distribution in the core must be appropriate. Four subzones are therefore used in the
block core (two in height and two in radius), which differ in 235U content.
A block zone is reloaded by remote control with the reactor shut down by means of an unloading-reload-
ing machine, which involves the following operation: removal of the control and safety rod mechanisms, in-
stallation of the recharge machine, insertion of the grip into the cavity in the body, adjustment in radius, azi-
muth, and height on the appropriate block, extraction of the latter, transfer of the block to a container, grip-
ping a fresh block, and setting in the appropriate position in the inverse order.
The core may be formed by free packing of spherical elements of diameter 60 mm into the cylindrical
cavity bounded by the lateral and end graphite reflectors (Fig. 2). The fuel elements are loaded along tubes
into the upper part of the core and moved within the core under gravity and are unloaded via an unloading hole
in the lower graphite reflector. The reloading is provided by the unloading-recharge unit with the reactor
working. Power control and emergency shutdown are provided by fitting rods into the spherical core; the first
group of rods lies in channels in the lateral reflector, while the second is inserted directly into the spherical
filling.
The reactor operates on the principle of single passage of the fuel elements through the core, where the
fresh elements in the upper part of the core are in the relatively cold coolant in the area of maximum heat
production, which provides favorable conditions for reducing the fuel temperature. The radial distribution of
the coolant flow is difficult to manage in that case, and this means that the equalization of the radial energy
production is very important. A two-zone distribution of the 235U enrichment is employed [5]. However, it is
preferable to equalize the energy distribution by controlling the speeds of movement of the fuel elements, which
can be provided by the case of several unloading holes or other design measures [6].
The temperatures required by the prototype system can be provided in zones with spherical or block fuel
elements; a specified helium exit temperature of 950?C can be realized for a given fuel temperature in either
case. However, the precise engineering facilities required may differ substantially. In the case of a prismatic
core, the system for controlling the distribution of the coolant over the modules is complicated and of inade-
quate reliability, while the use of four different forms of heat-producing assembly makes for additional diffi-
culties in manufacturing the blocks and operating the equipment. Separate facilities can be used to control the
energy distribution in a spherical core, although there is no doubt that considerable volume of experimental
work will be required to provide a final definition of the mechanics of the fuel and the gasdynamics within
the core. The thermal features of the core arising from the use of the single-pass principle indicate that there
is still considerable scope for raising the temperature, which is particularly important if such reactors are to
be used in metallurgy and chemistry.
The working parameters of the core will be determined to considerable extent by the details of the re-
charging mechanism, which must work reliably. A spherical core has certain advantages here, since this can
be reloaded with the reactor working without any modification to the equipment, while the mechanisms for re-
loading spherical fuel elements are simpler in design and perform only standard operations, and the corre-
sponding control system is simpler than the unloading and charging machine required for a prismatic core,
where the components are of large dimensions and mass and many different operations have to be performed.
There is a major disadvantage of the reloading system for a spherical core arising from the very restricted
access for repair while the reactor is working, but this can be partly overcome by using backup sections for the
major loading and unloading segments.
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In the case of a prismatic core, control and safety rod mechanisms of traditional design can be used,
similar to those in the BN-350 reactors. The control and safety absorbing rods then lie in special channels
within the columns. Similar mechanisms can also be used with a spherical core if tubes are fitted to hold the
control rods. However, the physical characteristics of the reactor are rather adversely affected if the tubes
are placed within the spherical filling. A new design of control-rod mechanism is therefore required for a,
spherical core, in which the rods can be inserted directly into the filling.
In both forms of core, the reflector is formed by graphite blocks, which are subject to rigid specifica-
tions for strength and size stability. The working conditions of graphite in a high-temperature reactor are
more severe than those in reactors of other types. The temperatures of the graphite blocks rise to about
1000?C and the blocks are exposed to a fluence of about 1022 neutrons /cm2 during the complete period of opera-
tion. Under these conditions, the graphite blocks are subject to large internal stresses and may alter in shape
considerably. It may be that graphite of existing grades cannot provide continuous operation in the reflector.
In the case of the prismatic core, the inner part of the graphite reflector could be changed by means of a load-
ing and unloading machine. No such machine is envisaged for the spherical core, while there is considerable
complexity in replacing the reflector by means of special service mechanisms, and therefore the most re-
sistant grades of graphite must be used in the reflector, which must remain in situ throughout the working life
of the reactor.
An important factor in the choice of core concerns the manufacture and processing of the fuel elements;
the large sizes of the elements in the prismatic case go with very severe working conditions, so careful ex-
perimental evaluation of these elements under reactor conditions is essential. However, it is impossible to
perform full-scale reactor tests on such fuel elements because of the large dimensions, and therefore full
viability confirmation in advance is impossible. In that respect the spherical fuel elements are undoubtedly
preferable.
A spherical core has considerable possibilities, particularly with regard to further temperature rise,
and it also has advantages in the creation and processing of fuel elements and the management of the graphite
blocks, since simpler units and mechanisms can be used in reloading and in controlling the energy distribution,
so this form is justified for the VG-400. Particular attention will then have to be given to the development of
radiation-resistant grades of graphite and reliable control-rod mechanisms.
LITERATURE CITED
1. A. P. Aleksandrov, Kommunist, No. 1, 63 (1976).
2. N. N. Ponomarev-Stepnoi et al., in: Nuclear Science and Engineering, Series Atomic-Hydrogen Power
[in Russian], No. 1, Institute of Atomic Energy,. Moscow (1976). p. 5.
3. F. M. Mitenkov et al., "Design features of a prototype high-temperature reactor ," in: Proceedings of the
All-Union Seminar on High-Temperature Power Engineering, Moscow, April 20-22, 1977 [in Russian].
4. D. Bedenig, Gas-Cooled High-Temperature Reactors [Russian translation], Atomizdat, Moscow (1975),
p. 69.
5. V. Maly, R. Schulten, and E. Teuchert, Atomwirtschaft,4, 216 (1972).
6. G. Lohnert et al., Report IAEA-SM-200/68, Julich (1975).
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
ANALYSIS OF NEUTRON YIELD PRODUCED
BY HIGH-ENERGY PROTON
Comparisons have been made between computational results obtained with the BNL
code system and experimental data measured by Vasil'kov et al. for 56 x 56 x 64 cm
natural and depleted uranium blocks surrounded by lead walls and primary proton
energies of. 400 and 660 MeV. The energetic protons from a linear accelerator are
used to produce an intensive neutron source in the uraniumblock; The computer code
system prepared at BNL to perform nuclear design analyses of linear accelerator
reactors consists of six main programs: NMTC for spallation-evaporation processes
above 15 MeV, HIST3D for the analysis of collision event records obtained by NMTC
to get P3 neutron source distribution, DLC-2 to compile 100 energy group cross sec-
tions, TAPEMAKER for format conversion, ANISN to collapse 100 group cross sec-
tions to fewer group P3 cross section sets, and the principal code TWOTRAN-I which
performs neutron reaction and transport calculations in the energy range below 15 MeV.
Our computational method gives conservative total neutron yields, i.e., underestimates
of about 16.8-29.8 % in comparison with measured values depending on proton energy.
Radiative capture 238U(n, y) density distributions have. been compared between the cal-
culation and experiment. The calculated distribution has the higher peak in the central
part of the target system and the steeper gradient both in the r and z directions.
. Since reprocessing facilities indispensable for the conventional light water reactor to fast breeder re-
actor fuel cycle are now considered to increase the potential risk of nuclear weapons proliferation, evaluations
have been initiated to find alternative nuclear energy systems that are not only more proliferation resistant
but helpful in stretching uranium resources. A linear accelerator reactor ?(LAR) is one of these systems of
great promise in producing fissile material in conjunction with proliferation-resistant fuel cycles.
This reactor uses a high-energy proton,or deuteron beam from a linear accelerator incident on a Pb-
Bi target to produce an intense neutron source. The target is surrounded by a lattice of Zr-clad rods of
fertile-fissile material which is called the blanket. At the initial loading, uranium with 2% enrichment is used.
The burning scheme depends on the options described below. Three options of design optimization are pre-
sented now [8]: (1) the optimization of the time-integrated production of thermal energy for conversion to
power; (2) the optimization of the production rate of fissile material, without involving reprocessing; (3) the
optimization of the production rate of fissile material. in conjunction. with reprocessing. These options cor-
respond to the linear accelerator-driven reactor, the linear accelerator fuel regenerator, and the linear ac-
celerator fuel producer, respectively.
The idea of using a linear accelerator to produce fissile material dates back to 1940. G. Seaborg and his
group succeeded in producing tiny quantities of 239Pu from 238U using deuteron beams. The first practical at-
tempts to promote the construction of accelerators to be used to generate intensive neutron sources were pre-
sented by E. 0. Lawrence in the U.S.A. and N. N. Semenov in the USSR in the late 1940s. The MTA pro-
ject at Livermore Radiation Laboratory, promoted by Lawrence, was abandoned in 1952, however, when
high-grade ores were discovered. A Canadian team at Chalk River has always been a strong proponent of
such an electronuclear facility.
Intensive theoretical works on spallation- evaporation reactions in heavy nuclei have been performed in
the U.S.A. and USSR. As early as in 1948, M. L. Goldberger studied the interaction of high-energy neutrons
Brookhaven National Laboratory, Upton, New York 11973. Published in Atomnaya Energiya, Vol. 47,
No..2, pp. 83-91, August, 1979. Original article submitted December 25, 1978.
602 0038-531X/79/4702-0602 $07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
with heavy nuclei by a Monte Carlo method under the assumption that the nucleus might be described by the
statistical model [1]. From late in the 1950s to early in the 1960s, Dostrovsky et al.' published a series of
papers on the Monte Carlo calculations of spallation-evaporation reactions using the statistical model for
degenerate Fermi gas [2-5]. The production of mesons was taken into account for the first time in the work
of Metropolis et al. [6].
When a high-energy proton, neutron, or pion interacts with a nucleus, several secondary nucleons (neu-
trons, protons) and pions are produced. These secondary particles may have energies sufficiently high to
initiate similar events with other nuclei, which develops to macroscopic cascade. Practical computer codes
have been developed to follow such cascades in a heavy nucleus using the Monte Carlo method at Oak Ridge
(U.S.A.), Brookhaven (U.S.A.), and Dubna (USSR). Bertini completed a medium=energy collision code using the
intranuclear cascade model, which was used to calculate correlated energy-angle nucleon spectra considering
the nucleus as a degenerate Fermi gas of protons and neutrons enclosed in a spherical well [7]. Chen et al.
improved the method of Metropolis et al. by introducing refraction of cascade particles when going through re-
gions of varying potential energy and considering diffuse boundaries [8]. Their Monte Carlo code is known by
the name VEGAS. A similar computational method has been developed by Baraschenkov et al. [9]. The methods
of Bertini and Baraschenkov et al. give good agreement with the known experimental data for the energy range
above several tens of megaelectronvolts [10, 11].
Bertini's code was incorporated by Coleman to the NMTC system designed for the analysis of nucleon
meson transport in a massive system [12, 13]. The NMTC code has been updated and used also at BNL and
the other laboratories [14, 15].* NMTC computes the transport of nucleons and mesons up to 3.5 GeV based
on the intranuclear cascade evaporation model [7] which takes into account both elastic and inelastic scattering
and is also based on the 05R model [16] for the particle transport in a three-dimensional heterogeneous mas-
sive system. These processes are computed statistically by the Monte Carlo method.
In the computer code system prepared at BNL to perform nuclear design analyses of LAR's, NMTC is
used to calculate all reactions, down to energy 15 MeV initiated by energetic protons of energy 1 to 1.5 GeV.
In the energy range below 15 MeV only the reactions induced by neutrons are calculated with the two-dimen-
sional neutron transport theory code TWOTRAN-II [17]. The yield of neutrons produced in the spallation-evap-
oration process is given by the NMTC calculation; the contribution of neutron fission reactions below 15 MeV
is calculated by TWOTRAN-Ii.
Measurements of neutron yields in uranium, lead, tin, and beryllium targets were carried out at the 3-
GeV cosmotron at Brookhaven [19]. These indicate that for a uranium target the yield is about 40 neutrons/
proton of energy 1 GeV and it is twice that obtained for a lead target.
Preliminary studies of the accelerator breeder concept have been performed at ANL, BNL, LASL, ORNL,
and AECL (Canada). However, few experimental data have been published on neutron yields and neutron flux
distributions for realistic reactor systems consisting of target, blanket, and shielding. Recently, Vasil'kov et
al. published their experimental results on 56 x 56 x 64 cm natural and depleted uranium blocks surrounded by
lead walls for primary proton energies of 300, 400, 500, and 600 MeV [20].
The BNL computer code system for linear accelerator reactors has been applied to these Russian ex-
perimental facilities in order to estimate the accuracy and tendency of the code system. Comparisons are made
in the present paper of the neutron yields, 238U(n, y) reaction density distributions, and number of fission events
betweenthe measured values obtained by Vasil'kov et al. and our computational results. Discussions are also
given on the differences between ours and Baraschenkov et al.'s computational models.
II. Computational Method
The particle transport analysis part of the BNL computer code system consists of six main programs:
NMTC, HIST3D [21], DLC-2 [22], TAPEMAKER [22], ANISN [23], TWOTRAN-II, and auxiliary programs:
FIND [24], SURF [24], MULTSUM [25]. The overall interrelations of these programs is indicated in Fig. 1.
The NMTC is used to calculate the spallation and evaporation processes above 15 MeV by the Monte Carlo
method. Collision events of neutrons slowed down below 15 MeV are filed by NMTC. The collision events file
is analyzed with HIST3D to get neutron distributions which are used as neutron sources for the transport cal-
culations of neutrons in the energy range below 15 MeV. The 100 energy group DLC-2 neutron reaction cross
*Coulter improved the intranuclear code VEGAS and incorporated it into NMTC.
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IOOG X SECTION
LIBRARY
FORMAT
CONVERSION
NEUTRON
TRANSPORT
TOTAL NEUTRON
YIELO
FIND
CORE: 56x56x64cm
FLUX DISTR.
{
BEAM HOLE: 8 x 8 x 16 cm
(GRAPHIC)
REACTION RATE
-
WIDTH OF Pb WALL. 10 cm OR 20 cm
l
-
RF
SU
DISTR.
PROTON BEAM DIAMETER: 4-5cm
Fig. 1. Neutronics part of BNL code
system for LAR'S.
Fig. 2. Target in Russian experiments.
sections are based on ENDF/B-III [26]. The program DLC-2 is used to make a file containing cross-section
data only for nuclides selected specifically. TAPEMAKER is used to convert the format of DLC-2 data to that
of ANISN, i.e.,.FIDO format, as usually called. The DLC-2 100 group sets are collapsed to fewer energy
group sets by the one-dimensional neutron transport code ANISN based on the discrete ordinate Sn method.
The final neutron transport calculations are performed with TWOTRAN-II, which is a two-dimensional Sn
method program and can take into consideration anisotropies in neutron source and scattering cross sections.
MULTSUM has been programmed to calculate reaction rate distributions.
It is important to give a brief description of the nuclear models used in the NMTC and Baraschenkov
et al.'s computational methods, paying attention to what are the similarities and differences between the two
methods.
As for the nucleon density distribution for nucleons in a nucleus, the same three-region configuration
fitted to Hofstadter's curve is used in both methods [7, 27]. The outer radius of each region is chosen by solv-
ing for r in the expression
p (r) = a,p (0), i=1, 2, 3,
where-a = 0.9, al 0.2, and a3 = 0.01. The density in each-region is- set equal to the average value of the con-
tinuous distribution in that region.
Protons and neutrons are assumed to have a zero-temperature Fermi momentum distribution in each
region. The momentum distribution function f(p) has the form
f (p) = p2/3pt (r),
where pf? is the momentum of a nucleon corresponding to the Fermi energy. Depending on the particle density,
the Fermi energy differs for each type of nucleon in each region. The composite momentum distribution for the
entire nucleus is not a zero-temperature Fermi distribution. This assumption is employed in both methods.
The emission of particles from excited compound nucleus is treated with the statistical model due to
Weisskopf. The detailed formulation was given by LeCouteur [28]. In the statistical model the level density
of the residual nucleus at excitation energy E is given by the formula
co (E) = wD exp (2 j/a (E-s)),
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2.5cm (PROTON BEAM)
Fig. 3. Volume equivalent cylin-
drical target in BNL calculation.
0
cr,
W 30
Z
20
i
01 -1
0 200 400 600
PROTON ENERGY (MeV)
Fig. 4. Comparison of neutron yields
in natural uranium target.
where a and wo are constants for a given nucleus and 6 is the pairing energy. The value of wo is not important,
since wo is considered to be a slowly varying function of mass and charge number and only ratios are used in
the calculation. The quantity a has a significant effect on the final results. According to LeCouteur, it is
given by
a=AIR[1+Y(A2/A2)],
(4)
where A = mass number, A= A - 2Z, Z = charge number, Y 1.5, and B 8 MeV. The pairing energies S have
been tabulated by Cameron [29].
A Monte Carlo method program based on the LeCouteur formulation and a Monte Carlo scheme due to
Dostrovsky et al. [3-5] was made by Dresner for calculating the evaporation of particles from excited com-
pound nuclei [30). The EVAP program of Dresner has been revised and updated by Guthrie [31, 321. In the
updated version nuclear mass excesses and binding energies are replaced with Mattauch et al.'s tabulation
based on anatomic mass unit of 1/12 of 12C. For nuclei not tabulated by Mattauch et al. but having a mass
number within ?10 of the stability valley of the periodic table, mass excesses are calculated. using the semi-
empirical mass formula of Cameron, which uses a set of "shell-plus-pairing" energy corrections. For these
corrections for nuclides with Z or N less than 11 the values obtained by Peelle and Aebersold are used [33].
The updated version EVAP-4 has been incorporated in NMTC with the subroutine name DRES [14].
In the calculations of Baraschenkov et al. very simplified approximation is used for the level density
parameter a. At first a constant value a = 0.05 MeV-1 was recommended [341. In their later studies of the
effects of a on the neutron yields for lead and uranium targets, it has been found that a = A/10 McV-1 gives the
best fit to the measured values obtained with the cosmotron at BNL and the computed neutron yields are re-
duced by 10 to 20% from those obtained with a = 0.05 McV-1 [35].
There are some differences also in the treatments of pions 70: and iro in the intranuclear cascade calcu-
lation in NMTC and Baraschenkov et al.'s method [13, 34]. The neutral pion is very unstable and for practical
purposes is assumed to decay into two protons at its point of creation. As for charged pions, the p-decay of
trf is not considered in the Baraschenkov method. Positively charged pions "which-:come to rest as a result of
ionization loss are not considered anymore. In NMTC, however, they are assumed to decay immediately into
a positively charged muon and neutrino. Muon decay in flight is taken into account using the known muon life-
Baraschenkov
et aL(calcJ
i
~
et al. (exp.)
BNL-
/(colt.)
i r
660
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200 400 600
PROTON ENERGY (MeV)
20 30 40 50
Z (cm)
Fig. 5. Comparison of neutron yields obtained
by us and Baraschenkov's calculations for ef-
fectively infinite natural uranium target.
Fig. 6. 238U(n, y) reaction density
distribution in natural uranium tar-
get. '
time, and muons which come to rest are assumed to decay immediately. Negatively charged pions which come
to rest may either decay or be captured by a nucleus, depending on the material atom density. In NMTC an op-
tion is provided as to the treatment of 7r-. If decay is specified, all 7r-mesons reaching the cutoff energy are
assumed to decay immediately into negatively charged moon and neutrino. If capture is specified, they are
formed to undergo nuclear capture. Baraschenkov uses the capture specification only. In both methods the
energy and angular distribution of the particles produced as a result of capture is obtained with the cascade-
evaporation model.
The cutoff energies for proton and neutron transport in NMTC are input values.. The cutoff energy for
neutrons corresponds to the energy at which a transition is-made from the treatment of nonelastic collisions
by the internuclear-cascade.evaporation model to that by the evaporation model. The most appropriate value
of this cutoff is not certain, but the work of Alsmiller and Hermann gives the value - 15 MeV [36]. Incidentally,
the uppermost value of the neutron energy in ENDF/B is 15 MeV._ The cutoff energy is usually taken to be 15
MeV, below which the behavior of neutrons is analyzed by the neutron transport theory. Baraschenkov et al.
take the cutoff energy of 10.5 MeV because they use the multigroup neutron cross section sets due to Abagian
et al. [37] in the analysis of neutron transport in the energy range below the cutoff. It is not clear, however,
if the cutoff energy of 10.5 MeV. is not appropriate in comparison with 15 MeV and if it will result in significant
effects or not.
About the computational method of neutron transport below the cutoff energy, no definite description is
found in Baraschenkov et al.'s papers. In our computational method, as written in the beginning of this paper,
the two-dimensional discrete ordinate S8 method is used with a P3.neutron source and P3 scattering cross. sec-
tions.
The major differences in the computational methods- mentioned above are summarized in Table 1.
III. Computational Results and Comparison with Experiments
The computer code system illustrated in Fig. 1 has been. applied to Russian experimental facilities used
by Vasil'kov et al. [20] in order to estimate the accuracy and tendency of the code system by making a com-
parison between experiments and our calculations and those of Baraschenkov et al. The reactor model em- .
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TABLE 1. Differences between Our Computational Methods and Baraschenkov et al.
Ours
Baraschenkov et al.
Level density parameter
LeCouteur formulation
Constant values 0.05 McV-1
in the statistical model
with.Cameron, and
or A/10 MeV-1
Mattauch et al.
tabulation
Decay of: pions
?++v
Not considered 7r- capture
7r- -- ?- + v or
capture :
Cutoff energy for the
15 MeV
10.5 MeV
cascade-evaporation
calculation
Neutron cross section data
ENDF/B-III
Abagian et al. multigroup
below cutoff
set
Neutron transport below
cutoff
Two-dimensional Sn
method with P3 source
and P3 scattering
Monte Carlo method?.
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TABLE 2. 30 Energy Group. Structure
Group Energy range
1
15.000-12.214 MeV
2
12.214-10.000 MeV
3
10.000-8.1873 MW
4
8.1873-6.7032 MeV
5
6.7032-5.4881 MeV.-'
6
5.4881-2.4660 MeV'
7
2.4660-1.1080 MeV
8
1.1080-0.49787 MeV
9
497.87-223.71 keV
10
223.71-111.09 keV
11
111.09-52.475 keV
12
52.475-24.788 keV-
13
24.788-11.709 keV
14
11.709-7.1017 keV-
15
7.1017-4.3074 keV
16
4.3074-2.6126 keV
17
2.6126-1.5846 keV
18
1.5846-0.96112 keV
19
961.12-582.95 eV "
20
582.95-353.57 eV :
21
353.57-214.45 eV
22
214.45-130.07 eV
23
130.07-78.893 eV
24
78.893-47.851 eV
25
47.851-29.023 eV
26
29.023-10.677 eV
27
10.677-3.9279 eV
28
3.9279-1.4450 eV,
29
1.4450-0.41399 eV-
30
0.41399-0.0 eV
ployed by Baraschenkov et al. is not the same as ours, so that the comparison between the two computational
methods is not exact quantitatively.
In the experiments by Vasil'kov et al. use was made of a target assembled from rectangular blocks of
natural (2 x 4 x8 cm) and depleted (8 x 8 x 16 cm) uranium. The total, linear dimension of the target was 56 x
56 x 64 cm covered with a lead layer having a thickness of 10 or 20 cm, as shown in Fig. 2.
The proton beam was injected into the -central part of the target through the beam hole of cross section
8 x 8 ,cm and depth 16 cm from the front surface of the uranium block. The diameter of the proton beam at the
entrance into the target was 4 to 5 cm.
Experiments were carried out with the extracted beam of protons having energy 660 MeV. For the ex-
periments at proton energies 300, 400, and 500 MeV, the initial 660-MeV protons were slowed down in a poly-
ethylene attenuator.
In the diagonal plane of the target, passing through the axis of the proton beam, a system of channels
was made for the arrangement, of detectors. The channels were arranged in parallel withthe proton beam and
located at a distance 6 to 45 cm from the axis approximately at each 3 cm. The dimension of a channel was
60 cm in length and 2 x 0.3 cm, in cross section.
When the proton beam is absorbed in a uranium target, there is. generated a source of fast neutrons with
energy 1 to 100 MeV (superposition of cascade-evaporation and fission), which, being scattered by uranium
nuclei, slow down to the energy range where the radiative capture of neutrons occurs.
238U (n, Y) 239U L 239Np239P U.
'During,the::glow'ing-down, neutrons?.ar.e multiplied further in consequence of the fission of uranium nuclei.
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TABLE 3. Differences between Our Computational Models and Baraschenkov et al (TWOTRAN calculation)
Ours
Geometry
Proton source
Cutoff energy and number of
groups
Cylinder of radius = 31.595 cm,
axial length = 64 cm, ..
with lead wall of width 10 cm
Plane source of radius = 2.5 cm
at z = 16 cm
(end-of beam hole)
15 MeV
30
S8 with P3 source.
P3 scattering
Cylinder of radius = 60 cm,
axial length = 90 cm,
without lead wall
Point source at z = 26 cm
(no beam. hole)
10.5 MeV
25
Monte Carlo method?,
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TABLE 4. Analysis of Russian Experiments by the BNL Code System for LAR*
Target
Ep
F
L
N
Neutron yield
Nat: U
660
0.8502?
0.2733
24.28 ? 3.28
'38.28 ? 5.17 (46 ? 4)
U-238
660
0.5934
0.2172
21.46 ? 3.19
29.53 ? 4.39
Depl. U
660
33.55 ? 4.98 (38 ? 4)
Nat: U
460
0.8043
0.2769
10.15 ? 3.19
'15.51 f. 4.87 (22.1 ? 2.4)
Pb-Nat. U
660
.0.6154
M46
20.32 ? 2,91:
28.26 ?14.05
Pb-U-238
660
0.4813
0.2350
19.68? 2.40
24.53 ? 3.00
*Ep proton beam energy (MeV):. F fission fraction normalized to, one source neutron
which is produced by the spallation and evaporation reaction in the energy range above
15 MeV. L = net leakage fraction from the system. N = average number of neutrons per
one primary proton produced by spallation-evaporation reactions in the energy range
above 15 MeV. Neutron yield = (1 +.F - L)N. Values in parentheses are the results' of
Russian experiments.
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TABLE 5. Number of Fission Events in Natural U Target (fissions/proton)*
ntotal
16.43 ? 2.22
18.5
? 1.7 (13.7 ? 1.2)
3.38 ? 0.46
3.9 ?
0.4 (1.5 ? 0.1)
n238
13.05 ? 1.76
14.6
? 1.3 (12.2 ? 1.1)
*Proton energy = 660 MeV. Values in parentheses are for depleted uranium.
The density distribution of (n,y) capture was measured by 239Np distinguished radiochemically from the
uranium sample irradiated at various points in the target. Measuring the density distribution A(z, r, 0) of the
(n, y) capture in the volume of the target and integrating this distribution, Vasil'kov et al. obtained the'total
number of captures (239Pu yields) per energetic proton [20]:
y = p f vA (z, r, 0) dV
(Vasil'kov et al.'s definition of neutron yield), where z is the direction of proton. beam, r, 8 are cylindric-
al coordinates, .and p is the density of metallic uranium. Equation (5) is the de finition,of neutron yield per
energetic proton.
The neutron yield in our calculations is defined as follows:
Y=[1+(F-L)]N,
where N is the average number of neutrons per primary proton produced,by spallation- evaporation- fission
reactions in the energy range above 15 MeV, F - L is the. contribution from neutron reactions in.the energy
range below 15 MeV per source neutron created by reactions above 15 MeV, F is the fission fraction below 15
MeV and L is net leakage from the system of neutrons below 15 MeV. On the other hand, its definition in the
calculations of Baraschenkov et al. is given by,
where Nc5 and Nc8 give the internal escape defined as the number of radiative captures of neutrons by 235U and
231U, Nesc being the number of neutrons which escape from the block through its sides and end faces [33].
The definitions given by Eqs. (5) and (6) are consistent in that the neutron leakage fraction is not included
in Y.
In our calculations the rectangular target was replaced by a volume-equivalent cylinder of metallic nat-
t ral uranium with a radius of 31.595 cm and axial length of 64 cm, as shown in Fig. 3. The radius of a beam
guide hole is 4.5135 cm. The proton beam radius was taken to be 2.5 cm. The atomic number densities of
235U, 238U, and Pb, in units of 1024/cm3, are 0.00035148, 0.0478546, and 0.033000, respectively.
The procedure of our calculations is as follows. In the NMTC calculation, the average was taken over
10 batches of 25 protons each. Since the sampling number is small, the statistical error is somewhat large.
The necessary number of samplings is not well defined.
The P3 neutron source distribution was prepared for the TWOTRAN-II calculation using HIST3D. As for
the anisotropy of neutron scattering, the P3 approximation was employed, and 30 group cross sections sets were
prepared using ANISN. The 30 energy group structure is shown in Table 2. In the TWOTRAN-11 calculations
the S8 approximation was used. Since the S3-P3_P3-30 group calculations by TWOTRAN-are very expensive,
the sufficiency of the degree of Sn approximation has not been examined. These computational models are sum-
marized in Table 3 with those of Baraschenkov et al. [34]. The target in the calculation by Baraschenkov et al. is not
the same as ours. It is a cylinder with a radius of 60 cm and axial length of 90 cm without alead wall. The proton
source was assumed to be an isotropic point source at z = 26 cm from the front surface, and no beam hole
is considered.
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
Since the entire calculation is very expensive, the calculations have been performed only for proton en-
ergies of 660 and 400 -MeV. Neutron yields are summarized in Table 4 and are compared in Fig. 4 with the
experimental values of Vasil'kov et al. [20] and the calculational results of Baraschenkov et al. [34]. As is
clear from Fig. 4, our model gives conservative results in comparison with experiment, i.e., underestimates
of about 16.8 to 29.8% in average values depending on proton energies. If we recalculate the neutron yield in
the definition of Vasil'kov, we get the value Y = 38.14 ?3.81, which is smaller by 0.4% than that in our definition.
This justifies the use of our definition in design calculations.
Vasil'kov et al. performed experiments also on depleted uranium targets. For the sake of comparison,
calculations were performed also for the pure 238U target, results for which are also shown in Table 4. Al-
though the degree of depletedness is not written in Vas il'kov et al.'s paper, if we estimate it as 0.33% (number
density percentage of 235U) from the data of 235U fission events summarized in Table 5, the neutron yield for
this depleted uranium can be estimated to be 33.55 ? 4.98, which should be compared with the experimental
value 38 ?4. From the values of neutron yields for natural U, depleted U, and 238U in the case of Ep = 660 MeV,- it
is seen that the neutron yield decreases linearly in depletedness.
For a proton energy of 660 MeV, Vasil'kov et al. also measured the degree of decrease in neutron yield,
replacing the uranium in the central part of the target with a lead block of the dimension 8 x 8 x 48 cm [20].
The measured ratio of neutron yields for lead-uranium and uranium target was 0.48 ? 0.2, while our calculation
gives a somewhat larger value, 0.738. The reason for this relatively large discrepancy is not yet clear. One
of the reasons which can be considered is that the beam size in the experiment mightbe smaller than that in the
calculation and the beam intensity may have a Gaussian distribution rather than the uniform distribution used
in the calculation.
A comparison between Baraschenkov et al.'s calculations and Vasil'kov et al.'s experiments is also made
in Vasil'kov et al.'s paper, but it is difficult to conclude that Baraschenkov et al.'s method gives an overes-
timate of neutron yield, because the target system is different.
If we neglect neutron leakage in our definition of the neutron yield, considering both our reactor system
and Baraschenkov's to be effectively infinite, the comparison between the two computational methods becomes
that shown in Fig. 5. The modified line for Baraschenkov's method is obtained by reducing the original value
by 10%, which corresponds to the difference in the level density parameters of.a = 0.05 MeV-1 and a = A/10
MeV-1, as was mentioned in Section II. The discrepancy in-the neutron yields is still large. Although the term
L in our definition is neglected, there are leaked neutrons in the energy range above 15 MeV. This high-energy
neutron leakage is one of the reasons for the discrepancy.
- Numbers of fission events per proton, summarized in Table 5, have been obtained by integrating the den-
sity distribution of fission events. The fission density distribution was measured with a miniature silicon sur-
face-barrier counter covered by a uranium layer. Contributions of 235U and 238U were distinguished by using
layers of different isotopic compositions [20]. The agreement between experiment and our calculations is quite
good.
In Fig. 6 distributions of radiative capture density for 238U are compared between our calculations and
Vasil'kov et al.'s experiments [20]. The unit of distribution is the number of.239Np nuclei per gram of uranium
and per incident proton. In the central region of the target system the calculated distribution has the higher
peak and steeper gradient both in the r and z directions. The agreement between calculated and measured val-
ues is quite good for curves 3 and 4. Figure 6 is, however, somewhat disconcerting. The calculated distribu-
tion is larger than the measured one, while the neutron yield obtained by integrating the distribution is smaller
in the calculation. This can be interpreted as follows. The decay in the r direction is steeper in the calculated
distribution than in the measured one. Since the outer region has a larger volume, the volume integral of the
distribution gives the larger experimental value for the neutron yield.
What causes disagreement between theory and experiment depends on the many assumptions and approxi-
mations used in the theory and experiment. Theory is based on assumptions of nuclear structure, nuclear re-
actions, and their measured data. Computation brings in further approximations. When we use the code system
available currently, one way of improving the calculations is to use higher-order approximations in the Sn and
Pn treatments. In LAIR, the external neutron source distribution is also important in the analysis of reactor
characteristics by TWOTRAN-l1. If in NMTC calculation a sufficiently large sampling number is used, the
statistical fluctuations in the source distribution decreases. This would result in a better agreement of flux
distribution between computation and experiment. Estimating the effects of the order of Sn and Pn will require
tedious and costly computations.
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From the comparisons presented above, it may be said that the S8-P3-P3-30 group approximation is
quite good. When much more experimental data are accumulated, more conclusive discussions will be possible.
LITERATURE CITED
1. M. L. Goldgerger, Phys. Rev., 74, 1269 (1948).
2. I. Dostrovsky, Z. Fraenkel, and P. Rabinowitz, P/1615, Proc. Second United Nations International Con-
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6. N. Metropolis, R. Bivins, M. Storm, J. H. Miller, and G. Friedlander, Phys. Rev., 110, 185 (1958).
7. H. W. Bertini, "Monte Carlo calculations on intranuclear cascades," ORNL-3383 (1963).
8. K. Chen, Z. Fraenkel, G. Friedlander, J. R. Grover, J. M. Miller, and Y. Shimamoto, Phys. Rev., 116,
949 (1968).
9. V. S. Baraschenkov, K. K. Gudima, and V. D. Toneev, "Computational scheme of intranuclear cascades,"
JINR 132-4065 (1968).
10. H. W. Bertini, G. D. Harp, and F. E. Betrand, Phys. Rev. C, 10, 2472 (1972).
11. V. S. Baraschenkov, A. S. Il'nov, N. M. Sobelevskii, and V. D. Toaeev, Sov. Phys. Usp., 16, 31 (1973).
12. W. A. Coleman, "Thermal neutron flux generation by high energy protons," ORNL-2206 (1968).
13. . W. A. Coleman, and T. W. Armstrong "The nucleon-meson transport code NMTC," ORNL-4606 (1970).
14. Radiation Shielding Information Center, ORNL, "NMTC, Monte Carlo Nucleon-Meson Transport Code
System," CCC-161.
15. A. Coulter, private communication, LASL.
16. R. R. Coveyou, J. G. Sullivan, D. C. Irving, R. M. Freestone, Jr? and F. B. K. Kan, "0511, A general-
purpose Monte Carlo neutron transport code," ORNL-3622 (1965).
17. K. D. Lathrop and F. W. Brinkley, "TWOTRAN-II: An interfaced, exportable version of the TWOTRAN
code for two-dimensional transport," LA-4848-MS (1973);
18. Department of Nuclear Energy, Brookhaven National Laboratory.
19. J. Fraser, R. E. Green, J. W. Hilbom, L. 0. D. Milton, W. A. Gibson, E. E. Gross, and A. Zucker,
Phys. Can., 21, 17 (1965).
20. R. G. Vasil'kov, V. I. Gol'danskii, B. A. Pimenov, Yu. N. Potokilovskii, and L. V. Chistyakov, At. Energ.,
44, 329 (1978).
21. J. F. Beerman, D. Hillman, Y. Nakahara, and H. Takahashi, in press.
22. Radiation Shielding Information Center, ORNL, "100G, 100 group neutron cross section data.based on
ENDF/B," DLC-2.
23. W. W. Engle, Jr., "A user's manual for ANISN. A one-dimensional discrete ordinate transport code with
anisotropic scattering," K-1693 (1967), contained in CCC-82, RSIC ORNL.
24. T. Sills, private communication.
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50274 (1970).
27. V. S. Baraschenkov, K. K. Gudima, F. G. Zheregi, and V. D. Toneev, "Consideration of nuclear boundary
diffusivity in intranuclear cascade model," JINR-R2-6503 (1972).
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(1958).
29. A. G. W. Cameron, Can. J. Phys., 36, 1040 (1958).
30. L. Dresner, "EVAP -A Fortran program for calculating the evaporation of various particles from ex-
cited compound nuclei," ORNL-TM-196 (1962).
31. M. P. Guthrie, "EVAP-2 and EVAP-3: Modifications of a code to calculate particle evaporation from
excited compound nuclei," ORNL-4379 (1969).
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
CALCULATION OF THE PRESSURE CHANGE CAUSED BY
SATURATED STEAM ENTERING A VESSEL
A. K. Zvonarev, V. N. Maidanik,
A. P.-Proshutinskii,-A. G. Tolmachev,
and V. K. Shanin
UDC 621.1.013.1
Our previous results [1] were concerned with the nonstationary flow of water from a pressurized vessel
into a sealed vessel of volume 3.4 m3 containing ceramic rings.
Calculations have been performed [2-6] on the parameters in-the passage of saturated steam into a sealed
vessel; however, the method used there is not applicable to the pressure variation occurring in a vessel with
packing that causes additional condensation.
Here we present a method of calculating the pressure-in such. a drum on the basis of the uneven heating
of the packing; the curves for the ring temperatures (Fig. .1) imply that,the layers in the packing are heated
sequentially, i.e., the air is displaced by the steam-air mixture. It is also found that the temperature dis-
tribution is almost uniform over the cross section of the packing.
The experiments indicate that the following process occurs: the steam entering the lower part of the
vessel V0,is instantly and uniformly: mixed with the air (Fig. 2). Then the steam-air mixture passes into the
ring packing, where the steam condenses.
The following assumptions were made in the mathematical description:
1) The parameters of the steam in the drum correspond to the state of saturation at the appropriate par-
tial pressure;
2) the heating of the packing is regular (this is adequately confirmed by temperature measurements);
3) the pressure and density of the steam-air mixture are to be determined from the total of the partial
pressures of the steam and air; -
4) the temperature of the air in the steam-airmixture is equal to the temperature of the steam at the
corresponding. part lal,pressure.
Then the balance equations for the vapor and air take the following form:
dMir _ _ dM17 - ,
dMay :
~v
(1)
dT. dT '
dT
(2)
My = Vvssm;
Ma = PaTxn;
(3)
Mia=.Pa (V - Vm),
(4)
where Gv is the flow of the saturated vapor into the drum; dMjv /dT and dM2V/dT, rates of condensation of the
steam on the walls of the drum and in the packing; Mv, amount of vapor in the drum at time T; Vsm, volume of
the steam-air mixture at time T; V, drum volume; Ma, mass of air in volume VO; Mia mass of air in the rest
of the drum; Pa, density of the air in that volume; and Pv and pa, partial densities of the vapor and air in the
steam-air mixture.
The condensation rate dMiv/dT, for the walls of the drum is given by
Translated from Atomnaya gnergiya, Vol. 47, No. 2, pp. 91-94, August, 1979. Original article submitted
June 5, 1978.
614 0038-531X/79/4'102-0614 $07.50 ?1980 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
Fig. 1. Temperatures of layers of ce-
ramic rings as functions of time: 1-4 .
are the numbers of the layers reckoned
from the bottom.
Fig. 2. Working
scheme for pres-
sure change in
drum.
Fig. 3. Pressure variation in drum for Dy = 15 mm,
Po = 12 MPa, and To = 300?C, Upper position of pipe:
solid line) fromexperiment, broken line) calculation
for k2 = 400 W/m2 ? degC, dot-dashline) calculationfor
k2 = 200 W/m2 ? deg C, and -line) calculation for
k2 =100W/m2?degC.
dM,v - k1Ft (Ts-TI)
di r
where k1 is the heat-transfer coefficient for the walls; F1, area of the wall in volume VO; Ts, saturation tem-
perature corresponding to the partial pressure of the vapor; r, latent heat of evaporation; and T1, temperature
of the inner surface of the drum wall.
This system of equations does not incorporate the change in partial pressure of the steam precisely; the
heat-transfer coefficients were also taken as constant, i.e., independent of the partial pressure of steam, which
is not correct. However, the experimental data are scanty, so these features were neglected.
There are also other factors such as poor contact between the insulation and the walls of the drum and
swelling in the insulating material that influence k1, so the value was determined by comparing the observed
and calculated pressure changes. The best agreement was obtained with k1 = 200 W/m2 ?degC, but inexact
determination of k1 has only slight effects on the results.
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
Fig. 4. Pressure change in a vessel: Dy = 10 mm, Po 12 MPa, To = 300?C. Upper
position of pipe: solid line) fromexperiment, broken line),-Calculation for k2 = 400 W/m2
degC, dot-dash line) calculation for k2 = 200 W /M2 ? deg C, and - line) calculation for
k2= 100 W/m2 ?degC.
Fig.5. Pressure change in vessel: Dy = 6 mm, Po = 12 IVIPa, To = 300?C. Upper posi
tion of pipe: solid-line) from experiment, broken line) calculationfor k2= 400 W/m2 ? deg C,
dot-dash line) calculation for k2 = 200 W/m2 ?degC, and -?- line) calculationfork2 = 100
W/m2 ?degC.
The temperature T1 was determined by solving the one-dimensional nonstationary thermal conduction
equation subject to the boundary conditions Ast(6Tst /6x) k1(Ts-T1) at the inner boundary and 7st(OTst/6x)=
0 at the outer one. Here we neglect the heat accumulated in the insulation,, because the thickness of the latter
was small by comparison with the thickness of the drum wall.
The rate of condensation on the rings dM2V/dT may be defined from the displacement of the mixture
through the packing (Fig. 2). At a time ~, a volume element A.V(~) begins, to be heated, and at the time T the
temperature rise is T2(~, T)- To, where T2(~, T) is the temperature of the layer material at time T for which
heating started at time ~, and To is the initial temperature.
The mass of steam condensed on the packing up to time T is
v(z)
M2V= "cams (T2(t, T)-T6)dV(t) (6)
0
or on the basis that dV(~) = (dVsm(t) /dT)d~,
c,ra2
r
ddM (g) (T2 (t,
) - To) ds, (7)
where c2 is the specific heat of the packing material and m2, is the mass of packing per unit free volume.
Differentiation of (7) gives
dMQV _ c2m2 f d!9m (o) dT2 (g, 't)
di r J di ' dt
0
The rate of temperature change in a layer of packing in the regular state is given by
dT2 (E, ti) - k2F9 (T8-T2 (t, t)),
dt c2ma
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
where F2 is the surface area of the packing per unit volume [7] and k2 is the heat-transfer coefficient for the
rings.
We substitute (9) into (8) to get
dMzy _ C2M2k2
dT r (AiTa-AZ),
where Al and A2 are intermediate integrals dependent on the upper limit T.
The differential equations for Al and A2 are
dA, _ dVsm
dT dT
(11)
dA2 =k2(T,A1-A2)+To dA_ .
(12)
.
dT dT
We differentiate (2)-(4) on the basis that Ma and Mia do not vary to get
,
dM dVsm
M
V
dP
sm-
v dti
do
(13)
dT
V2 dPV
sm 4
dpi dPa dpi dTs dPv
dVsm
-
04 dT
dPa dT dT,
dT
,
Mia/VSm
dVsm = Ma dpa dPp dPa
dT pa dP \ dT + dT
The following are expressions for the derivatives appearing in (13)-(15):
dpa = 1 dpa - - Pa
dPa RTs ' dT, RT, '
dT, T.., dpa
dPo rpv ' dP
1
RTo
where dpv /dPP = 0,54.10-5 sec2/m2 is virtually constant over the pressure range involved.
System (1), (5), (10)-(15) in the unknowns Pv, Pa, Vsm, All A2, Mv1, Mv2 and My was solved by a fourth-
order Runge-Kutta technique with automatic step size choice subject to the following initial conditions at T =
0: Pv=My=Mvl=MV2=A,=A2=0; Pa=0.1MPa; Vsm= V0.
Calculations were performed for an initial water temperature of 300?C in the source and pipe diameters
of 6, 10, and 15 mm; Figs. 3-5 give the values for P(T) and the measured values. To get the best agreement
between theory and experiment requires some adjustment of the heat-transfer coefficients ineachcase, partic-
ularly when allowance is made for the delay, which is not reflected in the calculations, which were based on
the assumption of regular heating and steam entering the drum and mixing instantly with the air. For ex-
ample, for Dy = 6 (Fig. 5) we get agreement for k2 = 100 W/m2 ?,degC, while for Dy = 15 the same applies for
k2 = 400 W/m2 -deg C, the reason beingthat the steam flow. rate and partial pressure increase with the diameter
of the pipe, and therefore so does the heat-transfer coefficient. These values of k2 agree with the observed
T2(T) curves (Fig. 1), while special experiments are required to determine k2 more precisely.
LITERATURE CITED
1. V. N..Maidanik et al., At. Energ., 47, No. 2, 117 (1979).
2. D. Brosche, Atomkernenergie, 19, No. 1, 41 (1972).
3. D. Brosche, Ein Rechenmodell zur Berechnung von zeitlichen and ortlichen Druckverteilungen in Reaktor-
Sicherheitsbehaltern. Laboratorium far Reaktorreglung and Anlagensicherung, Technische Universiti t
Munchen. Interner Bericht, October 1970 (to be published).
4. D. Aische, Atomkernenergie, 16, No. 2, 6 (1970).
5. M. Masarovic and B. Gaberscek, Nucl. Eng. Design, 17, No. 3, 428 (1971),
6.. N. G. Rassokhin and V. S. Kuzevanov, Mosk. Eng. Inst., Issue 200, 87 (1974).
7. S. G. Gerasimov (editor), Heat Engineering Handbook, Part 2 [in Russian], Moscow-Leningrad (1957).
Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
METHOD OF CALCULATING THE FUNCTIONALS OF CROSS
SECTIONS IN THE REGION OF FORBIDDEN RESONANCES
V. N. Koshcheev and V.. V. Sinitsa UDC 539.125.5.173.162.3
In the course of preparing constants for neutron-physical calculation of reactors and radiation shielding
it is necessary to obtain various functionals of cross sections (self-shielding factors [11, transmission func-
tions [21,-etc.) under the conditions of inadequate information about the resonance structure. In these cases
we usually employ the laws of statistical distributions of resonance parameters known from the theory of
resonance reactions. Integration over the distributions requires a considerable expenditure of computer time;
this stimulates the search for-effective methods of estimating the expectation values of the functionals. In the
simplest case (average cross-sections) the computational difficulties are successfully overcome with general-
ized Gaussian quadrature formulas [3-51. _
In the present paper we propose a computational scheme for estimating the expectation values of func-
tionals of a more complex form. This .scheme is based on the introduction of intermediate quantities (the
moments of the cross sections) and in order to calculate them we determine the optimal parameters of the
quadrature formulas of the highest algebraic degree of accuracy, i.e., optimal in relation to the considered
form of the functions being integrated.- The orientation of the parameters to a particular form of functional
permits a substantial reduction of the number of integration points and, therefore, of the time required for es-
timating its mean statistical value. -
Computational Scheme. The functionals of cross sections used in calculating group constants are written
in the form of integrals:
(1)
Fx (s) _ (oxF (o, s)), 0- oo? Exact values of it are
calculated from the formula
C(a)=(1+a)m/2a',-m/2 ( l y/2 r(k+1A/2) T (k+ z ; k+? l"`+1; z) (14)
(?/-) 1
Figure 3 gives the plot of approximation error a vs the parameter a for fluctuation factors appearing in the
cross-section moment ((V Y a"), - 1 < n < 1. It also gives the results of calculations with Gauss-Legendre
parameters [4] and with parameters with equal weights [5]. With almost equal maximum errors of approxi-
mation the parameters obtained require substantially fewer nodes in the physically important range of the
parameter a,
Conclusions. The proposed scheme makes it possible to estimate the expectation values of a broad class
of cross-section functionals and to find the limits of error for these estimates. The parameters obtained for
the quadrature formulas are much more economical than those ordinarily used for these purposes, which is
especially noticeable in the calculation of integrals of high multiplicity. The approximations used in the es-
timation of the fluctuation factor are valid only for determining the optimal parameters which can then be used
directly in calculating cross-section moments from more stringent formulas of the theory of resonance reac-
tions.
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
The authors are deeply indebted to M. V. Nikolaev and L. P. Abagyan for their useful discussion and
attention to the work.
1. L. P. Abagyan et al., Group Constants for- Nuclear Reactor Design [in Russian], Atomizdat, Moscow
(1974).
2. V. F. Khoknlovetal., in: Nuclear Constants [in Russian], No. 8, Part 4, Izd. Tsentr. Nauchn. Issled.
Inst. Atominform (1972), p. 154.
3. M. Beer, Nucl. Sci. Eng., 50,171 (1973).
4. R. Hwang and H. Henyson, Trans. Am. Nucl. Soc., 22, 712 (1975).
5. L. P. Abagyan, "Methods of calculation of resonance effects in group constants for fast reactor design,"
Candidate's Dissertation, NUAR, Dimitrovgrad (1971).
6. V. V. Sinitsa and M. N. Nikolaev, At. Energ., 35, No. 6, 429 (1973).
7. A. A. Luk'yanov, Moderation and Absorption of Resonance Neutrons [in Russian], Atomizdat, Moscow
(1974).
8. V. I. Krylov and L. T. Shul'gina, Handbook of Numerical Integration [in Russian], Nauka, Moscow (1966).
9. G. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Nauka, Moscow, Vol.
1 (1973); Vol. 2 (1974).
B. M. Lebed' and I. I. Marchik UDC 539.1.074.5:538.221
One of the major problems of experimental nuclear physics is that of obtaining high coordinate resolution
when recording fission fragments, protons, neutrons, etc. In the present paper we expound some of the physical
ideas about the possibility of realizing crystal coordinate detectors. (CCD) and give experimental results.
Physical Basis. How to construct CCD is considered with the example of ferromagnets, but the pro-
cedure is equally applicable to other ferroelectrics as well.
It is well known that ferromagnets in the ground state are divided up into regions of spontaneous mag-
netization, i.e., domains. When a constant magnetic field exceeding a certain value is applied, a ferromagnet
goes over into a state without domains, i.e., into the saturation state. This transition is a phase transition of
the first kind [1].
Suppose that the ferromagnet is in a constant field H which diminishes quasistatically from values de-
termining the saturation state to values which only slightly exceed the field Ho corresponding to the onset of the
formation of the domain structure. If the difference H-Ho is small so that in respect of order of magnitude
the energy MI H -Ho! is equal to the thermal fluctuations of the spindensity (magnetization), then the nuclei of
the new magnetic phase (domains) will be localized in space near precisely such fluctuations. The process of
nucleation can be controlled if the thermodynamic fluctuations M are suppressed by slightly increasing the
difference H - Ho and can be controlled by external perturbations of the spin density. The latter can be
achieved in several ways, the most feasible of which seem to be processes of the interaction of nuclear ra-
diation with a solid. A simpler method, resulting in sufficient fluctuations of the spin density, is that of local
thermodynamic heating of the substance along the particle track. Such a process is characteristic of heavy,
multiply charged particles of the fission-fragment type. It is known [2] that a channel in which multiply
charged particles travel heats up to a temperature considerably above the temperature of magnetic phase
transitions. The transverse dimension of the heating region is several thousand interatomic distances and is
quite sufficient for nucleation of a new magnetic phase whose characteristic dimensions are comparable with
those of the domain wall (- 0 is a unit step
function, 6r o = -kfbVK1K3 is the steady-state value of the increment in the major radius of the plasma filament,
w is the angular velocity of the natural oscillations of the plasma filament, R = r1/w2A3 is the normalized am-
plitude, and Q1 and a2 are the attenuation factors for the aperiodic and periodic components, respectively, of
the transient process.
Numerical Estimates. Analysis of the Plasma-Filament Motion. Below are numerical estimates of the
expressions obtained above, as calculated for the nominal operating modes of two machines:
t?, kA
r?, m . . .
a0, m . .
. . . .
U?, v . . .
b ?rL, T .
n .
k,, c-1 .
k,, Wb/m
k,, Wb/m .
k4, Wb/m .
k,i m/ T
k4, m/A
k7 . . . .
ks .
k?, m/T. .
A,, sect .
A,, seC . .
Tuman-3
T-10M
170
1.6.103
. .
0.55
2.3
0.24
0.75
. .
0.5
1
0.36
1
. .
2:5
1
1
3.5
. .
0.5
-0.5
. .
0.68.105
1.61.108
. .
0.489
6.2
. .
0.216
3.24
. .
0.461
5.46
-0.19.104
-52.48
-0,698.10-3
-0.762.10-5
. .
-245
-5.11
. .
0.218
0.163
. .
0.120
0.107
. .
0.175
16.0
. .
0.124.10-10
0.109.10-10
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
A 2, sec3 . . . .
0.676.10-12
0.866.10-10
K1, M /V . . . .
0.872
6.69
K2, V T
0.619
0.446.10-1
Ka, V/T
40.0=
4.28
0,, 8ec'1 . . .
5.71
0.624.10-1
a2, sec. . . .
6.33
0:320.10-'
(0, sec '1 . . . .
0.509.10?
0.430.10?
R . . . .
0.311
0.494
TI, sect
0.544.10=1
7.91
2, sec . . . . .
0.676.10-9
0.2.10-10
From these data as well as from Eq. (13) for the transient process it is seen that the motion of the
plasma filament from one equilibrium position to another is advisably considered to consist of two stages:
a practically instantaneous-transposition of the plasma filament to an intermediate position with a relative
amplitude R and a relatively slow transposition, accompanied by oscillations, to a new equilibrium position
with a relative amplitude equal to unity.
The initial transposition R, as well as the attenuation factors ai and 02, characterizing the degree of
-_inertia of the plasma filament, are highly dependent on its initial parameters..
Conclusions. The present paper gives the results of the elaboration of a mathematical model of the ra-
dial motion of the plasma filament in tokamak thermonuclear machines with, account for its ohmic resistance
as well as the total flux linkage of the circuit formed in the plasma filament. 'At the same time, no account
was taken of the effect of the metallic -structures of the machine on the radial motion of the plasma filament.
A significant limitation on the applicability of this model is the requirement of a small slope for the plasma
filament (a/r >_ 1). Under these conditions it has been shown. that the motion of the plasma filament from one
equilibrium position to another under a change in the vertical magnetic field is of a complex nature. The pa-
rameters of the elements of the motion depend markedly on the initial characteristics of the plasma filament.
Analysis of the plasma-filament model for stability led to easily interpreted conditions, one of which
had been known earlier. For present-day tokamak machines whose plasma filament has a high slope (a/r
1/3) the results of the study can be rather of a qualitative than a quantitative character. In the case of ex-
perimental confirmation of the properties, however, it is- desirable to use the present model in designing sys-
tems for stabilizing the parameters of the plasma filament and in modern tokamak thermonuclear machines.
LITERATURE CITED
1. J-. Hugill et al., Nucl. Fusion, 14, 611 (1974).
2. M. Fugiwara et al., J. Appl. Phys.,.14, No. 5, 675 (1975).
3. U. Sudzuki et al., JAERI-M-6050, Tokai, Ibaraki.
4. V. D. Shafranov, Problems of Plasma Theory [in Russian], Vol. 2,. Gosatomizdat, Moscow (1963).
Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
B. A. P e s ko v UDC 621.039.51
We consider a cylindrical reactor of radius R - 6 and height 2(H -- 6), where 6 is the augmentation dis-
tance. The initial equations are of the form
Ay+x2q'=0; x2=k--1;
(p (-z, r)=q (z, r); (p (H, r)=q (z, R)=0,
where z, r are the cylindrical coordinates measured in units of neutron migration length (z = 0, r = 0 is the
center of the reactor), and c'(z, r) is the one-group neutron flux. It is assumed that the material parameter
x2 and the neutron-multiplication factor koO depend on the coordinates whereas the transport cross section and
the neutron migration length do not. The energy-distribution density q = k"~P is determined by profiling k00.
The problem consists in finding the function k??(z, r), with the constraint Ir:s km, which minimizes the coeffi-
cient of volume nonuniformity of the energy distribution:
R-8 H-6
Kv = (R-8)2 (H-8) max q (z, r)I 2rq (z, r) dz dr.
z, r J J
0 0
We consider the case of separation of variables:
X2 (Z, r)= ?'1 (z)+?2 (v); q (z, r)= 1V1 (z) V. (r); (3)
+),1V1=0; deI =1V1(H)=0; az (4)
az -n
diU2 + r dd 2 +2221'2=0; 1h2 (R)= ddr2 I =0' (5)
r=0
where MpPi is, respectively, the component of the material parameter and the neutron flux distribution with
respect to the i-th coordinate (i = 1 - z, i = 2 - r). In this case, the energy distribution can be written as:
q (z, r) =f1 (z) f2 (r) W (z, r); W =1 _;v2%z/(ki?ka );
(6)
k2?=1+)2; ft=ka 1Ui; i=1, 2,
(7)
TABLE 1. Continuous and Two-Step Optimal
Profiling of One-Dimensional Reactors (R =
H = 7; 6 = 1.2)
Continuous
Two-step
hi -
M
b
gv
bi, 1
k, 1
80
1.16
4,02
1,072
3,52
1,02
1,123
9.12
1
t'8
3., if)
2
41
1,110
1
188
2,99
1
1,02
1,148
,
,
,
2,1
1,02
1,212,
2
1,28
4,54
1,091
4,01
1,05
1,190
1,20
3,77
1,192
3,28
1,05
1,236
1,16
3,06
1,304
1,64
1,05
1,361
Translated from Atomnaya Energiya, Vol. 47, No. 2, pp. 122-123, August, 1979. Original article sub-
mitted July 4, 1978.
0038-531X/79/4702-0659$07,50 ?1980 Plenum Publishing Corporation 659
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 Declassified and Approved For Release 2013/02/15: CIA-RDP10-02196R000800020002-3
Kv,
1,52
1,24 '?------ I
0,08 0,10 0,12 0,14 0,16 0,18 2l m
Fig. 1. Dependence of K?V on ai,m for various
cases of synthesis of flattened two-dimensional
energy distribution (B = H = 7, d 1): 00) con-
tinuous profiling; 11 X 12) number of zones over
height (11) and over radius (12), l1 = 2, 3, 12 = 2,
3; -) km= 1.33; ----) km= 1.42.
where f1(z) and f2(r), respectively, are the energy-distribution curves in the plane problem (4) and radial
problem (5) with multiplication factors kio(z) and 02(r).
If k??