SOVIET ATOMIC ENERGY VOL. 49, NO. 5

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• Publication Date: November 1, 1980
• Content Type: REPORT

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Russian Original Vol. 49, No. 5, November, 1980
SOVIET
ATOMIC
ENERGY
May, 1981 .
SATEAZ 49(5) 711-796 (1980),
ATOMHAR 3HEP1'Nfl-
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is a translation of Atomnaya Energiya, a
publication of the Academy of Sciences of the USSR.
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Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
A t
Associate Editors: N. A. ,Vlasov and N. N. Ponomarev-Stepnoi
Secretary: A. I. Artemov -
I. N. Golovin
V. I. l l'ichev
V. E. lvanov
V. F. Kalinin '
P. L. Kirillov
Yu. I. Koryakin`
A. K. Krasin
E. V. Kulov
B. N. Laskorin
V. V. Matveev
I. D. Morokhov
A. A. Naumov' '
A. S. Nikiforov
A. S. Shtan'-
B. A.-Sidorenko
M. F. Troyanov
E. I. Vorob'ev
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
May, 1981
Volume 49, Number 5
November, 1980
CONTENTS
Engl./Russ.
ARTICLES
Fast Reactors with Axial Position of Oxide and Metal Fuels in the Core
- M. F. Troyanov, V. G. Ilyunin, V. I. Matveev, V. M. Murogov,
A. A. Proshkin, V. Ya. Rudneva, and A. N. Shmelev,,,,,,,,, 711 275
Theory of Unsteady Slowing Down of Neutrons in a Heavy Medium with
Arbitrary Scattering and Capture Cross Sections - S. A. Podosenov
and G. Ya. Trukhanov ... .................................... 716 278
Measurement of the 238U (n, 2n) 237U Cross Section in the Neutron Energy Range
6.5-10.5 MeV - N. V. Kornilov, B. V. Zhuravlev, O. A. Sal'nikov,
P. Raich, Sh. Nad', Sh. Darotsi, K. Sailer, and I. Chikai ................... 722 283
Investigation of the Combined Adsorption of Krypton, Xenon, and Water Vapor
of the Off-Gas of Atomic Power Stations -I. E. Nakhutin, D. V. Ochkin,
and S. A. Tret'yak .............................................. 726 286
Thin Foils of Metal Nuclides for Nuclear Research - L. G. Lishenko,
V. N. Medyanik, T. S. Nazarova, A. A. Rozen, and G. V. Shula .............. 730 290
Current Limitation in an Accelerator with Variable-Phase Focusing
-A. S. Belei, V. S. Kabanov, S. S. Kaplin, N. A. Khizhnyak,
and N. G. Shulika ............................................ 736 294
Steady Proton Beam Injector with a Current of 1 A and Energies of 100 keV
with an Ion Source of the "Ion Pump" Type.- G. A. Koval'skii,
D. V. Karetnikov, M. I. Men'shikov, N. V. Pleshivtsev, and B. K. Shembel'...... 739 296
Problems of the Radiation Hazard of 14C - I. Ya. Vasilenko, P. F. Bugryshev,
A. G. Istomina, and V. I. Novosel'tseva ................. ........ 743 299
Operational Method for Studying 3H in the Ocean and Atmosphere under Marine
Conditions - V. N. Soifer, E. A. Boroukhin, V. A. Goryachev,
Yu. S. Pozdeev, and A. F. Sergeev ....... .. .. . . .. ?????.. . . . . .. 748 303
LETTERS TO THE EDITOR
Some Physical Characteristics of Fast Reactors with Heterogeneous Core Grouping
- E. P. Kunegin, L. N. Yurova, O. M. Kovalevich, S. D. Yurchenko,
and A. N. Shmelev ............................................ 755 309
Matrix Screw Die Method for the Calculation of a Complex Lattice in P3-
Approximation - V. E. Raevskaya and B. Z. Torlin ...... . . . . . . . . . . . . . . . 757 310
Investigation of the Rate of Growth of a Fatigue Crack in Structural Steels
-L.A.Vainer and V.F.Vinokurov................................ 760 311
Sensitivity Analysis in Study of Laws Governing Radiation Distribution According
to Monte Carlo Data -A. M. Zhezlov, A. I. Ilyushkin, V. A. Klimanov,
V. P. Mashkovich, and D. N. Rybin ............ 763 313
Energy Spectra of Neutron Radiation from Spent Fuel of VVER Reactor
- N. S. Shimanskaya...................... ..................... 766 315
Neutron Radiation Yield of Spent Fuel of VVER Reactor - N. S. Shimanskaya ........ 768 316
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CONTENTS
(continued)
Engl./Russ.
Steam Entrainment in the Downcoming Zone of a Circulation Loop - L. N. Polyanin,
A. L. Putov, and A. V. Efimov .................................... 770 317
Nonstationary Diffusion of Neurons in a System Consisting of Two Media Separated
by a Planar Boundary'- A. V. Zhemerev, Yu. A. Medvedev, and'E. V. Metelkin ... 773 319
Distortion of the Neutron Field in Reactors with Randomly Distributed Perturbations of
the Macroscopic Cross Sections -V. K. Goryunov ....................... 776 321
Fast-Response Regulator. in the Spatial Dynamics of a Reactor -A. M. Afanas'ev
and B. Z. Torlin........ ............................... . . . .. 779 323
Fast Response of the Regulator in a Cylindrical Reactor - B. Z. Torlin ............ 781 324
Calculation of the Overheating of Fuel Elements, Taking into Account the
Probability of Deviations of the Core Parameters -I. M. Kurbatov ............ 783 .325
Homogenization and Heterogenization Errors in the Calculation of RBMK
-S. S. Gorodkov ............................................. 784 326
Determination of the Flux Parameters in a Vertically Adjustable Ring
Channel of a Reactor -V. N. Oleinik ............................... 786 327
Yields of 1231, 1241, 1251, 1261, 1301, 1311, and 1321 upon the Irradiation of Tellurium by Protons,
Deuterons, and a Particles and Antimony by a Particles _ P. P. Dmitriev,
M. V. Panarin, and Z. P. Dmitrieva ................................. 789 329
The y Constant of a Radioactive Nuclide in the International System of Units
- N. G. Gusev and V. P. Mashkovich ................................. 791 330
Thick Target Yields of the 12C(P,y)13N Reaction -Yu. P. Antuf'ev, V. M. Mishchenko,
A. I. Popov, V. E. Storizhko, and N. A. Shlyakhov ...................... . 794 332
The Russian press date (podpisano k pechati) of this issue was 10/23/1980.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
FAST REACTORS WITH AXIAL POSITION OF
OXIDE AND METAL FUELS IN THE CORE
M.
F.
Troyanov, V. G. Ilyunin,
V.
I.
Matveev, V. M. Murogov,
A.
A.
Proshkin, V. Ya. Rudneva,
and A. N. Shmelev
In order to'improve the technicoeconomic parameters of fast breeder reactors, one must improve the
design of reactors with oxide fuel and search for new technological solutions which are based on, e.g., the use
of other heat-transfer media; also promising are fuel varieties such as carbides, nitrides, and metal fuels
[1, 2]; The utilization of metal fuel has been contemplated from the very beginning of the development of fast
reactors and recently has again attracted the attention of researchers [3]. It is generally accepted that metal-
lic fuel has certain advantages over ceramic fuels, e.g., a) high breeding ratio (BR = 1.7-1.9) and b) possi-
bility of building reactors characterized by insignificant changes of the reactivity during their operating per-
iod, which provides advantages in the control aspect and increases the continuous reactor operation without
reactor recharging (approximately to 1 yr or more).
It is also known that the technological properties of metallic nuclear fuel (particularly plutonium-con-
taining fuel) at the present time do not allow the same temperature parameters of the steam and water cycle
of an atomic power station as do the oxide fuels. This is mainly a consequence of the difficulties of obtaining
reliable fuel-element operation at temperatures in excess of 650?C and of the unsatisfactory compatibility of
this fuel with steel at temperatures in excess of 550?C [4]. If it were possible to use metal fuel and maintain
the parameters of the steam and water cycle characteristic of ceramic fuel at a rather high burnup (- 5'770 of
the heavy atoms), it would be possible to substantially increase the excess conversion, which, in turn, would
improve the technicoeconomic parameters of an atomic power plant equipped with fast reactors. A solution
to this problem might be found (along with technological developments of new alloys, etc.) by using certain
new core designs of fast reactors which make it possible to efficiently use metal fuel in the core.
For example, the possibility of using natural or slightly enriched uranium with a low (1-2%) pile-up
level of fission products in an oxide-fuel reactor has been contemplated. This idea found its embodiment in
the so-called heterogeneous design concept of the core of fast reactors [5]. The heterogeneous core facili-
tates the solution of the problem of radiative stability of the metal fuel, because the required degree of burn-
up can be considerably reduced. However, on the fuel-element jackets with metal fuel there remain tempera-
ture conditions characteristic of the jackets of fuel elements with ceramic fuel. This makes it difficult to em-
ploy the heterogeneous core design in a fast reactor.
The present article describes the results of an investigation of another concept, which makes it possi-
ble to use metal fuel in the core of a fast reactor under temperature conditions close to previously employed
conditions [ 6 ] .
We consider a reactor in which fuel elements with a metal fuel are situated on the inlet side of the
"cold" coolant. The relatively low temperature (400-480?C) of the coolant in this part of the reactor creates
conditions favorable for the operation of such fuel elements. In the region in which the coolant is at higher
temperatures (500-560?C), fuel elements with an oxide fuel are arranged. When the metal fuel is situated in
the "low-temperature region' of the core and the oxide fuel is situated in the "high-temperature" region, the
temperature parameters of a pure oxide reactor are preserved, yet at the same time, the total breeding ratio
is increased by about 0.15. The increase in the total breeding ratio results basically from the increase in the
internal breeding coefficient of the core, which is important not only for the breeding rate of the nuclear fuel
but also for optimizing the conditions of operation of a high-power fast reactor, taking into account changes
in reactivity during continuous operation.
Translated from Atomnaya Energiya, Vol. 49, No. 5', pp. 275-278, November, 1980. Original article
submitted June 3, 1980.
0038-531X/80/4905-0711$07.50 ? 1981 Plenum Publishing Corporation
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Ttie design can be reaiizea in various ways. one can conceive a single iuei eiemeni wim me tuei filling
varying with height, the fuels being enclosed in a single jacket. Another version consists of an assembly with
lattices of various fuel elements containing metal or oxide fuel.. In this case, the metallic and oxidic fuel ele-
ments are separated by an intermediate layer containing the steel shafts of the fuel elements and sodium.
As far as the technology is concerned, the use of a single fuel element with a gas-contact underlayer in
analogy to oxide fuel is the simplest version. When separate lattices of oxide and metal fuel elements are
employed, the metal fuel elements can have either a sodium underlayer or a gas underlayer. Though the
sodium-contact underlayer is technologically more complicated, this type of underlayer makes it possible to
increase the fraction of the metal fuel in the core by increasing the relative height of the metal fuel elements.
Besides that, in fuel elements with such an underlayer, the temperature of the center of the fuel may be re-
duced to 050?C and lower if required. When different types of fuel are distributed along the height of the fuel-
breeding system, the reactor parameters can be optimized by varying the parameters of the fuel element lat-
tices, the enrichment ratio of the oxide and metal fuels, and the height of the fuel elements.
Figure 1 shows one of the versions of a calculated model of a fast breeder with a composite core. The
calculations were made for a BN-1000 reactor with use of the multigroup BNAB-78 nuclear constants [7].
Below we list the initial data used as a basis of the nuclear-physics investigations and the analysis of
the breeding parameters of fast reactors with a combination of oxide and metal fuels:
Thermal power (MW) of the reactor ............ 4200
Temperature (?C) of the coolant:
inlet to the reactor .......... ......... 354
outlet from the reactor ................. 547
Fuel density (g/cm3) in the core:
oxide .................... ........ 8.5
metal ............................. 13
Maximum bumup (% of heavy atoms) of the fuel:
oxide., .......................... 10
metal ............... ............. 15
Volume fractions of the materials in the core:
fuel ............................. 0.45
building materials .................... 0.22
coil ant ........................... 0.33
Height (cm) of the core ................... 100
It was assumed that the isotope composition of the plutonium corresponds to the composition of the plu-
tonium piled up in energy-producing thermal water-moderated water-cooled power reactors. It was assumed
that the lower lattice ofthe fuel elements has a shielding end section in the form of metallic uranium and a
core portion with metallic plutonium or uranium fuel. Oxide fuel, PuO2-UO21 is mounted in the upper fuel-
element lattice; UO2 is assumed to be present in the shielding end portion. Internal axial interlayers com-
prising fuel elements with raw material in the form of ceramics or metals can be inserted between the lat-
tices containing the various fuels.
As far as the physics, is concerned, this model of the core of a fast reactor is one of the possible core
versions with axial heterogeneity. By contrast to the usually considered heterogeneity, more favorable condi-
tions of heat generation are obtained in the case of a metal fuel; this makes it possible to substantially in-
crease the fraction of the power released in the metallic subzone.
Some results of the calculations are listed in Table 1. In a reactor in which oxide and metal fuels are
jointly used and which has parameters close to the optimum breeding rate of the fuel, the oxide subzone is
characterized by increased enrichment and by a reduced intrinsic breeding coefficient. However, this reduc-
tion of the intrinsic breeding rate is more than compensated for and offset by the increased breeding in the
metallic subzone, of reduced enrichment.
The investigations show that a certain preferable breeding value of the metallic fuel exists in relation
to the breeding of the reactor as a whole. When this value in the subzone with the metallic fuel is reduced,
the,density of the heat liberation is decreased and that means that the height fraction of the fuel-breeding sys-
tem occupied by the fuel proper is increased. However, when the height of the fuel-breeding system and the
total power are maintained, an increase in the height of the less loaded metallic portion makes it necessary
to increase the density of heat liberation in the oxide portion of the fuel-breeding system. This process is
limited by the limit temperatures of the fuel core of an oxide fuel element. At the same time, when the en-
richment in the metal subzone is increased, a relative increase in temperature takes place and the acceptable
height of the metal subzone is decreased. This also means a reduction of the breeding rate in the metal subzone.
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TABLE 1. Characteristics of a Reactor with
Combined Use of Oxide and Metal.Fuels
Fraction of height of
core filled by metal
fuel
BN,Z1600 I Reactor with oxide and
reactor with! metal fuel
oxide with single with separate
fuel grid of fuell grids of fuel
elements elem.
Radial inhomogene-
ity coef.
Axial inhomogene-
ity coef.
Total breeding coef.
Enrichment, %; of
oxide fuel ZLE/
ZHE `
Enrichment,
ZLE/ZHE, of metal
fuel
Specific excess fuel
breeding [kg/MW-
(el) ? y];
Specific reactor
charge [kg /MW (el)] .
Ratio of rel. rate of
fission product pile -
up in metal-oxide
fuels
Reactivity loss during
120 days, 6keff/keff
Fraction of total
power supplied by
metal fuel
Max. temp. 'C of
metal fuel
Efficiency factor
(net %) of atomic
power station
Doubling time
(rel. units)
1,28
1,53
10,20/12,3=
6,19/7,49
1,31
1,49
10,52/12,84
6,54/8,00
*ZLE and ZHE denote the zones of low and
high enrichment, respectively.
The highly enriched subzone with the oxide fuel plays to some extent the role of an "igniting" subzone.
The result is that though the burn-up of the fuel in the metal subzone is relatively low (4-5% of the heavy
atoms), the fraction of the burning-up initial charge in this zone is relatively large. The corresponding burn-
up of the oxide fuel amounts to 8-10% of the heavy atoms in a single irradiation period of about 1.5 yr of the
composite fuel-breeding system. We note that an increase in the average degree of burn-up of the metal fuel
in excess of 5% of the heavy atoms does not substantially increase the nuclear-fuel breeding rate.
A higher intrinsic breeding rate in the metal subzone at a power fraction of about 40% in it and a rather
high burn-tip of the initial charge render in the composite core a total breeding rate which is about 1.25 times
greater than the breeding rate in an oxide reactor under otherwise equal conditions.
The increase in the internal breeding coefficient of the core in which oxide and metal fuel are used in
combination is another important factor. In the core models with oxide and metal fuels under consideration,
the breeding coefficient of the core reaches values which are slightly greater than unity. This means, in par-
ticular, that the reactivity changes much less than in the oxide core during .the reactor operation and, for un-
changed power of the control and safety rods, it is possible to substantially increase the time between re-
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E__ 920 ~_ 50 x.50
Fig. 1. Calculation model of a reactor with a composite
core: 1, 2) metal core of low and high enrichment, re-
spectively; 3, 4) oxide core of low and high enrichment,
respectively; 5, 7) lower metal and upper oxide end
shields, respectively; 6, 8) metal and oxide portions of
the side shield, respectively (dimensions indicated in
cm).
X0,99
0,980 60
time (days)
Fig. 2. Change in the reactivity during the
operation of a fast reactor using oxide and
metal fuels in combination: 1) BN-1600 re-
actor with oxide fuel; 2) reactor with com-
bined use of oxide (U + Pu)02 and metal U +
Pu fuel (height fraction of the metal subzone
reaches 40%0); 3) reactor with combined use
of oxide (U + Pu)O2 and metallic uranium
fuel (height fraction of the metal subzone
reaches 50%).
chargings, thus increasing the load coefficient of an atomic power station. This is very important from an
economic viewpoint [8]: It improves the reactor exploitation and increases the reliability of reactor opera-
tion. Figure 2 shows the time dependence of keff during reactor operation.
It should be noted that the use of enriched metallic uranium instead of the mixed uranium-plutonium
fuel in the "metal" subzone of the core entails a substantial improvement in the reactivity changes between
reactor rechargings, as compared with the reactivity changes in the c.ore of a reactor merely having mixed
oxide fuels. An intermediate version is possible, i.e., where the metallic fuel contains a certain amount of.
plutonium in addition to 235U.
In investigations of the work of fast reactors in nuclear power generation (the considerations including
reactors of various types), the specific annual production of excess secondary fuel from the fast reactor can
be used as an indicator of the optimal breeding conditions attainable with fast reactors [9, 10]:
WAEgb,
where rb denotes the specific annual production of secondary excess fuel in a fast breeder [expressed in
kg/MW(el) ? yr]; gb denotes the specific fuel load in the fuel cycle of a fast reactor [expressed in kg/ MW (el )] ;
and WAE denotes the annual rate of the development of the .nuclear power (yr I) (see Table 2). It follows from
the table that fast reactors, in which oxide and metal fuels are used in combination, have an increased speci-
fic load and an increased breeding coefficient relative to fast reactors with oxide fuel; this reactor type allows
faster rates in the development of the entire -nuclear energy generation balanced in regard to fuel. Finally, the
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TABLE 2. Specific' Production of Excess Fuel
from a Fast Reae`tor System (load coefficient
90.8)
0,01
0,05
0,10
0,12
0,14
Reactor with
oxide fuel
reactor with a single fuel-
element lattice with
oxide-metal fuel
0,258
0,382
0,151
0,268
0,018
0,127
0,070
0,013
*AE denotes atomic energy. Conditions of
self-sufficiency of fuel are impossible in
nuclear energy generation.
combined use of mixed oxide and metal fuels requires additional research on the possible operation of fuel
elements in such a core. This may somewhat complicate the design and technology of production of fuel ele-
ments in comparison-with the conventional oxide fuel. However, any way of increasing the breeding rate im-
plies problems. It cannot be ruled out that our proposed solution might be practicable and, at the same time,
efficient in improving the parameters of fast reactors.
The authors thank L. A. Kochetkov, E. A. Stumbur, V. E. Kolesov, V. A. Apse, A. I. Zinin, and L. V.
Tochenii for useful discussions during the execution of the present work.
LITERATURE CITED
1. A. I. Leipunskii et al., Fourth Geneva Conf., USSR Rep. No. 709 [in Russian] (1971).
2. V. V. Orlov et al., in: Trans. Second Symp. of the COMECON, State and Prospects in the Work on Build-
ing Atomic Power Stations with Fast Neutron Reactors [in'Russian], Vol. 3, Fiz. Energ. Inst., Obninsk
(1975), p. 168.
3. P. Lam and W. Barthold, Trans. Am. Nucl. Soc., 27, 753 (1977).
4. J. Kittel et al., Nucl. Eng. Design, 15, 373 (1971).
5. A. I. Voropaev; At. Tekh. Rubezhom, No. 11, 3 (1979).
6. V. G. Ilyunin et al., in: Trans. Second Symp., op. cit., p.. 37.
7. L. P. Abagyan et al., At. Energ., 48, No. 2, 110 (1980).
8. E. V. Kirillov, in: Trans. Second Symp., op. cit., Vol. 1,'p. 79.
9. V. V. Orlov, V. N. Sharapov, and A. N. Galanin, in: Experience in the Exploitation of Atomic Power
Stations and Ways of the Future Development of Nuclear Energy Generation [in Russian], Vol. 1, Fiz.
Energ. Inst., Obninsk (1974), p. 251.
10. V. G. Ilyunin et al., Preprint Fiz. Energ. Inst. No. FEI-1036, Obninsk (1980).
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THEORY OF UNSTEADY SLOWING DOWN OF
NEUTRONS IN A HEAVY MEDIUM WITH
ARBITRARY SCATTERING AND CAPTURE
CROSS SECTIONS,
S. A. Podosenov and G. Ya. Trukhanov UDC 539.125.523.5
The unsteady transport of neutrons in various media is of interest for many important problems in the
physics of shielding against penetrating radiation, reactor physics, nuclear geophysics, metrology of ionizing
radiation, biophysics, etc. Practical requirements have been satisfied in the main by numerical methods. At
the same time repeated attempts have been made to solve the appropriate kinetic equation analytically (cf.
[ 1-4] and bibliographies in them), but so far no analytic solution of the kinetic equation has been found in ex-
plicit form - even for an infinite homogeneous heavy medium with a source uniformly distributed in space, for
arbitrary energy dependences of the scattering and capture cross sections Zs (E) and Zc (E). The most im-
portant steps in this direction, in our opinion, were taken in [ 1, 3]. Kazarnovskii [ 11 found an approximate
solution of the appropriate kinetic equation for Zc = 0 and arbitrary Zs (v) in the form of a power series in
_ [V(T) - v]/v, where v (T) is the average neutron velocity at time T. The solution derived contains two
terms of the expansion proportional to 42 and 43. It correctly describes the energy-time distribution of the
neutron collision density k(v, t) only near the maximum of the distribution. The awkwardness of the method
used makes it difficult to derive the third term of the expansion proportional to a. Taking account of absorp-
tion Zc # 0, except for the trivial case Zc - 1/v, is possible in principle within the framework of the Kazar-
novskii method if 2;C/2;s > 1). Then the solution for 4' can be
written in the form [ 11
W = t ex p { i-1 T-t (v, t) + (Po (v, t) + ... }
71
P; P; = P"
W-t = P = ap
where y =1n v/vmin, and vmin is the minimum neutron velocity below which it is necessary to take acount of
-
-
v 0 T J- (y) F" I- Lr/ ( -"Foy .L U J 1 2 UU 21
U
t
, PU
PI
1+= xexPudx= -[- e ; (4)
o Py (Pv)2
I2 = x2 exPll?dx -- e"' [(Pu)-' - 2 (P!,)-2+2 (P,)-3] -2(Pv)-3.
0
the effect of neutron thermalization. Substituting Eq. (2) into (1), we obtain
L (y) ' 11PU-1
v(y)+i=h(y) PU
P!I-_
1P ]I _L1 hP .I'
1 -h e i [y h 2
L
Equation (4) is a linear inhomogeneous first-order equation for q0(y, T) which can be solved if the solution of
Eq. (3) is known.
Equation (3) has the complete integral
P=at-I- $ 1'2(y, a) dy+b,
where 02 (y, a) = Py and can be found from the equation
h (y) e`''=-1. -1
'-`2 VMin
Knowing the complete integral (5), it is possible to solve the basic problem of determining the integral
surface passing through a given curve. We separate out from the two-parameter family of integral surfaces
li (P, t, y, a, b) = at + f 'I'2 (y, a) dy + b - P = 0
a one-parameter family. To do this we choose the function b = b (a) in Eq. (7) so that the envelope of the one-
.parameter family
q) [P, t, y, a, b (a)] = 0, 1
00 acD db 0
W t ab as =
passes through the given curve, which we write in parametric form:
P=P(a); y=y(t); t= ~-to; to
On curve (10) Eqs. (8) and (9) reduce to identities. In principle it would be possible to determine b (a) from
system (8)-(10), but this is a rather complicated problem. As shown in [5], b(a) can be found by using the
equation
(DPP~+(Dj~+(Dvyt=0, (11)
instead of Eq. (9). The geometrical meaning of this equation is that the tangent to the curve (10) must lie in.
a plane tangent to the surface being sought. From Eq. (11)
Yf dy dP -a
2dt - dg .
The complete integral,(7) along curve (10) has the form
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a(-CO)+ \ `F2 - d~+b-P()=0,
d
a(I;-b0)+ f ( dg -a) d~-I-b-P=O,
b (a) = ~oa;o = const. (12)
From Eqs. (12), (9), and (7) we find the equation for determining the parameter a as a function of T and y:
T {o a f 'Y2 (y, a) dy 0. (13)
By using (13) to eliminate a from (5) we obtain in principle the solution of the problem posed (3).
We find the solution of the transcendental equation (6) by using a Burmann- Lagrange series [6, 7]:
2 (y, a) _ cn (g+af)n h-n; f
n=1
L (J) e-u;
?inin
( { dn-1 (, Jn/ I'='
g = 1 - h Cn = 7;-!
(o (y) _ (ek -1 - y)l y?
n-1l
~ rw (y) =o
4 10 136
c1 = 2; c2 C3 C4 = 135
Transforming from the variables y and T to v and T, and assuming that at T = T o and v = v0 P (To, vo) = c,
we obtain
P(v,T)=c+a(T-TO)+~ ~'cn yn(1)(a-{ L (x))ndc?
V, 71=1
In integrating Eq. (16) a is assumed constant, and is eliminated by using the equation
Lt x n-1
(IX 0.
t-To+ ncn ,n+i ~a+ 77,
Let us consider the case Ec = 0, for which
T-To+C1 LsXadx Zo=
Ls ~y)
+L
1(v); I(k))
an = - (n + 1) Cn+1I((nn++2))
( (v) ,Xk dx.
By using well-known formulas for the inversion of power series [8], we find the expressions
pp ff;; 1
a - ,I NnZo + a2/a1s;
n=1
03= GCi (2a2-a1a3); N4 = i (5a1a2a3-aia4-5az),
P (v, t) = c + (k -1) CkI((j)+ 1) (v)( NnZo )k (20)
k=1 n=1
Equation (20) is an integral surface of Eq. (3) for h = 1, L = Ls passing through the.curve of the general
form (10).
Let us find the equation of the curve along which the distribution function is maximum; this is equiv-
alent to the equation P [vm (T ), T I = c, where vm (T) is the velocity along this curve. In view of the arbi-
trary dependence of Ls on v, it follows from Eq. (20) that along this curve the following relation holds:
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Equation (21) agrees with the result in [ 11, and to within the factor (M + 2/3)/(M + 1) - 1, which must be
inserted in front of the integral, corresponds to the known formula determining the energy dependence of the
slowing down time in age theory [ 91.
Restricting ourselves to Z4 terms, we obtain at points close to curve (21)
P (v, T) 3 [Ic3) (v)) ' Zo 15 I([I(2)]-3 Z3 +
16 -7T564)
3 `4 [136 (4) 25 (3) 2 (2) -1(2) -4 4
-- T 135 I(5) - 12 (I)) (1(2))) (I(3 Z0.
vo
Zo[v (T), T]_O_T-To-2 ~ L``ate) dx.
vJT)
In order to compare with the result in [1] we expand the function (22) in terms of the quantity E = [vm(T) -
vl/v and find
... ,
P = - 2 K (T) e2 - 3 L (T) 9'+
3 K (T) 2 Lsv~m( )T)) II(3) (Um)1-ti
(24)
* 9 L. (vm) dLs (vm) (2) 1 9 Ls (Um) (2) 2 45 L!, (Um) (3) (2)
L (T) _ - 4 vm - dvm II(3) (Um)1 - 4 : v.4 I_r(3) (Um)] + 32 u''m (4) (Um) II(3) (vm)] "?
The expressions for K* and L* agree with analogous expressions in [ 11 for the values
c=Lo 0
KO =.
Let us consider the case Ec (v) x 0. It is clear from Eq. (17) that the simplest case to calculate is
Lc = av, a = const. For this case
P (v,T)_=P(U,T)-L- (T-To), (2'3)
where P (v, T) is the solution of Eq. (20) when there is no capture.
For an arbitrary velocity dependence of the capture cross section the quantity a + x/Lc (x) is not con-
stant, and this complicates the computational. scheme somewhat.
It follows from Eqs. (17) and (19) that
- (T - To -I 114)Z= Jak ak;
k=1
/ n
Yk C n ` k Ln-k(X) yi+k+k dx;
v. n=k c
RR
a = l NnZn,
n=1
where an is related to an by Eqs. (19).
Using (16) and (27), we obtain the solution in the form
k
P (v, T) = u [ (1- k) Yk ~ p;~Z" )k + ck LS (X) dx
h=t n=f / roJo PLC (.x).
a
a f-v/L,(v)=a+sf;
_
? - a ] Lc [U (i)1 ' ?t ? _ Lc (v) Lc IV (T)]
and taking account of (1R) and (17), Eq. (28) can be written in a form convenient for study:
V
P (v, T) _ >(1 - k) 1'k PnZn) k (T - TO) u (i) + en L n~ i) Ei (x, T) dx,
k=2 n=1 Le - (T)1 ro, n_1 x
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V 00
L8 / n) en- h )1k = ~ I C. xn+1 1 1, J E1- dx,
vo n=k
(k=0, 1, 0...); (31)
h -*n
- (ti-t0+ )'1) _ :J aka ; ak = (k+1) Tk+f, a= U NnZ
k=1 n=1
Pn is expressed in terms of the coefficients an by Eq. (19). The average neutron velocity v(T) is an un-
known function which must be found.
If Lc = a'v, ?1 = 0, and Eq. (30) goes over into (26). The last two terms in Eq. (30) characterize the
loss of particles from the system as a result of capture, and the first term gives the contribution to the dis-
tribution function of neutrons which have escaped absorption.
The maximum of the distribution function for the neutrons which have escaped absorption will corre-
spond to an average velocity v (T) for which the equation
Z [v (1), it = 0 (32)
is satisfied. From Eq. (32) there follows a formula relating the slowing down time of neutrons which have
escaped capture and the required velocity V(T):
2 2 n n-1
i - TO.= 2 uz dv - g l v2L du - v_ f V' dv ] + 77.Cn LUn+1 dv. (33)
c Ivl
For this value of the velocity v we obtain the following expression for P[v(T), T]:
VO 9p OD r
P=J -2r Lw dvl-_J YjCn pn+1 6i-' L +(n-1) ]dv.
L. (v)
n=2
V V
If Ls/Lc of K are given in
Table 1 together with the values of the average neutron fluxes, the values obtained for the 233U (n, 2n) cross
section, and their estimated errors without taking account of the errors in the recommended cross sections
of the reference reactions. J he error of the (n-, 2n) cross section includes the following: the flux (mean-
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0
6
7
l~l
10 11 En,IvfeV
Fig. 2. Experimental values of the 238U (n,
2n) cross section: d) our results; n, 0)
data from [2] and [3], respectively.
square error of weighted mean), number of 238U nuclei (0.(3%), efficiency of Ge(Li) detector (2%), corrections
for self-absorption (1.5%), yield of 208-keV y rays (1%).
Measurements at neutron energies of 7.50 and 8.99 MeV were repeated to test the reproducibility of the
results. It is clear from Table 1 that the experimental results agree within the estimated limits of accuracy.
Our results are compared with published data in Fig. 2. The good agreement with the results in [3] should be
noted, while the data of [2] give systematically higher cross sections.
The authors thank V. A. Tolstikov for making it possible for us to use the Ge (Li) detector, G. P. Ma-
khovaya and S. A. Kremenetskaya for performing the chemical analyses of the samples, A. I: Gonchar for help
in repairing the electronic equipment, the staffs of the Physical Measurement Center of the FEI and the EGP-
10 M accelerator for help with the work, and L. Vash (Institute of Experimental Physics of the L. Kossuth
University) for making the preamplifier for the fission chamber.
The authors are grateful to the Ministry of Education and the Academy of Sciences of the Hungarian
People's Republic for their attention to the work and for financial support.
. LITERATURE CITED
1. WRENDA 76/77: INDC/SEC/-55/URFS, R. Lessler (ed.), IAEA, Vienna (1976).
2. J. Knight, R. Smith, and B. Warren, Phys. Rev., 112, 259 (1958).
3. J. Erehaut and G. Mosinski, CEA-R-4627 CEN-Saclay, Gif-sur-Yvette, France (1974), in: Proc. Conf.
Nucl. Cross Sections and Technology, Vol. 2, Washington, March 3-7 (1975), p. 855.
4. N. S. Biryukov et al., Prib. Tekh. Eksp., No. 3, 66 (1971).
5. H. Liskien and A. Paulsen, Nucl. Data Tables, All, 569 (1973).
6. C. Williamson, J. Boujot, and J. Picard, CEA-R-3402 CEN-Saclay, Gif-sur-Yvette, France (1966).
7. D. Smith and J. Meadows, ANI/ 10M-9, Aug. (1974).
8. A. I. Gonchar, in: All-Union Conf. on the Automation of Scientific Research in Nuclear Physics [in
Russian], Inst. of Nucl. Research, Academy of Sciences of the Ukrainian SSR, Kiev (1976), p. 167; A. I.
Gonchar, S. I. Chubarov, and B. V. Nesterov, Prib. Tekh. Eksp., No.4, 69 (1974).
9. S. Nagy et al., Magy Fiz. Foly., 22, 323 (1974).
10. Nuclear Data Sheets, Vol. 6 (1971), p. 539.
11. R. Gunnink, "Gamma-library file output," Lawrence Livermore, Laboratory Special Commun., Univ. Cal.,
Livermore, Oct. 1 (1975).
12. M. Sowerby, B. Patrick, and D. Mather, Ann. Nucl. Sci. Eng., 1, 409 (1974).
13. V. Kanda and R. Nakasima, in: Proc. Conf. Neutron Cross Sections and Technology, Vol. 1, Washington,
March 4-7 (1968), p. 193.
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INVESTIGATION OF THE COMBINED
ADSORPTION OF KRYPTON, XENON, AND WATER
VAPOR OF THE OFF-GAS OF ATOMIC POWER
STATIONS
I. E. Nakhutin, D. V. Ochkin, UDC '21.039.73;66.074.7
and S. A. Tret'yak
A radiochromatographic system of purifying the off-gas from the short-lived krypton, xenon, and iodine
nuclides is.presently used in Russian atomic power stations and in foreign atomic power stations equipped
with the aid of the USSR. The basic elements of the system are filter-adsorbers filled with activated carbon
and a drying unit [ 1-3]. Dynamic adsorption and radioactive decay in the adsorber cause stationary conditions
at which the concentration of the radioactive gas decreases along the height of the sorbent layer. The adsorber
is designed for operation as "perpetual column" without regeneration of the activated carbon.
The composition of the off-gas strongly influences the efficiency of adsorber operation. For example,
the adsorption of radioactive rare gases on the activated carbon is affected by the presence of carbon dioxide
[ 4], water vapor, ammonia, freon [ 5 ], and various volatile organic materials the relatively high concentration
of which iin the gas phase may "poison' the adsorbent and reduce the efficiency of gas purification. For this
reason the greatest admissible concentration of the admixtures must be determined.
The drying unit usually comprises two alternatingly working adsorption columns, i.e., one is in opera-
tion while the -other one is regenerated by hot atmospheric air or is on standby. Since the -adsorbents desig-
nated for drying the gas have many shortcomings [6], one must in each case consider all the factors influenc-
ing the process and select the optimum adsorbent. In particular, it is 'indispensable to consider the adsorbent
capacity of rare gases, which determines the size of the protective radiation shielding of the drying unit and
the -release of -radioactive gas during regeneration of the adsorbent.
We have investigated the combined adsorption of water vapor, krypton, and xenon from air on activated
SKT-6A carbon under equilibrium conditions at various temperatures and from the nitrogen flow on NaA, NaX,
CaA, CaX, and NaM zeolites, Polish "Molecular Sieves 4A" zeolite, KSM silica gel, A-i alumogel, and acti-
vated SKT-3 carbon under dynamic conditions at room temperature.
Method and Results of the Measurements under Equilibrium Conditions. The distribution of the rare
gases between the gas phase and the adsorbent was determined in a closed circulation circuit by the technique
of labeled atoms (intensity of the gamma -radiation as a measure of the concentration of 85Kr and 133Xe radio-
nuclides). The partial pressure of the xenon did not exceed 8 ? 10-3 Pa, that of krypton did not exceed 6.7 Pa.
The water vapor pressure was maintained at a particular level with a humidifier placed into a cryostat and
included in the closed circuit. The combined adsorption of water vapor and air was measured by the mass in-
crease on a spring balance with a quartz spiral.
Figure 1 represents the kinetic adsorption curves -of water vapor adsorbed on activated SKT-6A carbon
at temperatures between -30 and + 20 ?C and at a relative humidity (p/ps) between 0.30 and 0.73. The .time
after the beginning of the experiment is plotted to the abscissa; the amount of adsorbed moisture (expressed
in grams per gram adsorbent) is plotted to the ordinate.
At a low pressure of the water vapor, the adsorption equilibrium established itself relatively rapidly. In
the range of the so-called "polymolecular adsorption and capillary condensation," the rate at which the equili-
brium was established decreased - the process lasted several days. - -
The equilibrium values of the water vapor adsorption on activated carbon were used to plot the iso-
therms shown in Fig. 2. The relative humidity p/ps of air is plotted to the abscissa, the amount of adsorbed
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 286-289, November, 1980. Original article sub-
mitted November 23, 1979.
0038-531X/80/4905-0726$07..50 '?-1981 Plenum Publishing Corporation
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20 Y0 60 0 20 40 60 0 20 90 50 t,h
Fig. 1. Kinetic curves of the adsorption of
water vapor on activated SKT-6A carbon at
a)-30?C;b) 0?C; c) +20?C and p/ps = 0.73
(1);
0.56
(2);
0.39
(3);
0.71
(4);
0.60 (5);
0.49
(6);
0.40
(7);
0.68
(8);
0.60
(9); 0.45
(10);
0.30
(11).
moisture, to the ordinate. The curve does not start from the coordinate origin: the relative weight at mois-
ture zero correspondss to the adsorption of dry air. The isotherms at 0 and 20?C are S-shaped, which is
characteristic of the adsorption of water vapor on activated carbon. The same figure shows the equilibrium
coefficients of adsorption of rare gases, r/p (cm3/g), the coefficients referred to the unit mass of activated
carbon.
.Method and Results of the Measurements under Dynamic Conditions. Technical nitrogen with a relative
humidity p/ps = 0.83 ? 0.02 was at room temperature admitted to. the column with the adsorbent; the
moisture of the gas leaving the column was continuously monitored.
During the experiment, the adsorbent became gradually moist and the H2O front was shifted along the
height of the column. At specific moments, which corresponded to various positions of the front, indicator
quantities of 85Kr or 133Xe were pulsewise admitted to the gas flow at the entry to the column. The radioac-
tivity of the gas at the outlet of the column was measured with a flow-type ionization chamber whose ioniza-
tion current was recorded with a recording instrument. The partial pressure of the krypton and xenon did not
exceed 5.3. 10 2 and 8.2. 10-4 Pa in the experiments.
Figure 3 shows a series of eluent curves of krypton, which were obtained in the NaX zeolite-filled col-
umn while it became moist; the curves correspond to various positions of the chromatographic H2O front.
Curve 1 corresponds to dry adsorbent, curve 4 to completely moist adsorbent. Curves 2 and 3 characterize
intermediate states.
The eluent curves were used to calculate the average time of the passage of the chromatographic front
of krypton and xenon, T, in accordance with the formula
i = J iI (T) dil 1 (t) di,
0
where I denotes the current of the ionization chamber and T, the time, reckoned from the moment at which
the radioactive gas was admitted.
The results of some of the calculations are shown in Fig. 4, where the amount of gas that passed through
the column since the beginning of the experiment is indicated on the abscissa, and the average time of pass-
age of the radioactive "marker" is indicated on the ordinate. The passage time of the chromatographic front
of radioactive rare gases decreases from a maximum, which corresponds to the dry adsorbent and depends
upon the equilibrium coefficient of adsorption, to a minimum, which corresponds to the completely moist ad-
sorbent.
The figure includes curves representing the relative moisture p/ps: at the beginning of each experi-
ment, the relative moisture of the gas leaving the column was insignificant; after that, when the H2O front
approached the column exit, the relative moisture increased and gradually reached a constant value equal to
the moisture of the gas admitted to the column.
Discussion of the Results. The experimental data indicate that moisture significantly influences the ad-
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Fig.. 2. Combined adsorption of krypton and
xenon, along with water vapor, on activated
SKT-FA carbon at 0?C; o denotes the ex-
perimental points.
~?0,5
0 .f 10 95 20 z, min
Fig. 3. Eluent curves of xenon which were
obtained with a column filled with NaX zeo-
lite; various degrees of adsorbent moisture.
sorption of rare gases on activated SKT-3 and SKT-RA carbon, NaX, CaA, CaX, and NaM zeolites, KSM silica
gel, and A-1 alumogel.
The "poor" adsorption kinetics of the water vapor adsorbed on activated carbon in the region of the so-
called capillary condensation (see Fig. 1) made it possible to calculate the effective coefficient of thermal
diffusion with the method of [71. For example, the Deff value estimated from the kinetic curve and corre-
sponding to 20?C and the relative humidity p/ps = 0.6 was (5.6-9.5) 10-4 cm2/sec. This relatively low rate of
the diffusion of water vapor in the granules of activated carbon influences the dynamics of the process. Thus,
when the moist gas is admitted, an "overswing" of moisture is immediately observed at the exit of the column
containing activated SKT-3 carbon; the chromatographic H2O front is strongly "smeared."
The equilibrium coefficients of krypton and xenon adsorption on activated carbon change only slightly
under the influence of adsorbed water in the interval of relative humidity corresponding to the initial portion
of the isotherm (see Fig. 2). The coefficients decrease sharply in the region of polymolecular adsorption and
capillary condensation. This fact determines the degree of the required drying of the gas sent to the radio-
chromatographic system of an atomic power station.
The isotherm of water vapor adsorption on zeolite depends only slightly on the temperature and is
clearly convex [81. Therefore, the H2O front in a column containing zeolite has the form of a step, which
means that the moisture capacity of zeolite can be almost fully used in practice.
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mint 0,8
Fig. 4. The average passage time of the chromato-
graphic (front of Xe (o) and Kr (0) in an NaA zeolite col-
umn and in a "Molecular Sieves 4A" zeolite column and
the relative humidity of the nitrogen leaving the column
as functions of the amount of gas sent through the column.
The strongest adsorption of krypton and xenon was observed on CaA zeolite; the rare gases are slightly
less adsorbed on NaX and CaX zeolites. The adsorption coefficient of xenon is for these three zeolites
greater than the adsorption coefficient of krypton. The inverse pattern was observed on acid-resistant NaM
zeolite on the basis of H-mordenite. The adsorption coefficient of krypton was greater than the adsorption co-
efficient of xenon, which obviously results from the relation between the effective dimensions of the pores and
the molecules. Unfortunately, this fact cannot be used for separating krypton from zenon in the gas purifica-
tion system of a nuclear fuel regeneration unit. The relatively poor adsorption kinetics of krypton on NaM
zeolite smears the chromatographic front and the eluent peaks of krypton and xenon in the column are not
separated.
Zeolites of the types NaM and "Molecular Sieves 4A," practically speaking, do not adsorb krypton and
xenon (see Fig. 4). These zeolites are used to dry gas in radiochromatographic gas purification systems of
atomic power stations [31. Drying apparatus filled with this sorbent requires very little biological shielding.
Furthermore, during the regeneration of the zeolite by hot air, a relatively small amount of radioactive ele-
ments is released; this release is associated with the free volume of the apparatus.
The isotherm of water vapor adsorption on fine-pore silica gel and alumogel depends rather strongly
upon the temperature [ 91. The liberation of heat during the adsorption of water vapor on the adsorbents of
this type causes a "protraction" of the chromatographic H2O front: a premature overswing of the moisture
is observed. It was impossible under dynamic conditions to make full use of the static moisture capacity of
these adsorbents.
The width of the eluent peaks observed in the dynamic experiments (see Fig. 3) cannot be explained by
longitudinal diffusion of the radioactive marker in the gas phase within the column. Estimates of peak blur-
ring caused by this mechanism yield values smaller than the experimental values by at least one order of
magnitude. Nevertheless, the eluent curves are well described by the theoretical function, provided that a
finite diffusion rate of the rare gases in the adsorbent granules or an external mass transfer in a thin gas
layer surrounding the granules is assumed in the calculations. Then details such as the asymmetry of the
eluent peak can be explained. However, the available experimental data do not make it possible to estimate
the separate contributions of internal diffusion and external mass transfer.
The linear dependence of the passage time of the chromatographic front of rare gases on the moisture
concentration of the adsorbent is interesting and of practical.importance. For example, by introducing an in-
dicating amount of a radioactive rare gas into the gas stream and by measuring the time of passage through
the piled-up adsorbent layer, it is possible to estimate the degree of adsorbent poisoning by moisture, or=
ganic material, etc. This method is conveniently used to determine the degree of poisoning of activated car-
bon in the adsorber of a radiochromatographic gas purification system of an atomic power station and to esti-
mate its efficiency. Obviously, the method is suitable also for determining the degree of poisening of the ad-
sorbent by hydrocarbons of high molecular weight in the gas- and petroleum-refining industry.
Conclusions. A significant influence. of moisture in the adsorption of rare gases on activated' carbon was
established. In a radiochromatographic system, in which activated carbon is employed, the relative humidity
of the gas must not exceed values at which polymolecular adsorption sets in.
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In estimating the transition processes in the adsorber during changes in the conditions of operation, one
must take into account the considerable adsorption of the carrier gas on the activated carbon.
In gas-purification systems of atomic power stations, the Russian NaA zeolite and the Polish "Molecu-
lar Sieves 4A" zeolite, which are characterized by considerable moisture capacity and good dynamic proper-
ties, can be recommended for the drying of gas. The moisture capacity of these zeolites depends only slightly
on the temperature, and the adsorbents hardly sorb any krypton and xenon, which is very important for the
biological shielding aspects of equipment.
The linear dependence of the time in which rare gases pass through the layer can be used in practice to
determine the degree of adsorbent poisoning.
The authors thank A. N. Dekalova for help in the present work.
LITERATURE CITED
1. I. E. Nakhutin and D. V. Ochkin, Inzh.-Fiz. Zh., 9, No. 1, 112 (1965).
2. I. E. Nakhutin, D. V. Ochkin, and Yu. V. Linde,. Zh. Fiz. Khim., 43, No. 7, 1811 (1969).
3. I. E. Nakhutin et al., At. Energ., 44, No. 3, 251 (1978).
4. A. M. Trofimov and A. N. Pankov, Radiokhimiya, 7, No. 3, 293 (1965).
5. R. Adams et al., Ind. Eng. Chem., 51, No. 12, 1467 (1959).
6. C. Colley, Brit. Chem. Eng., 17, No. 3, 229 (1972).
7. D. P. Timofeev, Kinetics of Adsorption [in Russian], Akad. Nauk SSSR, Moscow (1962), p. 95.
8. V. A. Sokolov, N. S. Torocheshnikov, and N. M. Kel'tsev, Molecular Sieves and Their Use [in Russian],
Khimiya, Moscow (1964), p. 38.
9. O. M. Dzhigit, A. V. Kiselev, and G. G. Muttik, Kolloidn. Zh., 23, No. 5, 553 (1961).
THIN FOILS OF METAL NUCLIDES FOR
NUCLEAR RESEARCH
L. G. Lishenko, V. N. Medyanik,
T. S. Nazarova, A. A. Rozen,
and G. V. Shula
The development of methods of obtaining thin foils of metal nuclides employed as targets in nuclear re-
search [1] was initiated in 1956 in Kharkov Physicotechnical Institute. At the present time four methods are
employed; the methods differ in the way in which the material is admitted and in the temperature conditions
of the deposition: electrolysis of aqueous solutions of metal salts, evaporation of the metal in vacuum, vac-
uum-thermal reduction of the metal from compounds, and decomposition of volatile metal halides on a heated
substrate. All the methods, except for the evaporation method, imply chemical reactions. Therefore, vacuum-
thermal processes can be used to obtain foils at a low temperature from compounds which do not decompose
under normal pressure. It should be noted that for obtaining foils from metal nuclides by evaporation, a
molecular flow of metal vapor is required. In order to improve the uniformity of foil deposition, the equip-
ment is usually provided with a device for shifting the substrate relative to the evaporator.
Each method has its particular advantages and shortcomings. Summarizing, it should be noted that
evaporation is used mainly for obtaining thin foils, whereas the chemical techniques, which are characterized
by high yields, are used to produce foils of greater thickness.
Electrolytic Deposition. Only a few of the many known electrolytes are used to deposit foils of metal
nuclides [2]. The reason is that in the case of a small amount of a nuclide, the electrolytes employed have a
low concentration of the metal to be deposited and are continuously depleted. The electrolytic technique is
characterized by low temperature of.deposition, by relatively low losses (up to 3%) of the nuclide, and by high
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 290-293, November, 1980. Original article sub-
mitted January 30, 1979; revision submitted March 18, 1980.
730 0038-531X/80/4905-0730$07.50 ? 1981 Plenum Publishing Corporation
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70-31 I 1 ~ I I
770 1270 1770 2270 2770
Temperature, ?K
Fig. 1. Temperature dependence of the rate of evapora-
tion of metals.
yield (90%) of the metal. In the majority of cases, sulfates of the metal nuclides (Fe, Ni, Co, Cu, Zn, Cd, Rh,
In, and Ag) are used as the components of the electrolyte; in some cases, chlorides or complex chlorides (Bi,
Sn, Ir, Ru, Pd, and Pt) or synthetized salts [2-5] of organic complex acids (Pb and Os) are employed. Cu, Ta,
steel alloys, and Al are used as substrates. In order to facilitate the mechanical separation of the foils, the
substrates are polished before their use. Copper substrates are dissolved in acids or solvents of various
compositions, depending upon the nature of the foil deposited [ 51.
The internal stress is increased in Cr, Fe, Ru, and Rh foils obtained by electrolytic deposition. There-
fore such foils are destroyed when they are removed from the substrate or when they are stored. Changes in
the conditions of deposition (current density, temperature of the electrolyte, and its composition) have little
influence upon the internal stress. The internal stress is substantially reduced when the electrolysis is per-
formed with an asymmetric alternating current or by subsequent annealing of the foil in vacuum [2, 3].
Electrolytically deposited foils are characterized by rather uniform thickness (within the limits ? 5%),
which depends upon the composition of the electrolyte, the electrolysis conditions, and the geometry of the
electrodes [5]. Since it is impossible to deposit foils of many metals by electrolysis, it is interesting to con-
sider the use of organic solvents in which either a salt of the metal or organometallic compounds can be dis-
solved. Significant progress has not been achieved in this field and only sparce information on Ge ['F] and Al
[7] foils produced with this method has been published.
Evaporation of Metal Nuclides in Vacuum. Though metallization by evaporation in vacuum is widely em-
ployed, the foils obtained from metal nuclides in this manner have been treated in only a few papers. The pos-
sibilities of the technique can be assessed with the known values [8] of the vapor pressure and the evaporation
rate of the, metals. It follows from the data that the deposition rate of a foil 'is rather high at a metal vapor
pressure of more than 1 Pa. The majority of metals have such a vapor pressure at temperatures of up to
2000?K, and heating to a higher temperature is required for a much smaller number of metals. The internal
stress developing within the foil limits the deposition rate.
The evaporators are usually made from refractory materials, mainly W and Ta, and also Mo, Nb, Pt,
Ni, and ceramics. In order to obtain foils of metals which are hard to evaporate, electron beam heating of a
molten droplet is usually employed so that the evaporator and the heating unit are not contaminated by the
material. The uniformity of the foil thickness depends mainly upon the geometry of the system, the type of
the evaporator, and the solid angle of the vapor flow. High uniformity of ? (3-5)% is obtained by eccentrically
positioned evaporators at a rotating substrate.
Substrates which do not dissolve or which dissolve in acids, organic solvents, and water are used for
depositing foils. The foils are mechanically removed from unsoluble substrates (of tantalum or steel alloys).
The linear foil thickness depends upon the parameters of the process such as the vapor pressure of the metal
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Fig. 2. Pressure dependence of the temper-
ature of deposition of metal nuclide foils.
evaporated, the rate of evaporation, and the deposition time. The quality of the foil is substantially influenced
by the vacuum which restricts the amount of gaseous contaminants introduced. Usually metal is evaporated
under a residual pressure of 10-7-1074 Pa.
The technique of producing foils from the nuclides of certain metals has been described in several
papers. Foils of Se [9, 10], Mn and Ge [9], Mg [11], Ti [12], Er and Sc [13], and Ti, Zr, and Hf [14] are de-
posited by evaporation from a tantalum (molybdenum) microevaporator at 600-1700 ?K. Lavsan 1-2?m thick,
steel alloys, or tantalum is used as the substrates. When thallium is deposited, one also employs a sub-
strate of zinc foil which is afterwards dissolved in hydrochloric acid; Ti, Zr, and Hf are deposited on Cu and
Mo which are separated by dissolution in diluted (1: 1) nitric acid. Thin target foils made from metals which
are hard to evaporate (Mo, Ta, Nb, W, Re, Os, Zr, and Hf) are deposited on a carbon substrate by evaporation
performed with the aid of electron beam heating [ 151.
Reduction of Compounds in Vacuum. Thermal reduction in vacuum allows the use of oxides of metal
nuclides for obtaining metal foils., The method is limited by the following details:
1. High vapor pressure and high evaporation rate of the reduced metal and relatively low volatility of
the metal-reducing agent.
2. Extremely low temperature of the reduction reaction.
3. High degree of purity of the metal-reducing'agent.
4. High vacuum of the reaction chamber (Pres - 10-' Pa).
It follows from Fig. 1 that Ce, La, Zr, and Th [ 16] are the most convenient. reducing agents of rare-
earth metals; Ta is conveniently employed as the material of the evaporator and reaction vessel. In some
cases, tantalum acted as the reducing agent at the same time. According to the thermodynamic data (Fig. 2),
the temperature of reduction of rare-earth metals from oxides in a thermal process in vacuum can be de-
creased with increasing vacuum in the reaction chamber; thorium is the reducing agent of highest efficiency
in this respect [171.
It was established in investigations of the kinetics [ 17-201 of thermal reduction of rare-earth metal ox-
ides in vacuum that the rate of deposition and the yield of the metal depend strongly upon the pressure with
which the reducing agent was compacted, the composition of the layer, and the temperature of the reducing
agent. Practically no metal leaves a layer which was not compacted. The optimum compaction pressure is
250-300 MPa. A thin (S = 1.0 ?m) foil of Dy, Er, Nd, Gd, Lu, Sm, Eu, and Yb nuclides was obtained [ 16, 21,
221 by rolling vacuum condensates when the oxides of these metals were reduced with La and Th. However,
high plasticity of the condensates and precision rolling equipment are required for this purpose.
When one wishes to obtain plastic foils, particularly those of rare-earth metals, both high vacuum in the
chamber and a preliminary treatment of the initial materials are of great importance. The initial- oxide of the
nuclide must be calcined in air at 1100?K to remove organic impurities, and, before the reduction, the charge
must be degassed in vacuum for a long time in the reaction vessel proper and at a temperature slightly below
the temperature of reduction [231. In the preliminary treatment, the total concentration of admixed oxygen,
nitrogen, hydrogen, and carbon in the foil is reduced to about 10 2%, which increases the plasticity of the foil
and, in addition, also allows the use of the purified metal, which previously was degassed in vacuum, as re-
ducing agent.
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TABLE 1. Optimum Conditions for Produc-
ing Foils of Metal Nuclides by Thermal Re-
duction of Oxides in Vacuum
Group (metal)
Reduc-
ing
agent
Optimum
compos.
of charge
(oxide:
metal),
moles
Optimum
temp. *K,
of educing
agent
Ref.
Alkali and earth-
alkali metals
Mg
1300
1271
Mg
2100
[211
Zn
1200
1281
Ca
1950
124]
Rare-earth metals
[16, 20,
23]
Yb
Zr
1:3
1200
[20, 21]
11o, Er, Dy, Sc
Th
:3
1800
[13, 16,
17,19,311
Ta
1211
Ta
[25]
Al
[26]
By reduction of the corresponding oxides with tantalum in high vacuum, the nuclides of Mg and Ti [21],
Ca [241, and Cr [25] were obtained in the form of films on substrates or in the form of foils. Though the use
of tantalum implies a higher reaction temperature, it appears promising to use tantalum because it eliminates
additional contamination of the foil by the metal of the reducing agent. Since no data are available, it is not
possible to reliably calculate the thermodynamically possible interval of the reduction temperatures and to
assess tantalum as a reducing agent. It is known from experiments that Ti and Mg [21], as well as Ca [24],
are reduced by Ta at relatively low temperatures (see Table 1). The method was used to produce foils of
nuclides of Fe (reduction of Fe203 by aluminum) [26], Eu (reduction of Eu203 by lanthanum) [21], Mg [27],
and Zn [28] (reduction of MgO and ZnO by titanium). It should be noted that the uniformity of a foil obtained
by thermal reduction of compounds in vacuum is affected by the same, factors as in the case of vacuum evap-
oration.
Decomposition of Volatile Metal Halides. The decomposition of volatile compounds of metals, mainly of
iodides and chlorides, on a heated substrate in vacuum is an efficient method of producing thin foils of metal
nuclides. The method is based on well-known work on producing titanium and zirconium of high purity by the
decomposition of tetraiodides of those metals in a closed evacuated volume [321. In the KhFTI there were de-
veloped a method and equipment [ 33-36 ] for obtaining foils of metal nuclides having a high melting point com-
pared to the decomposition temperature of the halide, low volatility, and a tendency to form highly volatile
halides.
In investigating the thermodynamics of the decomposition of halides [37], it was established that foils
are most easily produced from Ti, Zr, and Hf tetraiodides, Nb, Ta, Mo, and Re pentachlorides, W hexa-
chloride, and V and Cr diodides. The decomposition temperature of those compounds decreases with de-
creasing pressure as shown in Fig. 2, and the yield of the metal increases at the same time. With increasing
atomic number of the element and decreasing valency of it, the deposition temperature of the foil increases.
Since the deposition temperature of a foil must be much lower than the melting point of the metal, one can say
that a foil of metals of increased valency can be obtained by decomposotion of halides at increased pressure,
i.e., accordingly, at an increased rate, than foils of tetravalent metals.
Investigations of the kinetics of metal-foil deposition from halides [38-42] have revealed that the char-
acteristic bell-shaped curve of the temperature dependence of the deposition rate results from the simultane-
ous occurrence of three competing processes on the heated substrate: decomposition of the halide under for-
mation of the metal, reaction of the deposited metal with the halide vapor under formation of not-very-volatile
halides, and evaporation of the deposited metal. The halides of the metal nuclides used to produce foils are
synthetized directly from the elements in a degassed, evacuated glass apparatus and distilled into tubes [ 33,
34]. If necessary, the metal nuclide is initially obtained from oxides by thermal reduction with calcium.
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TABLE 2. Optimum Conditions for Produc-
ing Foils of Metal Nuclides by Decomposi-
tion of Nonvolatile Halides
Temperature, ?K
Mate-
Metal
Halide
Evapo-
substrate
rial of
sub
Ref.
rator
strate
Ti
T114
440
1400
Me
[33]
Zr
ZrI4
540
1500
?
(33J
Ili
Hf14
540
1500
?
(41]
NI)
NbC15
400
1400
?
[35]
Ta
TaCI
400
1400
[351
Mo
MOCI3
500
1200
Cu
[43]
W
WC]?
400
1600
Mo
[36]
Cr
Cr214
1070
1300
Mo
[331
V
V214
700
1300
Be
[35]
Dy
Dy!3
1200
1400
[44, 451
IIo
Ho13
1100
1500
144, 45]
Tm
TmI3
1100
1300
[44, 45]
Lu
Lul3
1100
1300
?
[44, 451
The halides are decomposed in a vacuum chamber (Pres " 10-3 Pa) on a hot molybdenum substrate.
The halide vapors arrive from the evaporator at the substrate via a vapor duct. The decomposition products,
as well as the unreacted halide, are retained in a trap cooled with liquid nitrogen [33, 34] and regenerated
thereafter. At Pres > 1 Pa the foil absorbs a considerable amount of gas and becomes brittle. The foil is
separated by dissolving the substrate in diluted (1: 1) nitric acid.
Optimum conditions for producing foils of metal nuclides by decomposition of volatile halides are listed
in Table 2. The yield of the nuclide in the foil usually does not exceed 50%. The uniformity of a foil over its
thickness depends strongly upon the geometry of the halide vapor flux relative to the substrate and varies
within ?6%. Since the method implies that metal foils are deposited on a substrate heated to a high tempera-
ture, the foils are contaminated by the material of the substrate. For example, the concentration of molyb-
denum in Ti, Zr, and Hf foils increases at increasing temperature of the substrate and decreases when the,
rate of deposition is increased. The maximum amount of molybdenum is observed in titanium foils [ 46 1.
LITERATURE CITED
1. A. P. Klyucharev and N. Ya. Rutkevich, Zh. Eksp. Tekh. Fiz., 38, 2857 (1960).
2. V. N. Medyanik, V. N. Karev, and A. P. Klyucharev, Ukr. Fiz. Zh., 9, No. 7, 798 (1964).
3. V. N. Karev et al., Zh. Priki. Khim., 39, No. 11, 2525 (1966).
4. V. N. Medyanik, V. N. Karev, and A. P. Klyucharev, Ukr. Fiz. Zh., No. 5, 560 (19(36).
5. V. N. Karev and V. N. Medyanik, in: Physics of Metals [in Russian], No. 26, Naukova Dumka, Kiev
(1969), p. 97.
6. C. Fink and V. Dakras, J. Electrochem. Soc., 95, No. 2, 80 (1949).
7. E. Peled and E. Gileadi, J. Electrochem. Soc., 123, No. 1, 15 (1976)'._
8. R. Honig, Radio Corp. Am., 23, No. 4, 567 (1962).
9. T. S. Nazarova and A. A. Rozen, Prib. Tekh. Eksp., No. 3, 226 (1974).
10. J. Galant, in: Proc. Annual Conf. on Nuclear Target Development, Atomic Energy Ltd., Chalk River
(1975), p. 171.
11. J. van Andenhove et al., in: Proc. Annual Conf. on Nuclear Target Development, Atomic Energy Ltd.,
Chalk River (1975), p. 127.
12. T. S. Nazarova and A. A. Rozen, Prib. Tekh. Eksp., No. 1, 217 (1972).
13. T. S. Nazarova and A. A. Rozen, Prib. Tekh. Eksp., No. 6, 246 (1975).
14. R. Glover, F. Rogers, and T. Tuplin, Nucl. Instrum. Methods, 102, 443 (1972).
15. P. Maier, Nucl. Instrum. Methods, 102, 485 (1972). -
16. L. Westgaard, and G. Byornholm, Nucl. Instrum. Methods, 42, 7780 (1966).
17. T. S. Nazarova and A. A. Rozen, in: Problems of Atomic Science and Technology, Ser. General Physics
and Nuclear Physics [in Russian], No. 3 (3) (1978), p. 65.
18. G. G. Gvelesiani and D. I. Bagdavadze, Soobch. Akad. Nauk Gruz. SSR, 42, No. 1, 151 (1966).
19. G. Schiffmacher and' F. Trombe, Ct. Rd. Acad. Sci., C 268, No. 2, 159 (1969)..
20. V. N. Karev et al., in: Metal Physics,.No.26 [in Russian], Naukova Dumka, Kiev (1969), p. 92.
21. S. Maxman, Nucl. Instrum. Methods, 50, No. 1, 53 (1967)..
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
22. ' E. Kobisk and W. (3risham, Mater. Res. 13ull., 4, M. V, nol llynu).
23. L. G. Lishenko et al., Prib. Tekh. Eksp., No. 1, 19 (196.8) .
24. G. Stinson, in: Proc. Annual Conf. on Nuclear Target Development, Atomic Energy Ltd., Chalk River
(1975), p. 100.
25. C. Bouchard, in: Proc. Annual Conf. on Nuclear Target Development, Atomic Energy Ltd., Chalk River
(1975), p. 74.
26. W. Riel, in: Proc. Annual Conf. on Nuclear Target Development, Atomic Energy Ltd., Chalk River
(1975), p. 167.
27. I. Sugai; Preprint Inst. Nucl. Study, Tokyo Univ., No. 150 (1975).
28. I. Sugai, Preprint Inst. Nucl. Study, Tokyo Univ., No. 149 (1975).
29. A. D. Bondar', V. N. Karev, and A. P. Klyucharev, Prib. Tekh. Eksp., No. 4, 136 (1961) .
30. A. D. Bondar', V. N. Karev, and A. P. Klyucharev, Prib. Tekh. Eksp., No. -2, 177 (1961).
31. T. S. Nazarova and A. A. Rozen, in: Problems of Atomic Science and Technology, Ser. General Physics
and Nuclear Physics [in Russian], No. 2(8) (1979), p. 31.
32. A. E. van Arkel, in: Methods of Obtaining Pure Metals [Russian translation], IL, Moscow (1957), p. 80.
33. A. D. Bondar' et al., Izv. Akad. Nauk SSSR, Ser. Fiz., 24, No. 7, 929 (1960).
34. L. G. Lishenko et al., Prib. Tekh. Eksp., No. 4, 37 (19638).
35. V. N. Karev et al., Izv. Akad. Nauk SSSR, Ser. Fiz., 32, 328 (1968).
36. L. I. Kovalenko and A. A. Rozen, Prib. Tekh. Eksp., No. 3, 260 (1970).
37. L. G. Lishenko and A. A. Rozen, in: Problems of Atomic Science and Technology, Ser. General Physics
and Nuclear Physics [in Russian], No. 3(3) (1978), p. 57.
38. A. P. Klyucharev et al.., Izv. Akad. Nauk SSSR, Ser. Met., No. 6, 81 (1968).
39. L. G. Lishenko et al., Izv. Akad. Nauk SSSR, Ser. Met., No. 3, 91 (1971).
40. L. I. Kovalenko et al., Zh. Fiz. Khim., 47, No. 6, 1606 (1973); VINITI Dep. No. 5513-73.
41. L. G. Lishenko and A. A. Rozen, in: Problems of Atomic Science and Technology, Ser. General Physics
and Nuclear Physics [in Russian], No. 3(3) (1978), p. 60.
42. B. S. Lysov, A. N. Tumanov, and V. N. Anikin, Izv. Vyssh. Uchebn. Zaved., Tsvetn. Metall., No. 4, 75
(1975).
43.- A. P. Klyucharev et al., Prib. Tekh. Eksp., No. 4, 197 (196Q).
44. L. G. Lishenko, T. S. Nazarova, and A. A. Rozen, Prib. Tekh. - Eksp., No. 4, 243 (1972).
45. L. G. Lishenko et al., Zh. Neorg. Khim., 18, No. 4, 921 (1973).
46. L. G. Lishenko and A. A. Rozen, in: Problems of Atomic Science and Technology, Ser. General Physics
and Nuclear Physics [in Russian], No. 2(8) (1979), p. 33.
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
A. S. Belei, V. S. Kabanov,
S. S. Kaplin, N. A. Khizhnyak,
and N. G. Shulika
In recent years, successes have been achieved in the creation of small-sized accelerating. structures of
heavy-particle linear accelerators, in which the stability of the motion is provided by means of variable-phase
focusing (VPF) [1, 2]. The VPF method is simple in application and, by using it, favorable conditions are
created for increasing the rate of acceleration. The acceleration process is started at a quite low injection
energy (0.07-0.08 MeV for protons), which is of decisive importance in the development of linear small-sized
heavy-particle accelerators.
However, there is an opinion [3] that the VPF method is unsuitable for providing stable acceleration of
intense beams of ions. For example, in [3] for a 1.8-MeV proton accelerator with asymmetric phase-variable
focussing (APVF), the limiting value of the accelerated current obtained does not exceed 32 mA and, by the
numerical computation of the effect of the space-charge forces within the scope of the "large particle" model,
the value is 15 mA. Such cautious estimates have originated as the result of the nonoptimum choice of the
operating characteristics of the accelerating-focusing channel. Using a new approach to the choice of ac-
celerator parameters with VPF [4], a heavy-particle linear accelerator can be developed with a higher value
of the limiting current, which also is the purpose of the present paper. . .
When investigating different versions of design of the accelerating-focusing channel, it was established
[4] that with a different distribution of the synchronous phase over the focusing period (containing several hf
accelerating periods), there is an optimum value of the number of hf periods n occurring in one focusing
period, which depends on the initial relative velocity /3 at the channel inlet and the specific rate of accelera-
tion. In order to maintain the working current in the center of the stability diagram, it is necessary with in-
crease of /3 to increase n also. By means of the method introduced, the accelerating-focusing channel in a
small-sized 3-MeV deuteron accelerator with VPF [5], consisting of three focusing periods, was calculated.
The first period contains a 3.5 hf period (structure in a ir-wave), the second - 4, and the third - 4.5. The syn-
chronous phase distribution over the hf periods of the accelerator obtained in this way is given in Table 1.
The accelerator is described in more detail in [5]. The principal parameters of the MLUD-3 accelera-
tor are given below (data relating to capture by the accelerator in the longitudinal and transverse planes, ob-
tained without taking account of space-charge forces):
Range of energy of accelerated
particles, MeV .................... 0.15-3
Operating wavelength, m ............ . 3
Strength of accelerating field in the gap, MV/m. 7.8-8.0
Total length of accelerator, m ............ 1.2
Diameter of resonator, _m ................ 0.5
No. of accelerator periods ................ 24
Diameter of drift tubes, m:
first ............................. 0.01
last ............................. 0.041
Extent of phase capture region at the
synchronous energy level, deg ............ 60
Transverse normalized acceptance for particles
with energy spread of i 15q cm ? mrad ....... 0.2'r
In this present paper, an investigation was carried out of the Coulomb current limit in the MLUD-3 ac-
celerator. The results were obtained by the numerical modeling method, using the "coarse particle" model.
The motion of the particles in the accelerator was investigated beforehand by the method of mathematical
modeling of the particles, without taking account of space-charge forces [6]. The regions of capture (accep-
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 294-295, November, 1980. Original article sub-
mitted February 27, 1980.
736 0038-531X/80/4905-0736$07.50 ?1981 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
TABLE 1. Synchronous Phase Distribution
with Respect to Accelerator Gaps
No. of
Phase,
No. of Phase
No. of
Phase,
gaps
deg
,
gaps deg
gaps
deg
.1
-35
0
-25
2
-10,5
55
40
3
43,5
55
55
4
65
50
60
5
31,5
25
50
6
-12
-15
15
7
-42, 2
-47,5
-30
8
-42,2
-47 , 5
-73,1
WW-WS,%
WS
12
~
-45 36 15 0
15 JO 95 60
R?, deg
-s
Fig. 1. Separatrix of the MLUD-3 accelera-
tor, without taking account of the space-
charge forces of the particles.
tance) in the longitudinal and transverse planes were determined. Figure 1 shows the separatrix of the ac-
celerator in the coordinates (W - Ws)/Ws, Orp. Here, W is the energy of an arbitrary particle; Ws is the
synchronous energy; Ocp is the deviation of the phase of the arbitrary particle from synchronous. At the en-
ergy level of motion of the synchronous particle for Ws = 150 keV, the extent of the longitudinal capture re-
gion amounted to 60? (accelerator capture coefficient 0.17)
The numerical modeling, taking account of the repulsive action of the space charge, was carried out by
using a program developed in [3]. For the numerical calculations, the spread of particles with respect to
initial energy was assumed to be equal to ?1%, the radius of the beam at the accelerator inlet was 0.25 cm,
initial slope of the trajectory was,30 mrad, 'and the accelerating field in the gaps was approximated by a
"square wave."_ The transverse acceptance of the accelerator, obtained without taking account of Coulomb
forces, is given in Fig. 2. In the course of the investigations, the current at the accelerator inlet Iacc was
determined for different values of the injection current Iinj. The normalized emittance of the beam ir/3ab, in
accordance with Fig. 2, was assumed to be equal to 1r ? 0.09 mrad' cm (Fig. 3). It can be seen that the acceler-
ator current increases linearly at first with increase of the injection current, then the increase slows down,
reaching 0.325 A with an injection current of 4 A. With further increase of the injection current, a drop in
the accelerator output current is observed. On the linear section, the accelerator capture coefficient right up
to an injection current of - 1 A is very close to the value obtained with zero intensity. This result is explained
by the fact that the main limitations of the beam current in the accelerator are due to longitudinal movement,
as the transverse emittance of the beam was chosen less than the emittance of the accelerator [7].
The dependence of the accelerator current on the emittance of the beam at the inlet is shown in Fig. 4.
The injection current is chosen equal to 4 A, which corresponds, according to Fig. 3, to the maximum accel-
erated current. On the axis of abscissa, the maximum slope, of the particle trajectory is R' = dR/dz, which
for a given beam radius R is proportional to the emittance. The curves in. Figs. 3 and 4 are drawn by taking
account of the mean statistical spread, proportional to 1/', where N is the number of "coarse" particles.
The maximum value of the current at the accelerator outlet corresponds to conditions of total coinci-
dence of the beam emittance with the channel acceptance (see Fig. 2), which are achieved for R' = 50 mrad.
With increase of the beam emittance, the accelerator current falls, as limitation with respect to the trans-
verse motion begins, because the beam emittance exceeds the channel acceptance. Somewhat unexpected is
the drop in the accelerator current with reduction of the beam emittance. It is possible that this is associated
with the conditions of its overfocusing or the development of instability with increase of the phase density of
the particles in the beam.
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Fig. 2. Radial acceptance of accelerator for
an energy spread of the particles at the inlet
within the limits of ? 1%a.
7 2'3 4 3 5 7
1frip A
Fig. 3. Dependence of accelerated ion cur-
rent on the injection current.
Fig. 4. Dependence of accelerated ion cur-
rent on the maximum initial slope of the par-
ticle trajectory.
The results given show that the VPF method is quite promising for the development of small-sized
linear heavy-particle accelerators with'a beam intensity of the order of several hundred milliamperes.
1. Ya. Fainberg, in: Proc. Symp. on High Energy Accelerators and Pion Physics,. Vol. 1, Geneva CERN,
(1956), p. 91.
2. M. Good, Phys. Rev., 92, 538 (1953).
3. Linear Ion Accelerators, Vol. 1, Problems and Theory [in Russian],.Atomizdat, Moscow (1979), p. 264
4. V. G. Papkovich, N. A. Khizhnyak, and N. G. Shulika, in: Problems of Nuclear Science and Technology,
Ser; Techniques of Physics Experiment [in Russian], No. 2(2) (1978), p. 51.
5. L. N. Baranov et al., in: Problems of Nuclear Science and Technology, Ser. Linear Accelerators [in
Russian] (1977), p. 12.
6. V. Yu. Gonchar et al., Ukr. Fiz, Zh., 24, No. 11, 1705 (1979).
7. I. M. Kapchinskii, Dynamics of Particles in Linear Resonance Accelerators [in Russian], Atomizdat,
Moscow (1966).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
STEADY PROTON BEAM INJECTOR WITH A
CURRENT OF 1 A AND ENERGIES OF 100 keV
WITH AN ION SOURCE OF THE "ION PUMP" TYPE
G. A. Koval'skii, D. V. Karetnikov,
M. I. Men'shikov, N. V. Pleshivtsev,
and B. K. Shembel'
In this paper, a constant proton beam injector* is described, for injection into a high-powered continu-
ous-action accelerator [ 1] with an input acceptance of 10 cm ? mrad. At the start of the project, only one in-
jector [2] was known with an intensity close to. 0.75 A, but it was insufficient for the problem posed and had a
beam energy of 100 keV.
The operation of a steady injector with a high beam intensity is characterized by considerable thermal
loads in the formation region and by a high electric field. The electrical strength of the accelerating inter-
electrode gaps in this region can be maintained only under good vacuum conditions which, in their turn, are
provided by small flows of a neutral gas from an ion source. In the injector described in [2], and also in in-
jectors [3, 4] capable of creating beams with an intensity of up. to 0.6 A, the pressure of the gas in the dis-
charge chamber of the source amounts to 1-10 Pa.
In the source developed by us, the discharge chamber is connected with the region of formation by a
large-area opening. The gas pressure in the discharge chamber is reduced to approximately 10-1 Pa. The
pressure drop between the discharge chamber and the precathode discharge region (in which it amounts to 1
Pa) is created because of the use of the ion pumping effect. This mechanism for removal of the gas was used
for the first time in the vacuum ion pump [ 51. In this paper, a ratio of the values of the pressure between the
precathode region and the discharge chamber of -500 is obtained.
The diagram of the "ion pump" source is shown in Fig. 1. The low-vacuum region 1, where the heated
cathode 2 with an extended emission surface is located, is joined by a narrow channel 3 with the main dis-
charge chamber 4, in which a higher vacuum is created. The plasma of the gas discharge 5, collimated by a
longitudinal magnetic field, extends to the anticathode 6. The body of the chamber 7 serves as the anode. The
plasma flow from the source into the vacuum takes place through the opening in the anticathode 8.
A stable discharge is established with a longitudinal magnetic field of 0.02-0.04 T. The maximum plasma
output also corresponds 'to these values of magnetic induction. With increase of the field above 0.06 T, the in-
tensity of the oscillations in the plasma increases strongly and, correspondingly, the radial flow of ions due
to Bohm diffusion. With increase of the arc current, in all cases there corresponds an increase of the proton
components which, in long chambers with a voltage in the discharge of U = 200 V, can reach 80-90%.
*Work carried out in 1967.
Fig. 1. Schematic diagram of an ion source
(the direction of flow of the gas in the ion
source is shown by the arrow).
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 296-299, November, 1980. Original article sub-
mitted November 30, 1979. .
0038-531X/80/4905-0739$07.50 ? 1981 Plenum Publishing Corporation 739
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
'2000 i 9600
Fig. 2. Diagram of the proton injector.
The structural design of the ion source, to a considerable degree, is dictated by the beam shaping condi-
tions. One of the most important elements of the shaping system is the plasma boundary of the ion emission.
The position of the boundary (in the absence of a magnetic field, perpendicular to the direction of the ion take-
off) is determined by the condition of equivalence of the pressure of the plasma electron gas and the pressure
of the external electrostatic field
eO E/2 --- nelcT e,
where eo is the dielectric constant of the vacuum; E is the strength of the external electrostatic field; ne is
the concentration of the electron gas at the boundary of the plasma, and Te is the temperature of the electron
gas.
The saturation ion current density at the plasma probe was found from the relation [6]
j == 0.4ien, V 21kT1/1n1,
where no = 1.65ne; e is the charge of the electron; mi is the mass of the ion. Using this relation, expression
(1) was reduced to the form
E - 4.9(i?103j1/2 (MO)1/1;V/m. (3)
Here j is the ion current density; M is the mass of the ion, amu, and 0 is the electron temperature, eV.
In characteristic operating conditions of the ion source (j = 0.1 A/cm2, 0 = 5 eV), the strength of the
field at the plasma boundary amounts to several kV/cm. By fixing the plasma density distribution over the
cross section of the ion take-off region, by choosing the geometry of the take-off system and taking account of
the relations given above, a configuration of the plasma boundary which is favorable for shaping the beam can
be created. The flow of primary electrons markedly increases the pressure on the plasma side. As a result,
the boundary of the plasma is deformed according to the density distribution of the dishcarge current. In this
source, in order to eliminate the effect of the primary electrons on the plasma boundary, a cylindrical elec-
trode is introduced, which is located behind the anticathode and has the identical potential. The primary elec-
trons are reflected electrically in the discharge column in the vicinity of the anticathode opening, without
penetrating the cavity of the cylindrical electrode, and the plasma flows freely from the source. In the major-
ity of ion sources, the plasma reaches the beam shaping region through the central opening of the output elec-
trode of the gas discharge chamber. Therefore, the maximum density of the plasma appears on the axis. The
increased plasma density in the central region and the weakened (due to the presence of the opening in the ac-
celerating electrode) external field lead to the appearance of a bulge at the boundary take-off surface, which
significantly worsens the beam shaping condition. In the source being considered, a discharge column of tubu-
lar configuration is used. With the motion of the plasma in the cavity'of the cylindrical electrode, the pre-
axial region as a result of radial diffusion also is filled with plasma, but its density is lower. Therefore, dur-
ing the ion take-off, a concave surface of the plasma is formed and a beam which is close to laminar is
formed.
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6'd ?150
/
I
A
1200
/
100-
9D 1000
70 000? `
60 600
50
401- 400
30
20 200
I 1 I I I I I 10
0 10 30 50 70 90
Iarr.. A
Fig. 3. Dependence of proton beam current on the arc
discharge current for an accelerating energy of 100 keV:
collimating opening with diameter 70 mm located at a
distance of 1.6 m from the source; A) utilization factor
of the gas flow for creating the proton beam; ?) proton
beam current; 0) current utilization factor of the high-
voltage rectifier for creating the proton beam.
Construction and Characteristics of the Proton Injector. The injector is shown diagrammatically in Fig.
2. The gas-discharge unit 1, with the magnetic. coils 2 and 3, is insulated from the body of the injector to the
total value of the accelerating voltage. It is installed in the vacuum container 4. The source is suspended on
tubular rods 5 at the upper collars of two straight-through high-voltage insulators 6. In order to increase the
electrical strength of the source, it is installed in the jacket 7 of polished copper plates. In the container, the
inside walls of which are plated with polished copper plates, the electrodes of the beam shaping system 8 are
installed. The second electrode, with a 'negative potential relative to the injector casing, is mounted on a sep-
arate rod which has an insulated lead-out 9. The third electrode is fixed to the wall of the container. A power-
ful focusing coil 10 creating a field of up to 0.7 T is installed on the outside of the front wall of the container.
The ion duct 11 joins the container space with the collimator space 12, in which a collimating copper cone 13
is positioned at a distance of 1600 mm from the ion source (in front of the inlet to the preaccelerator [ 11); the
diameter of the straight-through opening in the collimating cone depends on the conditions of the experiment.
The second focusing coil 14 is separated from the first by a distance of 300 mm. All the subassemblies of the
injector which are irradiated by the ions are cooled intensively with water, and the high-voltage part of the
injector by distilled water. The vacuum of 4 ? 10-3 Pa is provided by five oil-vapor pumps, provided
with nitrogen traps. The total pumping rate amounts to 15,000 liters/sec. The majority of the running
current measurements of the ion beam are carried out by an electrical method. The measurement er-
ror due to secondary electrons originating as the result of bombardment of the target by ions was eliminated
by superposing a transverse magnetic field on the inlet section of the Faraday cylinder. All the principal
measurements were necessarily duplicated by a calorimetric method. Measurements were carried out also by
noncontact methods [7] developed in the course of the investigations.
At the outlet from the injector, the shaped beam contains -70% of the protons. After passing through the
focusing coils and the collimator, the proton content-in the beam was increased up to 95%. The beam intensity
with an energy of 100 keV attained 1.3 A. For this, 50% of the gas flow reaching the source was converted into
the proton beam. The beam current amounted to -60% of the current load of the high-voltage rectifier. The
dependence of the beam current on the arc discharge current in the source is shown in Fig. 3. Figure 4 shows
the dependence of the beam current on the energy in the range from 40 to 110 keV. With extension of the chan-
nel up to 3.3 m, a beam current of 1.0 A with an energy of 85 keV is recorded after passing through the colli-
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1400
40 60 80 100 120
U, keV
Fig. 4. Values of the proton beam current with a
different accelerator energy: collimating open-
ing with diameter 70 mm located at a dis-
tance of 1.6 m from the source; ?) data of
[21; o) experiment.
1000
_ 800
10
Fig. 5. Dependence of beam emittance on the ion
current intensity (-, A) and the value of the dis-
charge current corresponding to a given beam in-
tensity ( --, 0) with a voltage at discharge of
70 V.
< 35r
0.51 15' '
0 200 400
Ii, mA
mating opening with a diameter of 85 mm (in this case, the second solenoid was separated from the first by.
1.5 m). The beam emittance, because of the inadequate thermal stability of the measurement equipment, was
determined for an energy of 70 keV (Fig. 5). The measurements were carried out at a distance of 1.6 m from
the source and with a diameter of the collimator opening of 70 mm. The beam intensity was controlled by the
change of the discharge current with a constant discharge voltage. A distinct correlation between changes of
emittance and the discharge current can be clearly seen in Fig. 5. It should be noted that the direct current
entering the current collector was always modulated by hf oscillations with amplitude. at the 20% level of the
average intensity The level of the modulations in the beam is above the level of the modulations by the hf
oscillations of the discharge current. The maximum intensity of the oscillations corresponds to the range
from a few tens tto .several hundreds of kHz.
On completion of development of the ion source, before connecting to the accelerator the accelerator
was tested in defined conditions (beam current 1.0 A, beam energy 100 keV) during three months over 8-10 h
per day, and it displayed stable operation with a high stability of the parameters.
Combined Operation of the Injector with the Accelerator. A diagram of the accelerator is shown in [ 1].
The total length of the beam channel up to the current collector of the accelerator amounted to 6.7 m. Owing
to the separating action of the five series-installed focusing coils, the content of protons in the beam at the
inlet to the current collector of the accelerator amounted to more than 99%. Below, the parameters of the in-
jector are given for a beam of protons with an intensity of 0.6 A reaching the accelerator current collector
(without switching on the hf acceleration).
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Heating power of cathode, kW ............. 5.5
Discharge current in source, A ,,, , , , , , , ,, , , 55
Discharge voltage, V ................... 75
Magnetic field in the ion source channel, T , , , , , 0.02
Gas flow arriving at the source, m3' Pa/sec ..... 4.0 - 10-'
Beam energy, keV ..................... 95
Voltage on first electrode relative to earth, kV . . -24
Load of high-voltage rectifier of injector, A .... 1.3
Diameter of opening in collimator cone, mm ... 50
Vacuum in injector, Pa .................. 2.7 ?10-3
When the hf resonators of the accelerator were switched on, a proton current of 0.25 A with an energy
of 500 keV was recorded in the current collector.
In conclusion, the authors express their thanks to participants in this project, in particular M. A. Niki-
tin, K. N. Nikitin, A. S. Skvortsev, E. N. Knyazev, O. A. Gusev, Yu. G. Gendal', and O. G. Matveenko, and also
to the director of operations on the startup and investigation of the accelerator, A. P. Fedotov.
1. B. K. Shembel' et al., At. Energ., 31, 1, 45 (1971).
2. W. Lamb and E. Lofgreen, Rev. Sci. Instrum., 27, 11, 907 (1956).
3. R. A. Demirkhanov et al., Prib. Tekh. Eksp., 2, 19 (1964).
4. N. V. Pleshivtsev et al., Prib. Tekh. Eksp., 6, 23 (1967); At. Energ., 22, 2, 128 (1967).
5. E. Lawrence, Science, 122, 3180, 1127 (1955).
R. M. D. Gabovich, Physics and Technology of Ion Plasma Sources [in Russian], Atomizdat, Moscow (1972).
7. G. A. Koval'skii et al., Prib. Tekh. Eksp., 5, 47 (1968).
PROBLEMS OF THE RADIATION HAZARD OF 14C
1. Ya. Vasilenko, P. F. Bugryshev, UDC 621.039.58:539.16.01
A. G. Istomina, and. V. I. Novosel'tseva
Nuclear explosions, the total power of which has reached 530 megatons, have been accompanied by the
formation of a substantial amount of radiocarbon - 14C - characterized by a long half-life (5760 yr) and a
low /3 radiation energy (0.156 MeV). The maximum concentration of this nuclide in the atmosphere was regis-
tered in 1965, when its level exceeded the natural background by approximately 100%. The total amount of ac-
cumulated radiocarbon was 5.8 MCi in 1972 [1, 2], As a result of the limitation of atmospheric nuclear ex-
plosions, the concentration of "bomb" 14C in the atmosphere is gradually falling. However, it still exceeds
the natural level by approximately 30%. By the year 2000, it is expected to have fallen to 3% (Fig. 1).
At the present time, the main sources of the ever increasing penetration of 14C into the environment
are the atomic energy enterprises. According to generalized data, the ejection of gaseous 14C from energy
reactors comes to hundredths of a Ci/MW(el) ? yr [3]. In this case -95% of the 14C is in the form of 14CO21
2.5% in the form of 14CO, and 2.5% in the form of hydrocarbonates [4]. By the year 2000, this situation may
lead to an approximately 200% increase in the concentration of radiocarbon in the atmosphere (Fig. 2). We
should note that the increase [5, 6] in the content of stable carbon in the atmosphere as a result of the com-
bustion of mineral fuel is leading to a certain drop in the 14C concentration as a result of its dilution.
Processes of exchange of 14C between the atmosphere, biosphere, and hydrosphere proceed rather in-
'tensively and are characterized by time constants of the order of several years. The period of half purifica-
tion of the atmosphere is assumed equal to 1.5-5 yr [ 1, 2]. Ultimately the bulk of the radiocarbon passes into
the world's ocean, which plays the role of a unique "buffer" and where, reacting with metals, 14C forms car-
bonates and bicarbonates. The time constant of the exchange of the surface layers of the ocean is -5-25 yr,
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 299-303, November, 1980. Original article sub-
mitted September 28, 1979.
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60
50
40
9960 9965 1970 1975 '9960 year
Fig. 1. Content of "bomb" 14C in the atmosphere (1)
and surface layer of the ocean (2) [1, 21. The excess
amount of 14C in comparison with natural content is
plotted along the y axis in Figs. 1 and 2.
and of the deep layers 100-1000 yr. It is believed that a complete exchange of the 14C in the atmosphere, like
that of stable carbon, occurs in 300-500 yr.
During the process of photosynthesis 14C is accumulated in plants, and then in the organism of animals
and humans. Moreover, terrestrial plants fix only 1/ 10 of the radiocarbon; the remaining 9/ 10 is -absorbed by
marine plants, chiefly by phytoplankton. The coefficient of transfer in the chain atmosphere-terrestrial
plants is equal to unity [7]. Equilibrium is established very rapidly, within 2-3 months. Radiocarbon can pass
into plants in small amounts from the soil through the root system as well. The content of 14C in the animal
organism is correlated with the past years' content of it in plants [8]. In 1963-1964 the concentration of the
radionuclide in plants approximately doubled in comparison with the natural level [9] Close to pollution
sources, the concentration of 14C in the atmosphere is higher than the average, which naturally leads to an in-
creased accumulation of radiocarbon in plant and animal organisms in these zones. Thus, plants at a distance
of 1-2 km from the stack of an atomic power plant contain 50-90% more 14C than those at a distance of 20-30
km [6]. Consequently, local foci of contamination by radiocarbon may be created.
Radiocarbon penetrates into the human organism with food products of vegetable and animal origin and
with water in the forms of various organic and inorganic compounds, as well as with air in the form of 14CO2.
The accumulation of radiocarbon in plants in the process of photosynthesis is the basic link in the biological
chain through which 14C is taken into the human organism with foods.
The penetration of artificial radiocarbon into the atmosphere leads to an increase in its content in the
human organism. Thus, the amount of 14C in the bodies of people who died in 1984-1965 exceeded the natural
level by approximately 50% [9]. Practically the same amount of 14C was in the bodies of people who died in
1973 [ 10]. The additional dose of irradiation on account of bomb radiocarbon is negligible, and in recent years
has been - 1 mrd/yr for the whole body. In the years to come it will gradually fall, since the levels of con-
tamination of food products by bomb 14C are decreasing. The period of half purification of products of animal
origin is equal to 6 yr [ 11]. The integral dose in the year 2000 will be 7, 22, and 19 mrd for the gonads, endo-
steal cells, and on the average for the organism, respectively [ 1, 21. During the entire lifetime of 14 C, its in-
tegral dose significantly exceeds the dose from other radionuclides of fission products. It will be created for
103 yr. We note that the fraction of irradiation of the whole body on account of natural radiocarbon is equal
to - 1.2 mrd/yr and comes to - 1% of the dose of the background irradiation. The doses of irradiation on ac-
count of the ejection of 1 A C by nuclear energy enterprises are gradually increasing (Fig. 3).
In an evaluation of the biological aspects of global pollution of natural media by radiocarbon, we should
keep in mind that carbon is one of the basic biogenic elements and is contained in all living tissues (fats, pro-
teins, carbohydrates, nucleic acids, enzymes, vitamins, and other biologically important compounds); thus it
may act as an internal irradiator of biomolecules. During the metabolic process, the radionuclide is dis-
placed from one class of compounds to another.
The biological action of the radionuclide is associated not only with radiation effects, i.e., its processes
of ionization and excitation of atoms and molecules by R-particles in the decay of 14C and by the formation of
highly biochemically active radicals, but also with the chemical action as a result of transformations of the
disintegrated carbon atoms into nitrogen atoms [ 14C (n, p) - 14N]. The transmutation factor (changes in the
chemical nature of the atoms and molecules) takes on special significance if radiocarbon is incorporated into
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77
300 /1 ,
Fig. 2. Concentrate of 14C in the atmosphere
due to ejection by nuclear energy enterprises
expected in the year 2000 [5, 91.
the molecule, damage to which determines the biological effect. Local changes in the chemical composition of
DNA (conversion of 14C to 14N) lead to gene and chromosome mutations which are not repaired. The probabil-
ity of damage due to f3 particles formed in the decay of 14C is immeasurably lower [ 121. We note that the re-
pairing enzymes in most cases repair single breaks in DNA induced by radiation effects. Double breaks are
repaired with greater difficulty. Mutations in the germ cells, if they do not lead to their death, may be mani-
fested in the progeny in the form of deviations from normal development, and also in the form of hereditary
diseases. Mutations in somatic cells can cause various disorders over long periods, including malignant neo-
plasms.
Pauling was the first to call attention to the possibility of an increased mutagenic action of incorporated
14C [ 13]. Many researchers attribute great significance to the transmutation action of radiocarbon. consider-
ing that the biological effectiveness per unit of sorbed dose is increased [14-17]. However, we should make
special note of the fact that the International Commission on Radiological Protection, analyzing the results of
these and other investigations, recommended the acceptance of an RBE of 14C equal to one. The same conclu-
sion was reached by the Scientific Committee on the Effect of Atomic Radiation of the United Nations Organiza-
tion (UNSCEAR), the National Academy of Sciences of the United States [18], and the National Commission on
Radiological Protection of the USSR [ 19 1.
In evaluating the biological effects of radiocarbon, the investigation of the kinetics of exchange of the
nuclide is of great significance.. The necessity for conducting such investigations is due to the fact that the
peculiarities of the exchange of various compounds of radiocarbon are not always taken into account in its
standardization [19, 21]. Only in Publication 10 of the International Commission on Radiological Protection
was attention paid to the peculiarities of the metabolism of certain compounds of 14C (bicarbonate, glycine,
acetate). These compounds, however, are not the main sources of the contribution of radiocarbon to the human
diet.
In our investigations [22, 23], a comparative study was made of the kinetics of the metabolism of the
basic inorganic and organic radiocarbon compounds, contained in carbohydrates, proteins, and fats, as well as
alcohols. The inorganic compounds Na24CO3, K24CO3, Ca14CO3 are characterized by a high absorbability (90-
100%), a relatively uniform distribution of 14C in the organs and tissues, and a rapid elimination from the
organism, chiefly through the lungs in the form of 14CO2. During the first hour, rats eliminate 77, 79, and
35%p of the introduced amount of radiocarbon in the form of the above-mentioned compounds, respectively,
through the lungs. By the end of 24 h, only 1-3% of the introduced 14C remains in the organism. Organic com-
pounds ([14C]glucose, [ 14C ] succinic acid, [t4C ]glycine, [ 14C ] palmitic acid, [14C]ethanol, ["Cl methanol) are
also characterized by high absorbability (95-100%) and a relatively uniform distribution of 14C in the organs
and tissues. Radiocarbon is eliminated from the organism chiefly through the lungs; however, it is eliminated
more slowly in comparison with inorganic compounds, since the 14C of these compounds is utilized as an en-
ergy and plastic material. After 24 h, the rat organism contained approximately 15, 50, 60, 10, 12, and 34% of
the activity after the administration of "Cl glucose, [ 14C ] glycine, "Cl palmitic acid, [ HC ] succinic acid,
[ 14C ] ethanol, and [ 14C ] methanol, respectively. In the initial period, a large concentration of 14C was regis-
tered in the organs and tissues with a high level of metabolism (liver, kidneys, gastrointestinal tract), and
subsequently in the adipose tissue and bone.
In the case of long-term intake of radiocarbon, an equilibrium state was established in rats after a
month from the beginning of the introduction of NaZ4CO3, three months after the beginning of administration
of [ 14C ] glucose, and four months after the beginning of administration of [ 14C ] glycine and [ 14C ] palmitic acid.
By this period, 7, 200, 1200, and 1300 daily introduced amounts of radiocarbon had been accumulated in the
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16'
X14;
~ 12
670
B
'b 6
.N 4
0 2
Fig. 3. Presumed doses of irradiation due to
ejection of 14C by nuclear energy enter-
prises: 1) adipose tissue; 2) whole body;
3) bone marrow; 4) gonads.
organism, respectively. The peculiarities of the metabolism of various radiocarbon compounds affected the
rate and value of the irradiation doses formed. When organic compounds were administered, the doses of ir-
radiation of the organs and tissues were 10 times as great as when inorganic compounds of 14C were taken in.
When the experimental data obtained are extrapolated, it may be assumed that in man, when 14C is re-
ceived in the standard diet, an equilibrium state is established 1.5 yr after the beginning of the intake of radio-
carbon, with a multiplicity of accumulation - 30 (the ratio of the radiocarbon content in the organism to the
amount consumed daily). These values are in good agreement with the recommendations of the UNNCEAR,
according to which the time of an equilibrium state is 1.4-1.8 yr [1, 2], while the multiplicity of accumulation
of 14C agrees with the multiplicity of accumulation of stable carbon and radiocarbon of natural origin (30-40
and 30-33, respectively). The nature of the irradiation depends on the form of the compound in which radio-
carbon is taken into the organism. When 14C is consumed in the diet, the maximum doses are formed in the
adipose tissue and bone marrow (yellow) and are approximately four times as great as the average dose of
irradiation of the body.
The doses of irradiation due to anthropogenic radiocarbon make a negligible contribution to the dose of
background radiation. The effect of low doses is of a stochastic nature and may be manifested chiefly in vari-
ous kinds of genetic disorders (deviation from normal development and hereditary diseases) and malignant
neoplasms. The hazard of the risk for society increases with increasing number of persons irradiated in the
population. The International Commission on Radiological Protection and the UNSCEAR, in evaluating the.
risk, recommend that one proceed from the concept of a thresholdless action of radiation and a linear dose
vs effect relationship. It is emphasized in this case that any irradiation that is unnecessary should not occur.
Such an approach is the best guarantee of reliability of radiation protection of man.
The results of estimates of the possible genetic and somatic consequences of environmental pollution
with 14C are presented in Table 1. The. following initial, assumptions were used in this:
global pollution of the environment and the established equilibrium in the chain air-food products-
human organism (coefficient of discrimination assumed equal to unity);
cessation of nuclear explosions in the atmosphere;
thresholdless linear dose vs effect relationship (the increase in the biological effect on account of the
transmutation effect is neglected).
As was noted above, the biological hazard of the accumulation of 14C in natural media is associated
primarily with its transmutation action. The transmutation of 14C incorporated into DNA is especially im-
portant to consider for such effects as gene and chromosome mutations, reproductive death of cells, which
are associated with direct damage to DNA. The quantitative evaluation of these effects encounters great
methodological difficulties. In an experimental determination of the relative genetic effectiveness (RGE) of
14C according to the indices of gene mutations (experiments on phage, yeasts, Drosophila), chromosome aber-
rations (experiments on onion rootlets, bean sprouts), and reproductive death (experiments on bacteria,
human cells in tissue culture), contradictory data were obtained; the RGE was 1-20 [14-17, 24-301. The
''standards used were x rays and y radiation with low values of the linear energy loss. Such discrepancies are
due to the great variety of experimental material and the various experimental. conditions. There are no suf-
ficiently substantiated materials on the value of the RGE of 14C at the present time. In our investigations the
value of the biological effectiveness of 14C was estimated by the coefficient 10 [23]. _ If we use this value of
the RGE, the yield of malignant neoplasms and congenital defects cited in Table 1 must be increased by an
order of magnitude.
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TABLE 1. Possible Somatic and Genetic
Consequences of Irradiation of a Population
of 106 Persons on Account of Anthropogenic
14C (number of cases in the whole life
from a dose in 1 yr)
Nature of
disorders
1980
198,
1990
11995 .
12000
2005
Malignant
'
0,01
0,04
0,1
0
2
0
4
0
8
tumo
s
,
,
,
Serious congeni-
0,004
0,01
0,03
0,06
0,1
0,15
tal defects '
*Per 106 newborn.
It should be noted that even in this case. it is impossible to detect the influence of anthropogenic 14C: the
mortality from malignant neoplasms of various localizations, reaches 1500-1600 cases.per year per 106 per-
sons [32]; the natural frequency of genetic damages is considered equal to 60,000 cases per 106 children, in-
cluding 16,000 severe cases [331.
In the estimates cited the possibility of accumulation of a genetic. burden in the population as a result of
the mutagenic action of 14C in an infinite series of cell generations and the consequent increase in unfavorable
effects in future generations was not taken into account. In this case the value of the RGE of 14C may be sub-
stantially increased. In the opinion ofAcademicianN, P. Dubinin [34, 35], 25% of the natural mutations are as-
sociated with the radiation background, and great significance is attributed to radiocarbon in this case. The
possibility remains that radiocarbon has, been of vital importance, as. a factor of variability in the process of
evolution of life on earth. It can be assumed that the bulk of the mutations are eliminated in the process of
evolution.
The investigations of the resistance of the plant and animal world to an increased concentration of 14C,
in the biosphere remain insufficient. The possibility remains that the ecosystems may have less stable links
than man. Therefore, the, increase in 14C concentration presents not only a hygienic, but also an ecological
problem on a global scale. To) answer these questions,, it will be necessary to conduct further complex sys-
tematic investigations on various species of plants and animals, including higher animals.
LITERATURE CITED
1. Radioactive Pollution as a Result, of Nuclear Explosions, Report of the UNSCEAR, A/AC 82/R, 298, June
17, 1975.
2. Sources and Action of Ionizing Radiation, Report of the UNSCEAR at the U.N. General Assembly, New
York, Vol. 1 (1978), p. 226.
3. Production of Nuclear Energy, Report of the UNSCEAR, A/AC 82/R, 329, June 15, 1976.
4., C. Kunz, W. Mahoney, and J. Miller, Trans. Am. Nucl. Soc., 21, 91 (1975).
5. A. D. Turkin, Dosimetry of Radioactive Gases [in Russian], Atomizdat, Moscow (1973).
6. V. P. Rublevskii, S. P. Golenetskii, and G. S. Kirdin, in: A. D. Turkin (ed.), Radioactive Carbon in the
Biosphere [in Russian], Atomizdat, Moscow (1979).
7. W. Broccer and A. Walton, Science, 130, No. 3371, 309 (1959).
8. A. P. Vinogradov, A. L. Devirts, and E I. Dobkina, Dokl. Akad. Nauk SSSR, No. 3, 688 (1961).
9. R. Nydal and K. Lovseth, Nature, 206, No. 4988, 1029 (1965).
10. M. Steinhouse and M. Baxter, Nature, No. 5614, 828 (1977).
11. Data and Reports, 14, No. 11, 679 (1973) .
12. L. M. Gracheva and V. G. Korolev, Genetic Effects of the Decay of Radionuclides in Cells [in Russian],
Atomizdat, Moscow (1977).
13. L. Pauling, Science, 128, 1183 (1958).
14. A. M. Kuzin,. Effectiveness of the Biological Action of 14C When It is Incorporated into Living Structures
[in Russian], Akad. Nauk SSSR, Moscow (1960).
15. A. M. Kuzin et al., Radiobiologiya, No. 6, 805 (1964).
16. A. M. Kuzin et al., in: Radiation Genetics [in Russian], Akad. Nauk SSSR, Moscow (1962), p. 267.
17. S. N. Aleksandrov, D. K. Popov, and N. K. Strellnikova, Gig. Sanit., No. 3, 63 (1971).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
18. Radiation Protection Recommendations of the International Commission on Radiological Protection,
ICRP, Publication 10, Pergamon Press, Oxford (1968).
19. Standards of Radiation Safety NRB-76 [in Russian], Atomizdat, Moscow (1978).
20. Recommendations of the International Commission on Radiological Protection [Russian translation], IL,
Moscow (1958).
21. Radiation Protection. Recommendations of the International Commission on Radiological Protection.
Second Publication [in Russian], Gosatomizdat, Moscow (1964).
22. I. Ya. Vasilenko et al., in: Radioecology of Animals. Materials of the First All-Union Conference [in
Russian], Nauka, Moscow (1977), p. 203.
23. I. Ya. Vasilenko et al., in: Summaries of the All-Union Conference: Long-Term Effects and Estima-
tion of the Risk of the Influence of Radiation [in Russian], Moscow (1978), p. 61.
24. J. Beal and N. Scully, Bot. Gas., 112, 232 (1950).
25. E. Suomolainen, 0. Jurpeinen, and R. Niini, Nature, 178, No. 4529, 337 (1956).
26. H. McQuade, M. Friedkin, and A. Atchison, Exptl. Cell Res., 11, No. 2, 249 (1956).
27. C. Purdon, Mutation Res., 2, No. 2, 156 (1965).
28. V. S. Skobkin and L. A. Mineeva, Genetika, 1, No. 3, 97 (1965).
29. G. Pluchennik, Genetika, 2, No. 5, 117 (1966).
30. R. Oliver, in: Biological Effects of Transmutation and Decay of Incorporated Radioisotopes, IAEA,
Vienna (1968), p. 165.
31. S. Apelgot, ibid., p. 147.
32. Morbidity of the USSR Population with Malignant Neoplasms and Cancer Mortality [in Russian], Medi-
tsina, Moscow (1970).
33. The Effects on Populations of Exposure to Low Levels of Ionizing Radiation. National Academy of Sci-
ences, National Research Council, Washington (1972).
34. N. P. Dubinin, Evolution of Populations and Radiation [in Russian], Atomizdat, Moscow (1966).
35. N. P. Dubinin, General Genetics [in Russian], Nauka, Moscow (1976).
OPERATIONAL METHOD FOR STUDYING 3H IN
THE OCEAN AND ATMOSPHERE UNDER MARINE
CONDITIONS
V. N. Soifer, E. A. Boroukhin,
V. A. Goryachev, Yu. S. Pozdeev,
and A. F. Sergeev
An important place in the realization of long-term. complex programs in the study of the circulation and
agitation of water masses in the world's ocean is occupied by the application of radioactive tracers, such as
3H, 14C, 228Ra, and 137Cs [ 1]. Tritium, along with deuterium and 180, is the most promising indicator of
movement of water masses and is used to study the processes of circulation and water exchange of a meso-
scale character (mass exchange across a thermocline, the interaction of the atmosphere with underlying water
surfaces, the ascent and descent of water masses). Their use is also promising in the study of vortex forma-
tion in the ocean.
Apart from measurements of 3H and 14C conducted recently (e.g., by the Scripps Oceanographic Insti-
tute), there was a gap for several years [2] between the selection of significant volume samples at separate
stations and labor-intensive technological analysis of them after set-up in coastal laboratories. This excluded
the possibility of an effective use of tritium and radiocarbon methods during work on areas in the ocean. Be-
sides this, additional difficulties arose in the protection of deep-water samples with ultralow concentrations
of 3H from contamination by 3H atmospheric moisture during analysis on dry land, where the concentrations
of 3H are 1-2 orders of magnitude higher than in the atmosphere above the ocean surface.
Translated-from Atomnaya Energiya, Vol. 49, No. 5, pp. 303-307, November, 1980. Original article
submitted December 24, 1979.
748 0038-531X/80/4905-0748$07.50 ?1981 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
Pure
Ar
Selection 4_
samplateaweeroY
s
Desaliniza-
tion
First-stage
electrolysis
Pure
Ar
Desaliniza-
tion
elec 51 sis 11
Alkaline 3%
KOH
Measure-
ment of
tritium
Pumping and
filling of pro-
portional counte
g -
sptrbeomea
sureu
"Dead
COZ
Pure
i Control o~ i
concentration:
by deuterium
Fig. 1. Design of tritium measurements in ocean water (sensitiv-
ity 0.2 ? 10'18 3H/H: 1) plastic bathometers, V = 6 liters; 2)
vacuum still, P = 3.6 kW, output 1 liter/h; 3) Co = 3% KOH, Cf =
30%; 4) distillation battery with 5 tanks, Vo = 500 ml, at = 2h;
5) Co=3%KOH, Cf = 40%; 6) 9 tanks, Vo=30 ml,Ot= 1h; 7)
synthesis units and pure methane, Vf = 16 liters, At = 8 h, out-
put 96-99%; 8) pumping units and counter filling, vacuum 102
torr (1 torr = 133.322 Pa), pressure 400 kPa, At = 2 h; 9) de-
tection block with 5 channels, 3H "window" 1-19 keV, u = 1-2%,
zt=10 h.
Sharp changes in the hydrometeorological conditions in the boundary zone of the atmosphere lead to sig-
nificant variations in the coefficient of the turbulent volume of moisture. Therefore, for the correct solution
to moisture-exchange problems on the area of water studied, it is necessary to have immediate measure-
ments of tritium on the vessel during field work. The variability observed in the concentration of tritium in
the vertical sections of the area of the ocean studied has, quite correctly, an unprecedented character. Ob-
taining preliminary data about the tritium field of a definite region during the work of the expedition allows
one to plan studies during the course of the entire voyage. It is evident that in the given case, not only is
there a saving in time and valuable material, but the possibility appears of conducting unique experiments in
the study of the circulation and movement of water masses in the ocean as well as in moisture-exchange on
the ocean-atmosphere boundary.
The presence of a tritium laboratory consisting of a measuring complex on the research vessel (RV)
allows one to reduce to several days the time from the moment of sampling to the moment when the results
are obtained and also lessens the danger of contaminating deep samples with atmospheric moisture during
storage and analysis.
In 1971 on the RV "Academician Kurchatov," the first experiment was conducted on 3H radiometry in
marine conditions, in the Pacific Ocean Oceanography Institute (POI) DVNTs AN SSSR Marine Tritium Labor-
atory devoted to work under expeditionary conditions with a complex program of studying the ocean and at-
mosphere using tritium and, eventually, radiocarbon methods.
Unfortunately, an ultralow level of 3H radioactivity in the ocean and, especially, the techniques of its
measurement do not allow one to conduct uninterrupted recording. At present, the concentration of 3H in
deep and surface waters is 0.1-1.0 parts per 1018, and in the atmosphere it is 10-100 parts per 1018. Taking
this into consideration, the basic problems in creating a marine measuring complex are the following:
1) analysis of the means and methods of selection of samples of atmospheric moisture for gradient
measurements of the flow of 3H (test volume 30-100 ml);
2) mastery of techniques of sample selection of deep water, studied for 3H, without contact with the at-
mosphere and with simultaneous determination of the hydrological background: temperature, salinity,
chemical composition of water at depth (approximate sample volume 3-5 liters);
3) reanalysis of the tuning and set-up of a marine measuring complex for a precise analysis of water
for 3H with a sensitivity to 0.2 per 1018.
Distil
lation
I I
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4 I 59Q (51) I 11~ 60 r
4 .
D
X2
- X
56
57 55
54
9
67
X14 X15
X25
X27
71
2f7
31 32
X40
X41
Fig. 2. Design of the pumping system: 1-56) valves; 57-58) vacuum hoses; 59-62)
vacuum meters; 63-68) traps; 69-70) reactors for methane synthesis; 71-73, 78,
81-83) loops to purify methane; 74-75) tanks with CO2 and H2; 84-85) proportional
counters; 76-77) reducers; 79, 80) buffer capacities.
A marine measuring system was created on the TOI to study 3H, 14C, and other radionuclides: we in-
cluded a marine tritium laboratory, automated thermohaline probe-y-spectrometer, a system for rapid analy-
sis of data, and automated meteorological stations for the gradient measurements with an apparatus for sam-
pling the atmospheric moisture.
Analysis in the marine tritium laboratory was accomplished by a concentrating electrolysis apparatus,
apparatus for distillation of samples (distillation batteries), vacuum apparatus with a sealed system and a
detection block with a protective shield (Figure 1).
The electrolysis arrangement consists of electrolyzers of the first and second stages (in 6 parts),* ar-
ranged in a support and cooled by running water with a consumption of not more than 3.5 m3/h. The dimen-
sions of the apparatus are 1340 x 1800 x 700 mm, mass 380 kg. The current for first-stage electrolysis is
100 A, and for the second stage 25 A. At the first stage the initial volume of the sample water is V0 = 3200
ml, the final volume is Vf = 500 ml; for the second stage V0 = 500 ml, Vf = 20-50 ml. To supply the electro-
lyzer we use individual regulating rectifiers of the bridge design with silicon diodes VK-200 with water cooling.
The distillation battery of the second stage consists of five tanks with condensers (volume 1.2 liters),
arranged in one thermal block and cooled by running water with flow of not more than 1.2 m3/h. The power of
the heater was 2 W. The dimensions of the battery are 196 x 360 x 400 mm, the mass is 70 kg.
The distillation battery of the second stage consists of nine tanks with a volume of 100 ml with refriger-
ators cooled by running water with flow of not more than 1 m3/h, and a heating block. The dimensions of the
batteries are 720 x 200 X 360 mm, the mass is X20 kg.
The vacuum arrangement for the synthesis of the counting gas and filling of the proportional counters,
built as a single testing unit, consists of the following loops: metallic vacuum system (negative pressure 4.3
Pa) with a loop of pure gas and circulating pumps,' two reactors for the synthesis of gas with an automatic
In several cases it was necessary to reduce the final volume of electrolysis to 1-2 ml. This was accomplished
by using electrolyzers of the third stage which are glass test tubes with electrodes of iron and nickel plates
placed in them.
t Pumps are designed and prepared in the Department of Molecular Physics of the IAE im. I. V. Kurchatova.
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I
Y4
1~
H
I I
- --- --
L-----
I
'5?sec ~15?sec ~ i5
ft CC CC AC
LT - T - _T_ - _T_
C C4 C3 CZ C 1 1-1
Fig. 3. Schematic of the "Baikal" electronic system: Y1) basis
amplifier, amplitude of input signals 1-100 mV, bandwidth 1 kHz-1
MHz, amplification coefficient 30 d_B, variation of amplification
coefficient 1.5%; Y2! amplifier for muon detector, amplification
coefficient 103, bandwidth 1 kHz-1 MHz; Y3) auxiliary amplifier,
amplification coefficient 30 dB; Al) attenuator, coefficient 0-30
dB; A2) attenuator, coefficient 0-20 dB; UD, LD) upper- and lower-
level discriminators, sensitivity 500 mV, accuracy of threshold and
windowwidth2%, stability of threshold over the temperature range
from +10 to -35?C 5%o for a time not less than 15 h; AC) anticoin-
cidence circuit; CC) coincidence circuit;. LG) linear gate, linearity
coefficient 2% in the range 0-3 V, stability of transmission coeffi-
cient not less than 1%; AO) analyzer output; Fl, F2) pulse shapers.
system of regulating the temperature of the reactors, a membrane pump* for the overpumping of gas inside
the system, two fore-vacuum pumps VN-461M and four 5-liter containers for storing the hydrogen, carbonic,
and synthesized gases. The dimensions of the system are 1500 x 750 X 140 mm, the mass is 360 kg. The
consumed power is 3.5 W.
Methane is used as the counting gas under a pressure to 400 kPa. The concentrated test water is spread
out on the zinc, isolated by hydrogen. Then a synthesis of methane is produced by the scheme
CO2 + 4H2 .= CH, + 2H2O
in the presence of a ruthenium catalyst, further , .
2H20+2Zn 2H2?ZnO etc.
This method of methane synthesis in one stage, demanding not less than a day for its realization, was
proposed by Lal [3]. In order to refine the method a corresponding apparatus (Fig. 2) was constructed and
prepared, including reactors with two regulating heaters in the upper and lower parts [4]. Plates with zinc
powder and a catalyst are placed inside the reactor. By industrial standards, the zinc powder contains up to
15% oxide which prolongs oxidation during storage and rarely reduces its chemical activity. This latter was
enhanced by the addition of bromide steel. The control tests showed that the vapor of bromide steel destroys
the oxide film, forming zinc bromide permeable to water, which with time is removed from the reaction zone
by sublimation. For this part, the powder is 10 wt.% -of, bromide steel, which provides practically a 100%
yield of the synthesis for 5 h during the decomposition of'-15-40 ml of tritium-enriched water.
The methane was cleaned with the help of chemical absorbers: from traces of moisture with anhydrous
phosphorous, from hydrogen by copper oxide shavings. Having been formed in the secondary reactions, the
*Pumps are designed and prepared in the Department of Molecular Physics of the rAE im. I. V. Kurchatova.
751
I
uon-
UD trol AC LD
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
TABLE 1. Results of Determining a for the
Second Stage of Electrolysis
V, 1 V,
ml I ml
No, IN,
counts/ counts/
min I min
V0 N
V No
500
33, 70
12:) , 0
14,8
12,0
12,8
5011
19,28
188,2
2(1,11
18,8
1(1,o
5011
311,63
129,11
16,3
12,1)
11,9
5(10
26.75
144,0
18,7
14,4
11,3
oxide of carbon was initially oxidized on copper oxide shavings to dioxide, and carbonic acid gas was absorbed by
askarit or by waterless caustic potassium.
The circulation of the gas throughout the absorber is guaranteed by a squeezed greaseless hose with a
large square piston, small working stroke and a frequency of 120 strokes/min. The gas in the system is
pumped by a vacuum-compressor with a nonstress membrane and pneumatic driving gear. The seal in the
counter with 400 kPa of gas is provided for by a residual pressure in the loop of less than 10 kPa.
The detector block with the protective shield was designed to measure 3H with the help of liquid scintil-
lators which do not require long `preparation of the sample. However, the efficiency of such measurements
does not exceed 30%, and the background is impossible to reduce below 10 counts/min, and the volume of the
sample is limited to several millimeters.
A greater detection efficiency (to 100%) and a large test volume (to 40 ml) at this background level are
the primary purpose of the counter of the inner filling. By an analysis of the form of the impulse, the back-
ground of the counter may be reduced to several pulses/min. Thus, proportional counters possess a sensitiv-
ity an order of magnitude higher than that of liquid scintillators. This determined its selection for a marine
measuring complex.
A proportional counter of a volume of 4 liters is used by the marine tritium laboratory. This may be
filled to a pressure of 400 kPa. A-gold-plated tungsten thread with a diameter of 28'?m served as an anode,
the cathode was the external noncontacting body of the counter. The feed of the counter was a pair of two high-
voltage rectifiers of type B5-24. Methane was used as the counting gas. The internal isolation of the cathode
fluoroplastic ribbon and adjusting ring of plastic prevents leakage during voltage on the cathode up to 3 kW,
which allows one to conduct measurements at a counter pressure up to 400 kPa. The counter supplies a
charge-sensitive preamplifier collected on two pole transistors IP 303G. The feed of the preamplifier is
f 12 V, the amplification coefficient is not less than 50. There is a beryllium window for calibration by an
external source on the face of the counter. The counter is surrounded by a mercury screen and ringed multi-
wire proportional chamber filled with a mixture of argon and methane (pressure 50 kPa) that includes, in our
design, anticoincidence. The counter, mercury shield, and chamber are found inside the iron external
screen with a wall thickness of 20 cm; for this we used radiation-pure materials. The mass of the shielding
equipment is 3.5 tons.
Electrical anticoincidence signals from the counter and chamber act on the electric detecting setup
"Baikal",* which realized amplitude and temporal selection of pulses and their recording (Fig. 3). Pulses
arrive at input 1 from the proportional counter, at input 3 from the anticoincidence shields, and at input 2 as
an inhibit signal. The differential discriminators form pulses at the upper and lower levels and also in the
"window." A linear gate admits pulses at the input of the discriminators in the absence of a signal at input 2.
The design of "Baikal" has 5 counters, the capacity of each being 106 counts. The first counter records the
pulses exceeding the lower-level discriminator (general counts), the second records all pulses falling in the
"window" in anticoincidence with the signals at input 3 (tritium canal). The third counter records all pulses
triggering the upper-level discriminator in anticoincidence with input 3 (background from extraneous radio-
activity). In the fourth and fifth counters, pulses accumulate which fire the lower-level discriminator in coin-
cidence with input 3 (cosmic background).
Laboratory experiments with marine tritium were conducted in 1975-78 in the Mediterranean Sea and
the Scotia Ocean .(Southern Ocean). During the time of the experiments with the measuring complex, we ob-
*Electric equipment and detector block are manufactured in SO AS USSR in our technological shop, estab-
lished on the basis of preliminary experiments of a model of the set-up on ten -trips of the RV "Academician
Kurchatov." The authors express thanks to all participants of this work.
752
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0 J4,5 35,0 5T/, 0 10 ZO t, ?C 0 2 4
-r
Fig. 4. Salinity distribution, temperature,
and tritium ratio (TR) at station No. 3109 in
the Southern Ocean.
tained the basic characteristics of the design, the recording characteristics of the detector, the background of
the counter, and the coefficients, of concentration for tritium samples during all stages of electrolysis.
On the starboard side of the vessel inside the protective shield, the background of the counter during
filling to a pressure of 200 kPa was 6.6 counts/min. Assuming an efficiency of 100%, this corresponds to a
minimum recorded activity of 150 GBq.
The values of the fractionation coefficient a at the first and second stages were determined by a well-
known method of calibrated solutions by the formula
N/No =_ (Vo/V)(?-' )/6,
where N09 N and V0, V are the tritium concentrations and test sample volumes before and after electrolysis.
Experimental results are presented in the table. The mean coefficient of fractionation for the second
stage at current of 25 A and a water-cooled temperature of 14?C is equal to 11.5 ? 1.0. Analogously, the value
obtained for the first stage of electrolysis at current of 90 A and a cooling water temperature of 14?C is 4.9 f
0.8. As an example, see Fig. 4, where we present the temperature distribution, salinity, and 3H concentra-
tion for station No. 3109 in the Southern Ocean (20?E, 38?S).
For a radiocarbon analysis of ocean water, a useful method is preparation of a counting gas. However,
one should not use "dead" carbon monoxide and hydrogen from water, but instead use carbon monoxide taken
from the seawater with a volume of 60-200 liters and hydrogen free of tritium.
Preceeding the selection of a water sample to measure 3H and 14C using a special bathometer, a verti-
cal band of ocean is analyzed by a developed probe- y- spectrometer to separate the structure of the water
strata and operational depth of sampling at the station. Most promising is the use of a developed system for
analysis of the samples with the goal of measuring 3H and 14C which allows one to measure successfully and
economically to fulfill complex long-term programs of studying the world's oceans.
Collaborators at the Laboratory of Nuclear Oceanography TOI DVNTs AN SSSR took an active role in
this work: N. A. Vorontsova, V. V. Kobylyanskii, S. B. Zverev, R. M. Amal'skaya, and V. N. Kanchuk.
For the. successful operation of the tritium laboratory, the authors are thankful for the great help from
the following group of collaborators at all stages of the work, from preparation to the marine experiments at
the site: the I. V. Kurchatov Institute for Atomic Energy (I. K. Kikoin, S. S. Yakimov, K. I. Balashov, et al.),
the Institute for Nuclear Physics and Experimental Factory SO AN SSSR (A. V. Sidorov, V. M. Aul'chenko,
S. E. Baru, et al.), Arctic and Antarctic Scientific-Study Institute (N. P. Smirnov, E. I. Sarukhanyan, et al.),
and also the crew of the RV "Professor Bogorov" and "Professor Zubov." The authors are deeply indebted to
them all.
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LITERATURE CITED
1. H. Craig, Earth Planet. Sci. Lett., 16, 47 (1972).
2. R. Michel and H. Suess, J. Geophys. Res., 80, 4139 (1975).
3. D. Lal and R. Athavale, Proc. Indian Acad. Sci., A63, No. 3 (1966).
4. V. N. Soifer et al., in: Problems in the Study and Use of Water Resources [in Russian], Nauka, Mos-
cow (1972), p. 131..
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
LETTERS TO THE EDITOR
SOME PHYSICAL CHARACTERISTICS OF FAST
REACTORS WITH HETEROGENEOUS CORE
E.
P.
Kunegin, L. N. Yuro.va,
O.
M.
Kovalevich, S. D. Yurchenko,
and
A.
N. Shmelev
The development and .assimilation of fast reactors are linked with finding the best optimum grouping of
the core both for the reactor-breeder cycle and for the reactor-converter cycle. The assumption is expressed
in [1] that a high-powered fast power-generating reactor with a high breeding factor (BF) can be arranged
from several cores (modules) of relatively small dimensions with highly enriched fuel, and located in the
breeding zone of metallic uranium. However, in order to achieve this course, in addition to the advantages
(high BF) there are also difficulties, e.g., in providing the increased power loading of the fuel, with compen-
sation of the change of reactivity during operation. In [2], the requirements are analyzed for the fuel of such
a reactor in order to achieve a sufficiently low specific investment of nuclear fuel in the reactor and in the
whole fuel cycle. It is shown that by comparison with reactors with a diluted core of the,BN type, the hetero-
geneous modular reactor in providing the necessary conditions of power release has advantages in both cy-
cles of interest. Within the bounds of the heterogeneously grouped core, there is the possibility of varying its
degree of heterogeneity. The question arises as to whether or not the change of the degree of heterogeneity
whilst maintaining the neutron spectrum leads to improvement of the physical characteristics.
Breeding Factor. Astudy of the breeding factor of an individual module with highly enriched fuel and
also of an infinite lattice of fuel modules of different dimensions, "linked" to the neutron flux, has shown that
in a number of cases a higher breeding factor can be achieved than the BF of the individual module. Table 1
shows the results of a calculation of the cylinderical cells of a lattice of fuel moduli with enriched oxide fuel
and sodium coolant (ratio of the volume fraction of the core components Efuel/ ENa /F_ steel - 0. 25/ 0.5/0.25
for uranium fuel, and Efuel/ENa/Esteel = 0.45/0.33/0.22 for mixed uranium-plutonium fuel, isotopic compo-
sition of the plutonium239Pu/240pu/241pu/242pu = 0.62/0.28/0.06/0.04), distributed in the breeding zone, and
containing as the raw material metallic uranium, sodium and steel [2]. The calculations were performed in
P1-transport approximation, using an 18-group catalog of microconstants obtained from the 26-group BNAB-
70 library [3], averaged over the integrated neutron fluxes in one-dimensional cylindrical geometry by the
M-26 program [4].
It was found that for the compositions of the fuel module being considered and the breeding zone, the
transition from the individual module to the even more finely divided lattice of modules "linked" to the neu-
tron flux in almost all cases allows the BF to be increased. With a change of density of the breeding zone and
its composition, the relationships may be changed, as a change of ratios of 238U and veff of the principal
fissile isotope occurs, which mainly also determines the BF. Thus, it follows from the examples considered
that the BF can be increased by comparison with a single module and, obviously, only investigations using
specific compositions of the fuel modules and of the breeding zone will show the advantages of one or other
core grouping from the point of view of achieving a high BF.
Change of Breeding Properties during Burn-Up. The results given in Table 1 of the calculation of the
change of reactivity for 10% burn-up of heavy nuclei showed that the reactivity of an isolated fuel module de-
creases with time. Despite the fact that in the breeding zone more fuel is formed than is burned up in the fuel
module, its contribution to the reactivity is insufficient. With the finely divided lattice of fuel modules, the
contribution to the reactivity of the fuel which is formed is increased, and with certain characteristic lattice
dimensions, to a significant degree it compensates the effect of fuel burn-up in the fuel module. With transi-
tion to an almost homogenized medium, the contribution to the reactivity from the fuel which is formed even
exceeds the reduction of reactivity in the fuel modules. Thus, in the cases being considered, transition to
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 309-310, November, 1980. Original article sub-
mitted June 4, 1980.
0038-531X/80/4905-0755$07.50 ?1981 Plenum Publishing Corporation 755
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
TABLE 1. Calculated Characteristics of Fuel Critical Cells with a Metallic Breeding Zone
Radius of core,
cm
Thickness of
shield, cm
Breeding ratio
Change in
reactivity,
75 % P u
2,74
2,5
-x-11 ,2
0,42
0,17
1,23
1,19
1,08
1,49
1,35
2
31
2
29
-1-9,7
-08
+ G,1
-3,1
,
+18,1
,
-7,8
2,57
-5,3
smaller modules linked to the neutron flux, for certain characteristic dimensions of the lattice, allow a small
change of reactivity during operation to be provided, which is inherent in fast reactors with a diluted core.
Conclusions. The advantage in the BF of some or other heterogeneous grouping of the core depends on
the relation between the dimensions and the composition of the core and the breeding zone.
The heterogeneous grouping of the core of high-powered fast reactors combines the advantages in the
BF of reactors with a high-power neutron spectrum and the advantages in change of reactivity during opera-
tion and smoothing of the energy release field of high-powered reactors with a diluted core. It may be men-
tioned that the advantages of heterogeneous grouping are more completely achieved with an increased power
loading of the fuel and with deeper burn-ups; this obviously requires the development of fuel elements capable
of operating in conditions of increased thermal loads but with a smaller fluence [2].
1. S. M. Feinberg and 0. M. Kovalevich, in: State and Prospects of Work on the Construction of Nuclear
Power Stations with.Fast Neutron Reactors, COMECO N Symposium [in Russian], Vol. 1, Fiz.-Energ.
Inst., Obninsk (1968), p. 165.
2. 0. M. Kovalevich and E. P. Kunegin, in: Nuclear Reactor Physics [in Russian], No. 5, Atomizdat, Mos-
cow (1977), p. 70.
3. A. P. Abagyan et al., Group Constants for the Calculation of Nuclear Reactors [in Russian], Atomizdat,
Moscow (1964).
4. N. S. Nikolaishvili et al., in: COMECON Symposium, op. cit., Vol. 2, p.. 75.
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
MATRIX SCREW DIE METHOD FOR THE
CALCULATION OF A COMPLEX LATTICE
IN P3-APPROXIMATION
V. E. Raevskaya and B. Z. Torlin UDC 621.039.51.12:539.125.52
As shown in [ 1], the calculation of the neutron distribution inside the multiring slugs of a complex lat-
tice in P3-approximation can be carried out by means of the matrix folding method. A detailed description of
a one-group program for the calculation of square or hexagonal multicells based on this is given in [2].
The results of calculations of complex annular slugs in a heterogeneous lattice by the procedure of [ 1 ]
and by other procedures [ 3, 4] have proved to be in good agreement [ 2, 51. All comparisons, however, have
been carried out for slugs of average blackness. It was obvious that for slugs with black layers, the matrix
folding method - which is attractive in its simplicity - is found to be inapplicable. Numerical verification has
shown that a significant error arises when the slug has layers with A/la > 3, where A is the thickness of the
layer; .la is the neutron moderation length in it. Analysis of the error of the method of matrix folding has al-
lowed an upper estimate of the relative error to be obtained in a layer with diffusion length L, which was
found to be proportional to exp(2O/L).
We shall consider a method of calculation which is free from this drawback. In its structure it is simi-
lar to the matrix screw die method [6] but does not lead to the accumulation of an error. Usually, this method
is used for the approximate solution of equations in finite-difference form. In this present paper, it will be
used as a stable method for synthesizing the exact solution of the problem in an annular slug, consisting of
uniform layers.
In [ 1, 2], a six-component representation of the vector of the neutron flux density in P3-approximation
is used. We shall find the solution in the form of two three-component vectors ' and J. The components of
cp will be, respectively, the first, fourth, and third, and of j - the second, sixth, and fifth components of the
previous six-component vector. In this case, for the i-th zone of the n-th slug, the equations
(r) A i +fn; i (r) B , i+C(l)i (r);
{t fin, i ~r)= K!2 (r) An, i+Ic2> (r) Rn Cc2n, r (1)
n, a n, i . i+ y )
are valid. The matrices In,i (r) and In21(r) with size 3 k 3 are composed of the elements of the first three,
and the matrices 1S i r) and Kn)i(r) of the same size are composed of the other three columns of the matrix
M(r) of the sixth order given in [1, 2]. In order to formulate the matrix with superscript (1) we shall use
the elements of the first, fourth, and third, and for the matrix with superscript (2) - elements of the second,
sixth, and fifth lines of the matrix M(r).
In Eq. (1), An'i and Bn'i are constant three-component vectors for the i-th zone of the n-th slug, and
for the central zones of slugs, An 1 = 0. Retaining the nomenclature of [ 1, 2], we obtain for the source vectors
Cn'i (r)=Ln, i col (c1, c4, c3);
C`n2,'i (r)=ln, i Col (c2, c6, c:,)?
The matrices formed in.this way will have the following important properties:
all elements of the matrices In)i(r) and Inli(r) are proportional to the modified Bessel functions I(r)
and will increase with increase of the radius r; '
all elements of the matrices eri~i(r) and K(ri~1(r) are proportional to the modified Hankel functions
K(r) and will decrease with increase of r;
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 310-311, November, 1980. Original article sub-
mitted October 22, 1979.
0038-531X/80/4905-0757$07.50 ? 1981 Plenum Publishing Corporation 757
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
in the zones with weak absorption, only the matrix In2i (r) can be singular.
We shall number the zones of the slugs and the boundaries between them, starting from-the center (ri is
the outside radius of the i-th annular zone of the slug): Taking expression (1) into consideration, the following
relations of the matrix screw die method can be obtained:
Wn, i1 (ri)= En, i+1Wn, i+1 (ri+1)+an, i+t;
in. i+1 (ri+1)=Yn, i+1Wn, i+1 (ri+1)+Dn, 41,
77 1.
En, i+1=111, +1 (ri) (l~I n 1,1 i+-( (1'1+1)I
77 1.
It. i+1 ='j n , , 2,i+1 (1'i+1) (rn)1 , ,i+1 (ri+i)1
6n, i+1 = ~~n, i+1 r1
- En, i+1K, )i-1-1 (r,+,)) L nl,)i+1)-1an,i+1-
n, i+1Cn, i+1 (ri+1)+C1ti)i+i (ri)f
i+1=[Kn2), i+1 (ri+l)1-
-Yn, i+l K7) (1 i (ri+1)I (fnl'i+11_1 an, i+1-
i+1Cn,)i+i (ri+1)+Cn,';+1
I(1)h(r)=j 1) (r)+kM (r)U(1) )-11(2).
n, k n, 1, n, !i'
f)1) )2)
n, i+1 = Kn, i+1 ikn'
,i+1 (r1);
fn'it1=})n, 7 ,i+1 (ri)-1n i + i (ri);
an, i+1=Yn, iC71 )i+1 (ri)-Cn, i+1 (ri)+Dn, i?
Yn, o
= 0 and Dn,o = 0, * and all other matrices
En,i+l and yn,i+1v just like
(2)
(3)
(4)
(5)
vectors on,i+1 and Dn,i+1r are calculated successively by means of the recurrent relations (4)-(7), starting
from the outside boundary of the first zone and up to outer boundary of each slug rout'
At the outside boundary of all N nonequivalent slugs of the multicell, according to [1, 2],, we have
N
Wn (run)= ~~ P(l) , hAh+Cn); n=1, 2, ..., N;
h=1
N
in(rnn)= I Ah+C;L21; 1z=1, 2,..., N,
h=1
where Flnk. and Fn2) are matrices with size 3 x 3 and with elements for which the computation algorithms
are described in [2].
From expression (8), by eliminating A1, .,. , AN, it is easy to obtain
h= F21 11; D= C2- TC1;
cD=col (W11 W21 WN); J=c('l (i1, i2, , iN);
F1-{Fn, h!'2=(Pn'h);
We form likewise the vector Dsl = col (D1, D2,,.,, Dn) and the diagonal-cellular matrix Ysl = { Yn},
where Dn and yn are the vector and matrix, calculated respectively by means of Eqs; (5) and (7) for the outer
boundary of the n-th slug.
Using expressions (3) and (9), we obtain
(D = (F - 1'sl)-1 (Ds1 - D). (10)
After calculating the neutron flux density b at the outer boundary of the slugs, relations (2) and (3) can be
used for determining the neutron flux density also at the inner boundaries of the zones. Since in the overwhelm-
*We note that [k72)1 (0))_1 0 and in" (0) = 0.
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ing majority of cases interest lies only in the first component of the vector cp (zero harmonic), an appreciable
economy of computer memory can be achieved by not storing the matrix yn,i and the vector DnSi completely.
In order to calculate, the first component of the vector j (first harmonic, used for determining the average
neutron fluxes in the zones [ 1, 2]) it,is sufficient to store only the first lines of the matrices Yn,i and the first
components of the vectors Dn i.
The matrix screw die of the vectors An,i and Bn,i can be limited by a procedure identical to that ex-
plained. Although in order to obtain the same information about the neutron flux density distribution over the
slugs, it is necessary to store appreciably larger bulks of matrices, in some cases (e.g., in order to deter-
mine the average neutron fluxes in zones without absorption) this limitation of the computational processes
can be justified.
After generating the first version of the program for calculating the complex lattice in P3-approxima-
tion by the matrix screw die method, it was found possible to carry out the calculations of multicells with
slugs containing layers with a high ratio of A/la. In order to verify the procedure and to estimate the errors
due to the assumed approximations, in particular, the results of the calculation of a uniform lattice with multi-
layered slugs in P3-approximation and the calculation of the effective cell with the same slug by the integral
equation method [7] were compared. It was found that even in a slug washed from both sides with water with
an absorbing layer with O/la - 5, the maximum divergence in the neutron distributions did not exceed 150/c,
and it occurred in the zone with weak absorption. The error in the determination of the thermal neutron utili-
zation factor amounted to a total of 0.12%.
The program was written in FORTRAN language for the BESM-6 computer. The calculation time for a
single version was -20 sec for double lattices of uniform slugs, and - 40 sec for double lattices of 30-zone
slugs. The maximum time of -4 min is required for the calculation of the multicell with size 8 X 8, contain-
ing 20. nonequivalent 30-zone slugs of twenty kinds.
1. A. D. Galanin and B. Z. Torlin, At. Energ., 36, 2, 125 (1974).
2. V. E. Raevskaya and B. Z. Torlin, Preprint Institute of Theoretical and Experimental Physics No. 60
(1977).
3. V. V. Smelov, At. Energ., 33, 5, 915 (1972).
4. Ya. V. Shevelev (ed.), Methods of Calculating Thermal Neutron Fields in Reactor Lattices [in Russian],
Atomizdat, Moscow (1974).
5. A. D. Galanin, V. V. Smelov, and B. Z. Torlin, At. Energ., 37, 1, 76 (1974).
6. G. I. Marchuk and V. I. Lebedev, Numerical Methods in Neutron Transport Theory [in Russian], Atom-
izdat, Moscow (1971).
7. A. Ya. Burmistrov and B. P. Kochurov, Preprint Institute of Theoretical and Experimental Physics No.
49 (1976).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
INVESTIGATION OF THE RATE OF GROWTH OF
A FATIGUE CRACK IN STRUCTURAL STEELS
L. A. Vainer and- V. F. Vinokuro'v UDC 620.171
When investigating modern methods of assessing the efficiency of structures under conditions of cyclic
loading, it is necessary to know the mechanisms of development of fatigue cracks. The first investigations of
the kinetics of fatigue crack development in irradiated low-strength steels of foreign manufacture showed that
as a result of neutron irradiation - causing significant changes of the strength and plasticity characteristics -
the rate of growth of cracks is essentially unchanged [1]. At the same time, for irradiated cylindrical sam-
ples of high-strength steel with an annular notch of the types 12KhN3MFA and 1OKhSND, a marked increase of
the rate of growth of the crack was established [2]. The results do not agree and they are difficult to com-
pare, in consequence of the complexity of the procedure for investigating the kinetics of growth of a fatigue
crack in irradiated materials. It is of definite interest, therefore, to establish a correlation between the re-
sults of tests of samples with cyclic and static loading.
As the material for the investigations, steels 12KhN3MFA and 15Kh3MFA were chosen, and steel
15Kh3MFA was investigated in two states differing in tempering temperature, which ensured a different level
of strength. Compact samples were investigated by eccentric tension. The thickness of the steel 15Kh3MFA
samples was 16 mm, and of the steel 12KhN3MFA - 10 mm. These samples were irradiated in the core of the
VVR-M research reactor (see Table 1). The samples were tested on a special remote-control hydraulic
machine by means of pulsating tension at room temperature with a frequency of 3-5 cycles/min [3]. During
the tests, a diagram was plotted of the load vs expansion of the crack, which allowed the length of the crack to
be determined by an experimentally established calibration graph of sample pliability vs length of crack.
The results of the tests, processed in accordance with Paris's expression [4]
20000 -
10000_
7000
7,900
5000
0
z
1000
700
? 508
E 300
100 t
70 0fP
u0
0 0O
n0
31
0
0
00
0
7 I I I _L__I__L11J_I I_f
10 20 30 "0 60 80 100 200 300 400
AK, kg/mm3/2
Fig. 1. Relation between the rate of growth of the crack
and OK for steel 15Kh3MFA: 0, ^) tempered at 690
and 620?C; ?) tempered at 690?C, irradiation up to a
fluence of 1. 1019 neutrons/cm2 at 120 ? 10?C.
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 311-313, November, 1980. Original article sub-
mitted November 5, 1979.
0038-531X/80/4905-0760$07.50 ? 1981 Plenum Publishing Corporation
000
0
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
TABLE 1. Mechanical Properties of the
Steels Investigated
Material
?
?
Np N
r
?
?
R
a
~ C v
0?
o
.
,o
~
1
rx
12KhN3MFA
-
910
990
17
75
110
temered at
j,
1.11120
12/,0
1260
4
27
40
670
C
15Kh3MFA
-
560
700
20
73
180
tempered at
1.1019
730
820
17
65
170
690 C
,15Kh3MFA
965
1050
17
65
10))
ered at
temp
so 68 NO 100 2/2o J00 400
AK, kg/mm3/2
Fig. 2. Relation between rate of growth of
the crack and AK for steel 12KhN3MFA,
when irradiated up to a fluence of 1. 1020
neutrons/cm2 at 200?C (A) and without ir-
radiation (A).
dl/dN = C(AK)n' . (1)
(here AK is the spread of the stress intensity factor during the cycle; l is the length of the fatigue crack; and
C and m are coefficients) are given in Figs. 1 and 2. It can be seen from the data given that a change of both
the tempering temperature and the neutron irradiation up to a fluence of 1. 1019 neutrons/cm2 at 120 ? 10?C
leaves the rate of growth of the fatigue crack in steel 15Kh3MFA almost unchanged. At the same time, neutron
irradiation up to a fluence of 1. 1020 neutrons/cm2 at approximately 200?C increased the rate of growth of the
fatigue crack in steel 12KhN3MFA. It follows from the data given in Fig. 2 that irradiation has led to a paral-
lel shift of the dl/dN vs AK curve to the side of higher values of dl/dN, which corresponds to an increase of
C without a significant change of the index m.
Some irradiated and unirradiated samples were tested by static tension at room temperature and a speed
of movement. of the clamp of 0.1-0.2 mm/ min. Values of Ic were determined - the energy necessary to in-
crease the crack at the.instant of the start of its increase [51. In accordance with Paris's procedure [R)
I~ = aA/P, (2)
where A is the energy absorbed by the system sample-testing machine at the instant of start of growth of the
crack; a is a coefficient; and F is the net cross section of the sample. The value of A is determined by
planimetric measurement of the hatched region of the diagram of the load vs movement of the moving clamp,
bounded along the axis of abscissa by the value Ac, corresponding to the start of growth of the crack (Figs. 3,
4).
It follows from analysis of the data given that the value of Ic for steel 15Kh3MFA was unchanged with
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
r,
tons
1 2 3 d, mm
Fig. 3. Diagram of the load vs movement of the moving
clamp for samples of steel 15Kh3MFA at 20 ?C: 1, 2)
without irradiation, tempered at 690 and 620?C, respec-
tively; 3) tempered at 690 ?C, irradiated up to a fluence
of 1. 1019 neutrons/cm2 at 120 ? 10?C.
1500
xb41000
500
0,2 0,4 0,6 0,6 1
4 , mm
Fig. 4. Diagram of load vs movement of
moving clamp for samples of steel
12KhN3MFA at 20?C without irradiation (1)
and with irradiation (2) up to'a fluence of
1. 1020 neutrons/cm2 (-200'C); P is the
load.
both change of tempering temperature and neutron irradiation up to a fluence of 1 ? 1019 neutrons/cm2 at 120 ?
10?C. At the same time, neutron irradiation up to a fluence of 1. 1020 neutrons/cm2 at 200?C led to an appre-
ciable reduction of Ic for steel 12KhN3MFA.
In comparing the data of the rate of growth of a fatigue crack with the results of the tests on static ten-
sion, a relation was established between the resistance characteristics to the development of the crack during
static and cyclic loading. Neutron irradiation of steel 12KhN3MFA, having caused a reduction of Ic by a fac-
tor of 5.8. (see Fig. 4), led to an increase of the rate of growth of the fatigue crack by a factor of 2.4 (see
Fig. 2). Thus, it may be supposed that the coefficient C in (1) is inversely proportional to f = Kc, where
Kc is the stress intensity coefficient at the start of unstable spreading of the crack, serving as the viscosity
index of failure of the material with the thickness being tested.
A similar relation follows from Forman's expression [7]:
dC/dN = C, AKm/[(1 R) K? - OK], (3)
where R is the coefficient of asymmetry of the cycle.
Thus, the results of the tests by static tension can be used for an approximate estimate of the effect of
neutron irradiation on the rate of growth of a fatigue crack in structural steels.
1. P. Shakhinyan et al., Am. Soc. Engineers-Mechanics, Ser. D, 96, No. 4, 1 (1974).
2. V. F. Vinoburov and A. V. Vasil'chenko, Problems of Nuclear Science and Technology. Ser. Physics of
Radiation Damage and Radiation Metal Behavior [in Russian], No. 1 (6) (1978), p. 36.
3. L. A. Vainer et al., At. Energ., 45, 2, 137 (1978).
4. J. Irvine and P. Paris, in: Failure, Vol. 3 [Russian translation], Mir, Moscow (1976).
5. G. S. Pisarenko, V. P. Naumenko, and G. S. Volkov, in: Determination of the Crack Resistance of Mater-
ials, Based on the Energy Contour Integral [in Russian], Naukova Dumka, Kiev (1978), p. 6.
6. J. Rice, Trans. ASME, J. Appl. Mech., 35, 379 (1968).
7. R. Forman, V. Kearney, and R. Engle, Trans. ASME, Ser. D, 89, 3, 339 (1967).
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
SENSITIVITY ANALYSIS IN STUDY OF LAWS
GOVERNING RADIATION DISTRIBUTION
ACCORDING TO MONTE CARLO DATA
A. M. Zhezlov,. A. I. Ilyushkin,
V. A. Klimanov, V. P. Mashkovich,
and D. N. Rybin
The study of the general physical laws governing radiation transfer according to the data of direct cal-
culations by the Monte Carlo method entails a number of difficulties, the main one being the complexity of
analysis of the results obtained with appreciable statistical errors, which are particularly large in one-dimen-
sional problems of deep penetration. These difficulties can be overcome by using the method of analysis of
the sensitivity of the calculation results to the initial parameters of the problem [ 1, 21; this method is based
on the application of a dependence of the relative sensitivity of some linear functional R of the radiation field
(e.g., dose, heat release, etc.) to some initial parameters Xi (interaction cross section, functions specifying
the source, etc.) which are found in general form from [ 1, 21
SRIR
P (xi)= SKI/y! , (1)
where OR is the variation of the result with the variation 6Xi. In the case of independent OXi the deviation of
the result R with an error to quantities of second-order smallness is of the form
SR=RE P(X) (5Xi/Xi)- (2)
In the Monte Carlo method the procedure used most for calculating the functions p(Xi) has been that of
correlated sampling [3], which at times proves to be rather ineffective because of the considerable computer
time expended. Analysis of the distinctive features of the Monte Carlo method makes it possible to suggest a
general and quite simple way of calculating the functions p(Xi). The essence of this way can be explained by
considering the example of analysis of the sensitivity to a source whose perturbation 6S (Xi, 4) is given in
piecewise-constant form:
SS (X i, ~) f A (X,) for ~ E Oi; .
S (Xi,) 10 for g 4 oi,
where ~ is a point in the studied region of phase space (e.g., an energy group in a spectrum), and O(Xi) is
any function specifying the magnitude of the perturbation.
On the basis of the general theory [ 1, 2, 41, taking account of the last expression for the function of
relative sensitivity to the source, we get
Ps (Xi, oi)= `0* (~) S (Xi, ~) d~,
0i.
where the integral is the contribution to the functional in question from particles emitted by the source in the
region 0i; this source is taken into account with the conjugate function *( ). This integral can be calculated
by differentiating the contributions to the respective "pockets" of a detector during calculation of the contribu-
tion to the detector, e.g., from the initial energy of the particles (from the coordinate or angle of emission
from the source), which makes it possible then to get the energy (spatial or angular) dependence of the rela-
tive sensitivity to the source. From the last expression there clearly is a possibility of estimating the value
function 4*(~) on the basis of the results of direct calculations.
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 313-315, November, 1980. Original article sub-
mitted December 11, 1979; revision submitted June 23, 1980.
0038-531X/80/4905-0763$07.50 ?1981 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
U,4
d Q3
I y
0,2 L
GL ~ L-' _J
U 2 4 6 0 2 4 6 E, MeV
Fig. 1. Energy dependences of relative sen-
sitivities of energy flux density of scattered
y rays to the assignment of a point isotropic
source, with a fission spectrum in a homo-
geneous air medium of density 1.225 kg/m3
'(a) and near the air-earth interface for
Hs = 10 m (b) at a distance of 0.5 (-), 1.5
(---), and.2.5 (-?-?-) km.
Fig. 2.. Geometry of problem and diagram
for reckoning angles for reflection of quanta
from earth.
To illustrate the possibilities of sensitivity analysis and of the proposed method of calculating p(Xi) let
us consider some results of its implementation within the framework of a local estimate with a shift of range
by an improved variance-minimizing technique (MDB method [51) as applied to the practically important prob-
lem of transfer of y rays from a point isotropic source with a fission spectrum [R] in a uniform air medium
and near the air-earth interface to distances of up to 3500 kg/m2. Analysis of various dependences of the
relative sensitivity makes it possible to formulate laws of radiation transfer near to and far from the earth.
With an increase in the distance an increase is observed in the energy of the quanta which make the main con-
tribution to the principal functionals of the field of scattered radiation (Fig. 1); this can be used for significant
sampling of the exit energy of quanta from the source. The main contribution to the complete functionals of
the field from those quanta which interact with the earth is made by quanta which collide once with the earth.
Their contribution (up to 22% of the energy flux density) is an order of magnitude'or more greater than the
contributions from quanta with more reflections from the earth. For all of the considered values of the source
height Hs (0.01:5 Hs v, in Eqs. (5) and (6) n
must be replaced by v and v by n, respectively. The case of symmetric position of the sensor and the end of
the rod (n = v) requires special treatment. When, for a = 0, v tends to n, Eq. system (1) becomes degener-
ate and a second (multiple) root w0, i.e., a second-order pole, appears (a situation corresponding to a second-
order Jordan box exists). This, in turn, means that in the description of the time dependence, there appear,
in addition to terms of the form exp wt, terms of the form t exp wt. The degeneracy at n = v vanishes when
a # 0. For small a we have in place of Eq. (6)
B' _ ? n
COsin Bo . (7)
oo coO Bo
The formulas so far obtained can be used to estimate the error introduced into the parameter w by substitut-
ing the real K value by an infinitely large K value. A comparison with calculated values has shown that
though the formulas are very simple, they can be used not only for a qualitative evaluation of the effect but
also for its quantitative estimation. Numerical calculations were made with a modified version of the FOSC
program [5] which has been designed for determining w in more complicated, yet one-dimensional reactor
models. When Chebyshev polynomials were used in the program, it was possible to take into account the life-
time of the prompt neutrons and the inertia of the electric drive. Calculations were made with variations of
various system parameters within wide ranges.' The results were most significantly influenced by the posi-
tions of sensor and rod, the reactivity coefficient a, and the regulator amplification coefficient K. Figure 1
shows the dependence of w on K in various versions of the sensor and rod positions. The stationary distribu-
tion 0 was assumed as sinusoidal, (M/H)2 - 2. 10 3, A = 60 (which corresponds to T = 600 sec), (3 = 7.5
10 3, and a = 10-2. The lifetime of the prompt neutrons was assumed as 10 3 sec; the time constant of the in-
ertia of the motor was assumed as 1 sec, but these values were practically without influence on the function
shown in Fig. 1. In w, a coordinates, curves 1-4 are transformed into clear straight lines, whereas the ratio
Ow/w0 calculated with Eqs. (4) and (6) differs from the results of the numerical calculations by approxi-
mately 1%0.t
*When the expression under the root is negative, w becomes complex.
t The w0 value in the case of a sinusoidal stationary neutron field is given with great accuracy by Eq. (3) with
bz=(M)2n3(ne-1)/[4n sine \2n/ \1+2 4n21-1
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Our investigations lead to the following important conclusions. The w values hardly differ. from woo in a
wide interval of K, i.e., at those K values the regulator can be considered a fast-response regulator. The
greatest difference between w and w o (-17%0) is noted at K = 4.5. 10 2 (left end of curve 1). At this K value,
T = 30 sec, and an imbalance A4/4)0 = 3. 10-2, the rate at which reactivity is introduced by the rod of the auto-
matic regulator amounts to 6. 10 3 /3/sec, i.e., the rate is smaller by one order of magnitude than permitted by,
the rules of nuclear safety [6]. Depending upon the positions of the sensor and the rod, an increase in K can
imply either an increase or a decrease in stability. Finally, it should be noted in analogy to the increase in
stability upon spacing the sensor from the rod (known from previous publications [2-4 , 7]), all the effects
listed above are not described in the pointwise approximation.
1. A. Hitchcock, Stability of Nuclear Reactors [Russian translation], Gosatomizdat, Moscow (1963).
2. P. S. Postnikov and E. F. Sabaev, At. Energ., 26, No. 1, 56 (1969).
3. A. M. Afanas' ev and B. Z. Torlin, At. Energ., 43, No. 4, 243 (1977).
4. I. Ya. Emel'yanov et al., At. Energ., 46, No. 2, 82 (1979).
5. A. M. Afanas'ev, Preprint Inst. Theor. and Exp. Phys. ITEF-83 [in Russian], Moscow (1979).
6. Rules of Nuclear Safety of Atomic Power Stations [in Russian] (PBYa-04-74), Atomizdat, Moscow (1976).
7. A. M. Afanas'ev and B. Z. Torlin, At. Energ., 44, No. 6, 530 (1978).
FAST RESPONSE OF THE REGULATOR IN A
CYLINDRICAL REACTOR
The radial stability of a cylindrical reactor with a fast-response automatic central regulator was con
sidered in [ 1]. The processes occurring in the reactor were considered slow enough so that the delay of the
regulator could be disregarded.
Let us consider on a simple model the extent to which and the limits within which this ideal is correct.
Disregarding prompt neutrons in a one-group diffusion approximation with feedback in the form of a simple
inertial link [2] with a positive reactivity coefficient a we obtain after linearization and Laplace transforma-
tion:
M2 0(p +(k0 9)q- Pcp+ked-ax 1 the equation has
the particularly simple form
,,w ti 2 K (6)
,
When a = 10-2 and K = 0.5,* the w o value obtained in the approximation of a fast-response regulator
differs from the accurate solution by less than 4%. This calculation reveals that, for determining the stability
of systems with a time constant of about 1 min in the feedback Or more than 1 min), the approximation of the
fast-response regulator is quite 'satisfactory. The approximation',is -the better the smaller a and the greater
the efficient amplification'coefficient K of the regulator and also the greater the time constant T, because K
also increases with increasing time constant.
LITERATURE CI'TE`D
1. B. Z. Torlin, At. Erierg., 45, No. '6, 4:57 (1978)-.
2. J. Ya.'Exnel'yanov et al., At. Energy, 46, No. 2,'82 (1979).
3. E. Jahnke, F. Emde, and F. Losch,"Speci'al Functions [Russian translation], Nauka, Moscow (1964).
4. Rules of Nuclear Safety of Atomic Power Stations [in Russian], No. PBYa-04-74, Atom zdat,'Nloscow
'(1976).
*For.the imbalance 04'/ 0 = 3 '10 2 =and'''T = 60 sec, this corresponds"to a rate of 0.03-5ji/sec'ofintroducing
reactivity; 'this is'two times smaller than the value allowed by the rule's of nucle'ar'safety'[41.
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 Declassified and Approved For Release 2013/02/14: CIA-RDP10-02196R000800040005-8
CALCULATION OF THE OVERHEATING OF FUEL
ELEMENTS, TAKING INTO ACCOUNT THE
PROBABILITY OF DEVIATIONS OF.THE CORE
PARAMETERS
I. M. Kurbatov UDC 621.039.517.5
In actual calculations of random deviations of the fuel element temperature, the sequential probabilistic
approach has been increasingly used. The method deals with the nature of the deviations of the important core
parameters and makes it possible to take into account the laws governing core parameter changes when the
result of the common influence of numerous overheating factors is assessed [ 1-41.
But in such calculations the maximum deviations of the important parameters of a single fuel element
are often used as factors of overheating for the technological channel or for a cell of the core; this is done by
expanding the influence of each of the' deviations over the entire group of fuel elements forming the channel.
Since the maximum deviations of some parameter will hardly occur in all fuel elements of the channel,
the approach often leads to unjustifiably large results of the calculations. We consider in the present. work a
method of taking into consideration the influence of the "group effect" upon the overheating factors with which
the random deviations of the fuel-element temperature in the core channel are calculated.
When the core channel consists of m homogeneous fuel elements with, randomly changing parameters,
the probability that all m elements which are assembled in the channel have unfavorable values of some im-
portant parameter .9' (condition of a hot channel resulting from a particular parameter) can be obtained from
the following relation [ 51:
P,1 f (m) _ (PM)! (M- tn)!
M!(PM-nt)
where M denotes the total number of fuel elements from which the core channels are composed by the random
sampling method; and p denotes the probability of a certain fuel. element parameter falling into the interval. of
unfavorable values (p depends on the probability distribution of the deviations of the parameter). Then 1 - P
defines the interval of admissible deviations of the parameter; pM denotes the total number of fuel elements
having unfavorable values of the parameter in the set M.
For M >> in Eq. (1) is reduced to
Par (m) = PM- (2)
When some value PM(m) is assumed (considering,. e.g., requirements to the thermal reliability of the
core), then we have
P = ,VPn1 Gn)? (3)
The P value obtained and the known probability distribution= of the parameter under consideration can
be used to determine the limit deviation of the parameter for a cell with the deviation to account for
the given PM (m) value. Thus, for Pj i (3) = 0.00135 (probability of a normal distribution of a random quan-
tity going on one side beyond the 30? limit; this probability is often assumed as a tolerable risk value in reli-
ability calculations) :
which corresponds almost to the deviation limit of a normal distribution of the parameter (factor of overheat-
ing for a cell):
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 325-326, November, 1980. Original article
submitted March 19, 1980.
0038-531X/80/4905-0783$07.50 ? 1981 Plenum Publishing Corporation 782
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Usually (A.9-) max = 3a is assumed for a fuel element, and this means that the factor of overheating is
reduced about 2.5 times in the case under consideration. Accordingly, the fuel temperature deviation caused
by this factor is reduced.
When the channel is composed of elements of two types (e.g., fuel elements and rotating substitutes),
we obtain in analogy to Eq. (1):
P(~nl.ma)= (P1M1)!(M-mi)!'(P2M2)!(M2-m2)! 4
M1!(P1M,-nm1)!'M2!(P2M2-na2)! ( )
For P1 = P2 = P the problem is reduced to the preceding problem. When P1 # P21 one can consider various
combinations of the -P1 and P2 values which lead to a given PM1M2 (m1, m2) value.
LITERATURE CITED
1. A. Ya. Kramerov and Ya. V. Shevelev, Design Calculations of Nuclear Reactors [in Russian], Atomizdat,
Moscow (1964). 1
2. A. I. Klemin, Probabilistic Design Calculations in Project Work on Nuclear Reactors [in Russian],
Atomizdat, Moscow (1973).
3. Principles of Not-Channel Factor Calculations for Fast Reactors, IAEA-166, Vienna (1974).
4. V. A. Khranovskii and I. M. Kurbatov, At. Energ., 44, No. 3, 258 (1978).
5. I. V. Dunin-Barkovskii and N. V. Smirnov, Theory of Probability and Mathematical Statistics in Tech-
nology [in Russian], GITTL, Moscow (1955).
HOMOGENIZATION AND'HETEROGENIZATION
ERRORS IN THE CALCULATION OF RBMK
S. S. Gorodkov UDC 621.039.51.12:539.125.52
The energy distribution in a channel reactor can be calculated with about equal success with a homoge-
neous grid or mesh program or a heterogeneous program (based on the source - sink method). As the differ-
ences in ,the results of these calculations are not small (up to 1-2% in keff and up to 10-20% in the neutron
flux), the question of which of the algorithms is better arises. In order to obtain an answer, we. made use of
the fact that various small-group cell constants are used in each algorithm without considering that these con-
stants were obtained from a one-cell multigroup kinetic calculation which is almost the same in both algor-
ithms. Therefore the multigroup kinetic calculation of the reactor need not be necessarily used as a standard.
Let us consider the model problem of a composite lattice in which the neutron transfer is described by the
two-group diffusion equation
~- (~>t D= ~Dt o s- ( E~ E E' vE1-vEf
`Ql 0 Dt -Et-2 Et
rt
The characteristics D and E are constant over the individual cells of the composite lattice and close to the
characteristics used in the calculations of high-powered water-cooled, channel reactors (RBMK). Thisproblem
can be exactly solved with the homogeneous grid program having a step width of the grid much smaller than
the step width of the lattice. When thereafter a solution with the heterogeneous program is obtained, the dif-
ference of the results provides an idea of the error which. the heterogeneous approximation causes in the cal-
culation of RMBK. For this purpose, we replace each cell of the composite lattice by a heterogeneous cell con-
sisting of a homogeneous moderator with a filiform source-sink configuration on the axis [ 11, The neutron
field component which is of angular symmetry has in the cell the following form:
o(r)=l )io(,)+Ko(,)al y, (2)
Translated from Atomnaya Energiya, Vol. 49, No. 5, pp. 326-327, November, 1980.
784 0038-531X/80/4905-0784$07.50 ?1981 Plenum Publishing Corporation
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TABLE 1. Some Results of a Comparison of the Calculation of Sublattices of RBMK
Com
osite
p
lattice
' eff. o~
Maximum in
cells R
Average in
In cell P
cells R
Heterogeneous
0,29
-0,50
0,36
-2,84
7,84
0,14
0,37
0,25
-2,20
8,95
1
47
-2
88
2
06
-14
43
6
17
Homogeneous grid, version A
,
1,80
,
7,52
,
3,85
,
-7,57
,
18,27
Homogeneous grid, version B
-0,34
1,57
1,10
3,76
-8,85
-0,59
0,74
0,35
5,86
-10,75
Exact solution
1
18
- heterogeneou
-2
54
s
1
89 -11
59 -1
67
Homogeneous-grid, version A
,
1,66
,
7,25
,
3,55
,
-5,37
,
9,32
Homogeneous-grid, version B
-0,63
1,91
1,33
7,60
-16,69
-0,73
-0, 69
0,47
8,06
-19,70
P
R
R
R
C
R
R
R
P
R
R
R
C
R
R
R
R
R
R
P
R
R
C
R
R
P
R
R
C
R
R
R
Fig. 1. Two types of composite lattices: R)
technological channel; P and C) immersed
and retracted absorbing rods, respectively.
(1 01 l.
1 L2/(i-L2) 1/, (P. (TL)
1? (,/J/r) 0 11 1 K? (r/j/t) 0 ll
I0= (0 1 (r/L)l' K0 2. (0 K(r/L)l
T denotes the age of the neutrons; L denotes the diffusion length of the thermal neutrons in the moderator;
'PT and cp L denote free coefficients; and is denotes a 2 x 2 matrix the elements of which are chosen so that
the heterogeneous cell is equivalent to the initial cell. Among the several forms of equivalency we preferred
the one which implies the simplest relation between the homogeneous and heterogeneous constants and re-
quires that the ratio between the neutron leakage through the boundary and the average neutron flux over the
cell (~ = D(b) is the same in the homogeneous and heterogeneous cells. This condition leads to the equation
2 D = CZ (1t- Kta)1 [Z (I+ Ka)1-,
(3)
from which "a. can be determined. In Eq.(3), I1 and K1 denote the integrals of (8/an) Io (r) and (8/an) Ko(r);
over the surface of the cells; and I and K denote the average values of I0(r) and K0(r), respectively, taken
over the cell volume. The heterogeneous calculation renders the coefficients 0, whereupon ~ can be deter-
mined with the formula
P=Z(I+Ka)tp? (4)
In addition to the comparison of the heterogeneous calculation with the exact calculation, the homogeneous cal-
culation made with a single mesh point or cell was included in the comparison. The mesh points can be situ-
ated either at the centers (version A) or in the corners of the cells (version B). These schemes are used in
the vast majority of reactor calculations, because a twofold reduction of the step width of a two-dimensional
mesh causes an eightfold increase in the number of calculations.
The two types of composite lattices used in the calculations are shown in Fig. 1. The homogeneous
characteristics of the cells are close to those used in the calculations of RBMK. Each solution was normalized
to the thermal neutron flux average over active cells. The results of the comparison are shown in the first
part of Table 1. The error of heterogenization is so small that it would be advantageous to use the heteroge-
neous calculation instead of a coarse mesh calculation in the solution of homogeneous problems of this type.
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An interesting detail is that version B which is conceptually equivalent to version A is actually more accu-
rate.
The problem may be considered from the opposite viewpoint by assuming that the heterogeneous calcu-
lation is the exact calculation. The homogenization errors of this problem are equal with an accuracy of the
sign of the heterogenization errors of the preceding problem. A comparison of,the coarse grid solution with
the heterogeneous solution (in the case under consideration, with the exact solution) reveals that the advantage
of version B over version A decreases. One can therefore say that accurately executed homogenization
and heterogenization contribute very little to the overall error in the calculation of RBMK when compared
with the other approximations such as the two-dimensional, the small-group, the coarse-grid approximations,
etc.
LITERATURE CITED
1. S. S. Gorodkov, At. Energ., 48, No. 6, 370 (1980).
DETERMINATION OF THE FLUX PARAMETERS
IN A VERTICALLY ADJUSTABLE RING CHANNEL
OF A REACTOR
V. N. Oleinik UDC 621.039.5:532.5
The distribution of the coolant over the core cross section in shell-type reactors depends on the fea-
tures of the flow at the entry section of the inner-shell hydraulic system. One of these sections in a water-
moderated water-cooled power reactor is the vertically adjustable ring channel between the reactor shell and
its cut-out portion. The coolant is supplied to the vertically adjustable ring channel via one or several inlet
nozzles, i.e., the coolant' supply is centered. Vortex zones develop close to the inlet nozzles. The fields of
velocity and hydrodynamic pressure over the circumference of the vertically adjustable ring channel are sig-
nificantly nonuniform [1). Farther from the inlet nozzles the distribution of the hydrodynamic parameters in
the vertically adjustable ring channel becomes more uniform. However, a full equilibration of the flux in the
exit cross section of a vertically adjustable ring channel may not occur. It is therefore of great importance
in practice to determine by calculation the hydrodynamic flux parameters over the length and the circumfer-
ence of the vertically adjustable ring channel for various numbers of operative inlet nozzles. Experiments
have shown that the hydraulic flow losses are small beyond the limits of the vortex zones in a vertically ad-
justable ring channel. We therefore determine the hydrodynamic flow parameters under the assumption that
the flow is related to a potential.
Assume that a flow of nonviscous liquid or fluid enters through the inlet nozzle in a vertically adjustable
ring channel having internal radius R1, external radius R2, and an impenetrable flow separator. Since the
width of the vertically adjustable ring channel is always much smaller than its average radius R = 0.5 (R1 +
R2), the changes of the flow parameters over the width of the vertically adjustable channel can be disregarded.
Thus, we consider the flow of a nonviscous fluid on some cylindrical surface having radius R and height H.
We represent the inlet nozzle as a source with the output Q and the linear dimensions 26 along the axis
and 2RE over the circumference (Fig. 1).
The equation for the velocity potential U (z, co) in the flow region under consideration is of the form
1 82U (T2U
Q14&.R z0-Sm; (Po+E