SOVIET ATOMIC ENERGY VOL. 46, NO. 3

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• Document Creation Date: December 23, 2016
• Document Release Date: February 12, 2013
• Sequence Number: 3
• Publication Date: March 1, 1979
• Content Type: REPORT

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Russian Original Vol. 46, No. 3, March, 1979
September, 1979
SATEAZ 46(3) 161-258 (1979)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPf VIR
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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'SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy 'is a cover-to-cover translation of Atomnaya
Energiya, a publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes --available both advance copies. of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
V. V. Matveev'
I. D. Morokhov
A. A. Naumov
A. S. Nikiforov
A. S. Shtan'
B. A. Sidorenko
M.'F. Troyanoy
E. I. Vorob'ev
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews,.Chem-
ical Abstracts, Engineering Index, INSPEC-
Physics Abstracts and Electrical and, Elec-
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Nuclear Science Abstracts.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
September, 1979
Volume 46, Number 3 March, 1979
CONTENTS
Engl./Russ.
ARTICLES
Increasing the Efficiency of Uranium Utilization in the RBMK-1000
Reactor - I. Ya. Emel'yanov, A. D. Zhirnov, V. I. Pushkarev,
and A. P. Sirotkin ........................ ' ....... ............ 161 139
Theoretical and Experimental Research on the Temperature
Effect of the Reactivity of Heterogeneous Critical Assemblies
with Strongly Blocked Absorber - V. I. Bagretsov, V. I. Lependin,
V. I. Matveenko, and V. N. Morozov ................................... 164 142
Optimization of Physical Characteristics of a Heterogeneous
Reactor- B. P. Kochurov and V. M. Malofeev ............................ 168 146
Development of the Surface Pseudosource Method for Calculating
Neutron Fields in Cells with a Bundle of Fuel-Element Rods
- N. I. Laletin and N. V. Sultanov .... ........................... 172 148
Measurements of the Fission Cross Section of.239Pu by Neut'rons'
with Energy from 10 eV to 100 keV - Yu. V. Ryabov. .... ....... .. .. 178 154
Measurement of the Total Neutron Cross Sections of 153Eu, 154Eu, and 155Eu
- V. A. Anufriev, S. I. Babich, A. G. Kolesov, V. N. Nefelov,
V. A. Poruchikov, V. A. Safonov, A. P. Chetverikov, V. S. Artamonov,
R. N. Ivanov, and S. M. Kalebin ...................................... 182 158
Blistering in Niobium under Implantation of Helium Ions at Energy
Expected in Thermonuclear Reactor - S. Das, M. Kaminsky (USA),
V. M. Gusev, M. I. Guseva, Yu. L. Krasulin, and Yu. V.:Martynenko (USSR) ........ 185 161
Helium Blistering under High Irradiation Doses - I. N. Afrikanov,
V. M. Gusev, M. I. Guseva, A. N. Mansurova, Yu. V. Martynenko,
V. N.. Morozov,.and 0. I. Chelnokov ...................................... 190 165
Microdosimetric Characteristics of Neutrons at Energies between 50 eV
and 10 MeV - V. A.Pitkevich and V. G. Videnskii .................... ..... 197 170
Albedo of Concrete for Low-Energy Gamma Radiation - M. P. Panin
and A. M. Panchenko ............................ 201 174
LETTERS
Distribution of Scattered Gamma Radiation from a Pulsed Source
- D. A. Kozhevnikov .................... ....... ............. ... 206 178
Design of Tesla Transformers Used in Direct-Voltage Accelerators
- D. Kh. Dinev ................ ............. ? ................... 208 179
Radiation Alteration of the Properties of Graphite over a Wide Range
of Irradiation Temperature and Neutron Flux - Yu..S. Virgil'ev,
I. P. Kalyagina, and V. G. Makarchenko ................................. 210 180
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CONTENTS
The Formation of Transuranium Nuclides in Connection with the Combined
Use of VVER and RBMK Power Reactors - T. S. Zaritskaya,
(continued)
Engl./Buss.
A.K. Kruglov, and A. P. Rudik...................................... 213 183
Yields of 28Mg upon the Irradiation of Magnesium and Aluminum
by Alpha Particles - P. P. Dmitriev and G. A. Molin ............ . . , , , 216 185
Some Properties of Fluctuations of the Neutron Field in a Nuclear Reactor
-E.A.GominandS.S,Gorodkov .................................... 219 187
Reciprocity Property of Systems for Suppression of Xenon Oscillations
- B. Z. Torlin ................................................. 222 189
Interpretation of Data on the Total Scattering Cross Section of Cold
Neutrons in Condensed Hydrogen-Containing Media
- V. E. Zhitarev and S. B. Stepanov , ... 224 190
An Analytic Solution of the Kinetic Equations of a Point Model
of a Reactor - A. A. Shepelenko ..................................... 227 192
SPECIAL ANNIVERSARIES
Academician Lev Andreevich Artsimovich - B. B. Kadomtsev ............. ...... 229 195
Nikolai Aleksandrovich Perfilov - K. A. Petrzhak .... ...... , ... . . .. . . 231 197
COMECON NEWS
Thirty-Fifth Conference of the COMECON Permanent Commission
Atomenergo -Yu. S. Troshkin .............. . 233 199
.Diary of Collaboration ............. ............. ............... 234 199
INFORMATION
Soviet-French Collaboration in the Field of the Peaceful Utilization
of Atomic Energy - B. A. Semenov .. ... ... .................... . . 236 201
CONFERENCES, MEETINGS, AND SEMINARS
International Exhibition and Conference on the Nuclear Industry,
"Nuclex-78" - Yu. M.-Cherkashov ... . .............. . .......... . . . . ... 239 203
Third American-Soviet Seminar on Steam Generators for Fast Reactors
- V. F. Titov ................................................... 241 205
Meeting of the International Working Group of IAEA on High-Temperature
Reactors - V. N. Grebennik ..... .............:............... ...... . 243 206
International Conference on Neutron Physics and Nuclear Data
for Reactors and Other Applied Purposes - G. B. Yan'kov .................... 245 207
Symposium, "International Guarantees-78" - N. S. Babaev .................. .... 247 209
Soviet-American Conference on "High-Frequency Plasma Heating
in! Toroidal Systems" - V. V. Alikaev ................ ................. 249 210
Nineteenth International Conference on High-Energy Physics
- V. I. Zakharov ................................................ 250 211
All-Union Seminar "Electronic (Automatic) Methods of Concentration
of Minerals" - B. V. Nevskii, M. L. Skrinichenko, and A. P. Tatarnikov............ 252 212
Ninth Radiochemical Conference in Czechoslovakia - A. S. Solovkin ................. 253 213
NEW BOOKS
Atomic-Hydrogen Power Generation and Technology - Reviewed by Yu. I. Koryakin.. ... 256 215
V. V. Goncharov, N. S. Burdakov, Yu. S; Virgil'ev,'V. I. Karpukhin,
and P. A. Platonov. Action of Irradiation on the Graphite in Nuclear
Reactors - Reviewed by A. P. Sirotkin .................................. . 257 215
A. B. Mikhailovskii. Plasma Instabilities-in Magnetic Traps
- Reviewed by A. M. Fridman ............................. ............ 258 216
The Russian press date (podpisano k pechati) of this issue was 2/26/1979.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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UTILIZATION IN THE RBMK-1000 REACTOR
I. Ya. Emel'yanov, A. D. Zhirnov, UDC 621.039.542.34
V. I. Pushkarev, and A. P. Sirotkin
Increasing the unit power is one way of improving the economics of atomic power plants. As applied to
RBMK (high-power water-cooled channel) reactors, this was reflected in the development of the RBMK-1500,
RBMK-2000, and RBMK-2400. The possibility of increasing the channel power of the RBMK-1000 by a factor
of 1.5 through heat-exchange intensification is realized in the RBMK-1500 and the power is thus increased to
1500 MW(E) without altering, the reactor dimensions and design. In the RBMK-2000 design, the channel diam-
eter, the number of fuel elements in the channel, and the lattice pitch have been increased, thus making it
possible to develop a reactor with double the power, i.e., with 2000 MW(E), within the same overall dimensions
as the RBMK-1000. The creation of a channel with increased power opens up new potentialities for improving
the technical and economic characteristics: increasing the burn-up fraction and reducing the consumption of
fuel assemblies and the specific consumption of natural uranium.
Operating experience with uranium-graphite reactors [1, 2] showed that fuel recharging can be carried
out continuously in them during operation. This makes it possible to avoid considerable variations in reac-
tivityduringthe reactor operation, to reduce the unproductive capture of neutrons in the control rods, and thus
to intensity-the energy production and the fuel burn-up fraction at a low uranium enrichment. As shown by the
physical and technicoeconomic calculations of the RBMK-1000 [3, 4], with the present prices for fuel and fab-
rication of fuel elements, the reduced fuel component cf of the electricity production costs is a minimum with
an initial enrichment of 1.8-2%. At the same time, calculations established that with a higher enrichment and
with the reactor operating in a continuous recharging mode the power of the freshly charged channels rises
and the fuel residence time increases. On the basis of the available data and bearing in mind that, first, there
was insufficient experience in operating fuel elements with a high burn-up fraction (^- 25-30 MW ? day/kg U)
with linear loads of 300-400 W/cm and a fuel residence time of five years and, second, the cf minimum is not
pronounced, a comparatively conservative solution was adopted in the RBMK-1000 for .steady-state operating
conditions of continuous recharging of fuel with a 1.8% enrichment (Table 1). The use of cf as an optimization
criterion is arbitrary to a certain extent.
Experience from the operation of the first RBMK-1000 reactors showed that in respect of both the linear
loads in the fuel elements and maximum channel power (according to the conditions of heat-exchange crisis)
the fuel element and fuel assembly design provides for certain reserves. Moreover, as the fuel is burned up
and as the auxiliary absorbers, compensating the initial excess reactivity, are withdrawn, the stability of the
energy distribution diminishes. As shown by calculations and confirmed by experiments, the deformation of
the distribution of the energy release with a time constant ranging from several minutes to several tens of
minutes for the first azimuthal harmonic is determined primarily by the positive steam void coefficient of
reactivity z . A decrease in this coefficient makes the energy distribution more stable. The most economic
and optimal reduction of the steam void coefficient and increase in the stability of the energy distribution in
the RBMK are attained by increasing the ratio of fuel nuclei to moderator nuclei. The fuel-to-moderator
nucleus ratio is improved in operating reactors by raising the enrichment whereas in reactors in the design
stage it is possible to reduce the number of moderator nuclei, e.g., by reducing the lattice pitch or the effective
density of the moderator.
Increasing the fuel enrichment results in a higher burn-up fraction and a change in a(p, improving the
stability of the field, and in a lower consumption of fuel and fuel elements. An increase in the enrichment and
the corresponding increase in the burn-up fraction in turn cause a rise in the power of the freshly charged
channel, the fuel residence time, and the linear loads in the fuel elements. The possibility of increasing the
channel power 1.5-fold is confirmed by the construction of the RBMK-1500 channel. The data given in Table 2
should be considered mainly as comparative and not absolute data inasmuch as the calculations were performed
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 139-141, March, 1979. Original article sub-
mitted July 17, 1978.
0038-531X/79/4603-0161 $07.50 ?1979 Plenum Publishing Corporation
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TABLE 1. Characteristics of Reactor Using Fuel of Design and Increased Enrichment
Index
RBMK-1000 RBMK-1500
Initial enrichment, %
1,8
2,0
2,4
3,0
3,6
1;8
2,0
Fuel burn-up fraction, MW ?day/kg U
18,5
22,3
28,8
37,6
45,7
17,8
21,6
Comp. of discharged fuel, kg/ton:
236U
3,9
3,5
2,9.
2,5
2,2
4,4
3,8
236U
2,1
2,5
3,1
'4,0
4;8
2,1
2-,4
239Pu
2,2
2,2
.2,2
2,1
2,1
2,2
2,2
240pu
1,8
2,0
2,3
2,5
2,6
1,8
2,0
241pu
0,5
0,5
0,6
0,6
0,7
0,5
0,5
Poison
19,4
23,3
30,1
39,3
47,8
18,6
22,8
Change in o:,, rel. to design value, 8
-
-1,3
-3,5
-6,4
-9,0
-1,5
-2,7
Uranium consump., ton/yr?GW(E) with
N = 0.8:
50,5
42
32,5
25
20,5
52,4
43,3
Enriched
169
158
151
148
148
174
165
Natural
16
13,3
10,2
7,9
6,5
16,5
13,6
Fuel component:
electricity cost.kopek/kWh
0,252
0,232
0,216
0,208
0,208
0,260
0,240
reduced cost cf. lopek/kWh
0,370
0,362
0,370
0,405
0,445
0,335
0,325
TABLE 2. Channel Power and Linear Load
in Fuel Elements as Function of Enrichment
of Charged Fuel
Characteristic
RBMK-1000
RBMK-
1500
Enrichment, ?
1,8
2,0
2,4
3,0
3,6
1,8?,
2,0
Power of freshly
charged channel
with account for
k W
2650
2800
3150
3500
3800
4050
4250
Limiting power of
channel with ac-
count for 3och. kW
3050
3250
3650
4050
4350
4680
4910
Linear load in fuel
element in freshly
charged channel
gnom, W/cm
1
295
315
350
390
420
455
485
Limiting value q
with account fo?
3ot. W/cm
360
385
430
480
520
560
595
Fuel assembly
period. eff. days
1100
1350
1730
2260
2750
700
860
for a steady-state fuel-recharging mode. To determine the power of fresh channels we used the coefficients of
nonuniformity kr and kz, obtained with allowance for the operating experience with the RBMK-1000, and the
calculated overload factors. For reactors operating with 1.8% enriched fuel the coefficient of nonuniformity
over the radius, kr, was taken to be 1.4 and the coefficient of nonuniformity over the height, kz, was taken to be
1.4. On the basis of operating experience with the RBMK-1000 the rms error vch of the determination and
maintenance of the channel power was assumed to be 5.2%, and that of the linear load in the fuel element, Qt,
was assumed to be 7.7%. In calculating the annual consumption of natural and enriched fuel, we assumed that
the load factor cp was 0.8 and that the 235U content in the spent material from the enrichment plants was 0.25%.
The return of 235U into the fuel cycle from the spent fuel was not taken into account. Thus, increasing the
enrichment of the fuel in the RBMK-1000 is a realistic way of raising the efficiency of fuel utilization. In this
case,' from the point of view of the allowable channel powers and linear loads in the fuel element, enrichment
to 3.6% is possible. It was decided to increase the channel power and linear loads in the fuel element by up to
1.5-fold in the RBMK-1500 [5, 6]. In the given case the fuel assemblies were provided with heat-exchange
intensifiers. No changes were made in the channel construction and in the inlet and outlet equipment. With
a more moderate increase in the enrichment and, therefore, in the channel power, fuel assemblies without
intensifiers can be used. For example, a transition to a 2% enrichment of the fuel can be made without any
structural changes in the fuel assemblies. The maximum values given in Table 2 for the power were obtained
with the assumption that the algorithm for equalizing the power over the reactor core remains the same as in
operating RBMK-1000 reactors. Along with this, we can propose measures (some of which have already been
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
tested in reactors) permitting an extension of the possibility for equalizing the energy distribution in the
reactor core. Among these we can classify the use of absorption rods inserted in fresh fuel assemblies and
withdrawn as the channel power decreases, the use of depleting absorbers, optimization of the recharging
procedure, etc. A certain, reserve in respect of equalization of the energy distribution is due to the possibility
of increasing the operational reactivity margin resulting from the operating conditions of the atomic power
plant in the energy system.
Increasing the enrichment leads to a reduction of the consumption of fuel dlements and natural uranium.
The annual consumption of fuel elements drops by 20-30% in the transition from variant to variant and is
halved when 3% enrichment is employed. The consumption of natural uranium with this enrichment drops by
20 tons to 150 tons/yr. The 235U content in the spent fuel is brought down to 0.25%, i.e., to the level in the
spent material from enrichment plants, and is reduced to _0.2% when 3.6% enrichment is employed, thus
removing the problem of the necessity of removing it from the spent fuel. Increasing the initial enrichment
significantly changes the steam void coefficient of reactivity, reducing it in comparison with the 1.8% enrich-
ment and shifting it in the negative direction. This improves the stability of the energy distribution but
requires special consideration in the case of transient conditions.
If the change in the parameters under discussion (channel power, linear load in fuel element, change in
steam void coefficient of reactivity) does not cast doubt on the possibility of raising the enrichment, then
increasing the burn-up fraction to 40-45 MW ? days/kg U and the calendar residence time of the fuel elements
in the reactor core to 10-12 years with an enrichment of 3 and 3.6%, respectively, requires special investiga-
tion and verification, although the construction of fuel elements with an oxide fuel burn-up of 45-50 MW ?
days/kg U can be considered feasible [7, 8]. It is more difficult to ensure the life of fuel elements under
reactor conditions over a long period of time.
Raising the channel power 1.5-fold opens up new prospects for the RBMK-1000 and markedly improves
the economic factors of the fuel cycle through an increase in the fuel enrichment. The use of fuel with a 2.4-
3% enrichment in the RBMK-1000 requires the construction and experimental testing of the efficiency, of fuel
elements permitting a burn-up fraction of up to 40 MW ? days/kg U and having a guaranteed viability for a
residence of about 10 yr in the reactor core. This is one direction in which experimental and design work
as well as research should be conducted in order to improve the RBMK-1000.
1. A. M. Petros'yants, Current Problems of Atomic Science and Engineering in the USSR [in Russian],
Atomizdat, Moscow (1976).
2. Atoms in the Service of Socialism. An Album [in Russian], Atomizdat, Moscow (1977).
3. A. P. Aleksandrov et al., At. Energ., 37, No. 2, 95 (1974).
4. I. Ya. Emel'yanov, P. A. Gavrilov, and B. N. Seliverstov, Control and Safety of Nuclear Power Reactors
[in Russian], Atomizdat, Moscow (1975).
5. N. A. Dollezhal' et al., At. Energ., 40, No. 2, 117 (1976).
6. A. P. Aleksandrov and N. A. Dollezhal', At. Energ., 43, No. 5, 337 (1977).
7. V. G. Aden et al., At. Energ., 43, No. 4, 235 (1977).
8. V. A. Tsykanov and E. F. Davydov, Radiation Resistance of Fuel Elements of Nuclear Reactors [in
Russian], Atomizdat, Moscow (1977).
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THEORETICAL AND EXPERIMENTAL RESEARCH
ON THE TEMPERATURE EFFECT OF THE REACTIVITY
OF HETEROGENEOUS CRITICAL ASSEMBLIES
WITH STRONGLY BLOCKED ABSORBER
V. I. Bagretsov, V. I. Lependin, UDC 621.039.519.4
V.,I. Matveenko, -and V. N. Morozov
Theoretical and experimental investigations on the temperature effects of reactivity in regular, hetero-
geneous critical assemblies with a simple shape permit a conclusion to be drawn about the most applicable
methods of physical computation, which ordinarily cannot be done by studying actual systems. It is of partic-
ular interest in this connection to study cores containing a strongly blocked absorber since in this case the
computations entail difficulties associated with the necessity of taking proper account of the pronounced aniso-
tropy of the angular distribution of the neutron flux. The paper presents the results of investigations carried
out over a wide range of temperatures (T=2-240?C) in critical assemblies of the TES-ZM reactor [1], con-
taining cadmium and gadolinium rods uniformly arranged in the lattice of fuel elements.
Characteristics of the Assemblies. High-temperature experiments were carried out on the MATR-2
stand in a thick-walled vessel-allowing the critical assemblies to be heated to 300'C [2]. The maximum
temperature in the measurements was limited by the technological capabilities of two-ring fuel elements of
the K-17 type [3], designed-for a pressure P-4 MP/cm2. Fuel elements with a length of 600 mm made of 17%
enriched uranium dioxide and containing 3.48 g 235U per cm of length were placed at the nodes of a hexagonal
lattice with a pitch a =68 mm. The dimensions of the fuel rings with a 0.3-mm stainless steel can were 41.8 x
2.9 and 29.2 x 2.9 mm. The design of the stand has provision for compensation of reversible changes in the
reactivity with a three-blade shim rod of boron steel, placed in the space between the fuel elements. To
ensure nuclear safety four rods of the control and safety system in 30 x 3-mm hermetically sealed steel tubes
were placed between the fuel elements.
We studied three variants of critical assemblies, differing as to the number of fuel elements and absorb-
ers, and absorber material. Instead of a central fuel channel each assembly was provided with a 50 x 3-mm
cooled steel channel which held a neutron-sensing element for pulsed measurements of the reactivity. One
of the assemblies studied consisted of'fuel elements without absorbers (34 fuel elements); in two others the
central water space of each fuel element held absorption rods of cadmium oxide (68 rods) or gadolinium oxide
(74 rods) in a mixture with aluminum oxide. Diagrams of the active core are given in Figs. la, b, c.
The absorption rods-of cadmium oxide with a density y =0.5 g/cros and of gadolinium oxide (y =0.65 g/
cm3) had identical dimensions- (diameter of absorber 10.4 mm, steel can 0.3 mm thick, length of absorber 480
mm) and occupied a central position over the height of the active core. In all the experiments the critical
assemblies were surrounded-with a water reflector 25 to 40 cm thick.
Experimental Procedure. In each variant the critical state of the assemblies completely flooded with
water at a temperature of 15-20?C was attained by choosing the number of fuel elements in the. assembly accord-
ing to the adsorber used with the control and safety rods completely withdrawn from the active core. As the
assemblies were heated up the shim rod was either moving or was in some fixed position, depending on the
method of measuring the reactivity. For assemblies with a cadmium rod we experimentally assessed how the
shim rod affects the temperature effect of the reactivity of the assembly depending on the position of the boron
steel shim rod (at the top, in the middle, or at the bottom of the active core). The reactivity of the systems
was determined in the experiments by two methods: by measuring 8p/BT=f(T) and then integrating this rela-
tion within the appropriate limits; and pulsed measurements with the shim rods in a fixed position.
In the first method the system must be put into the supercritical state and the supercriticality must be
measured, with the temperature variation of the reactivity being compensated by moving the shim rods. The
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 142-145, March, 1979. Original article sub-
mitted January 30, 1978.
164 0038-531X/79/4603-0164 $07.50 ?1979 Plenum Publishing Corporation
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On -f-1
-60 0-2
0P0 00000 0-3
0000 000 O-4
00oo0N0-0 0-5
Fig. 1. Diagrams of critical assemblies: a) without absorber, b) with gad-
olinium rods, and c) with cadmium rods; 1) shim rod; 2) steel cans of rods
of control and safety system; 3) absorption rod; 4) fuel element; 5) cooling
channel with SNM-.11 counter.
Fig. 2. Temperature dependence of reactivity of
assemblies: a) without absorber, b) with gadolinium
rods, and c) with cadmium rods. The experimental
points (c) were obtained by a pulsed method with the
shim rods at the top (0), in the middle (0), and at
the bottom (s): ---) experiment with the relation
ep/BT=f(T); -) calculation.
shim rod efficiency covered the positive temperature effect of the reactivity with a large excess in all assem-
blies studied and did not exceed 2.4(3eff for the pure assembly and 1;7/ eff for assemblies with absorbers.
In measurements by the second method a neutron generator was placed near the side of the high-
pressure vessel and the reaction of the system to the pulse introduced was recorded by an SNM-11 corona
counter installed in the center of the active core. The reactivity of the system (in units of /acr) was found
from the a-method formula (4]:
P/15cr = aA/acr Acr - P/Pcr,
where acr is the damping decrement of the fundamental harmonic of instantaneous neutrons, Acr is the gener-
ating time of instantaneous neutrons, /acr is the effective fraction of delayed neutrons in the cold critical state
at 20?C, and a, A, and /3 are the analogous values for the system at the temperature T.
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
Fig. 3. Temperature dependence of relative change in
number of fuel elements in critical state (Ncr) for
assemblies with fuel-element spacing pitch of 3.15 cm
(1), 2.36 cm (2), and 1.89 cm (3): AN Ncr (20?).- Nc r (T)
N = Ncr (20?)
---) experiment [13]; -) calculation.
The value of 9 is quite conservative and, as shown by calculations in a 21-group Pl approximation by the
9M program [5], its variation with the temperature can be neglected.
A characteristic feature- of the assemblies studied was that criticality was attained with the shim and
control rods completely withdrawn for two substantially different assembly temperatures; this makes it
possible to experimentally determine the change in Acr at these temperatures, using the relation acr = acr/
Acr [4]. For the assemblies studied, with allowance for the calculated value of /3 in the cold and hot critical
states, respectively, Acr is equal to: 4.85-10-5 and 4.67. 10-5 sec in the pure assembly,4.41. 10-5 and 4.08-
10-5 sec in the assembly with gadolinium, and 4.44 ? 10-5 and 4.08. 10-5 sec in the assembly with cadmium. The
results of the pulsed measurements were processed by taking Acr into account with the assumption of a linear
dependence of the neutron generation time on the temperature.
According to estimates, the error of determination of the reactivity of a system by both methods did not
exceed 3-3.5%. This error doubles when the temperature effect is determined as the difference of reactivities.
Method of Calculation.--Calculations of the physical characteristics of the assemblies were carried out
according to the program of Polivanskii [6]. In doing this we used a low-group diffusion approximation and a
multizone reactor model in a two-dimensional (r, z) geometry. The real geometry of the assemblies, con-
sisting of three fundamental physical zones (active core, neutral measuring channel, reflector), was replaced
in the calculations by a multizone model (7-12 zones) reflecting the real features of the composition. The
presence of the steel cans of the control and safety rods in the active core was taken into account with the aid
of perturbation theory. _
In our calculations we employed a two-group approximation, with a group interface equal to 0.671 eV;
the macroscopic group constants were determined by averaging over multigroup spectra obtained in various
approximations. The constants of the epithermal groups of neutrons were averaged over a nine-group spec-
trum of the moderation of a homogeneous bare reactor with equivalent dimensions. In this case the constants
of 235U, Ge, and Cd were found by taking account of their heterogeneous distribution. in the active core. The
probability of avoiding resonance absorption in 238U was found by taking account of the mutual screening of the
fuel elements in accordance with [7]. In calculating the absorption of epithermal neutrons in gadolinium and
cadmium, we used data on allowed and disallowed parameters from [8, 9]. The macroscopic constants of the
thermal group of neutrons for the lattice of the active core and the central measuring channel were obtained
by modeling these zones with Wigner-Seitz cells, by calculating the space-energy distributions of the density
of the thermal neutron flux in these cells with account for the effects of thermalization and averaging the con-
stants over the neutron spectra obtained.
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The space-energy distributions of the density of the thermal neutron flux in the cells were calculated
in a ten-group approximation by the formulas of a modification of the Sn method with a linear balance approxi-
mation [10]. The neutron scattering anisotropy was taken into account in the transport approximation only
for those neutrons which, upon scattering, did not go beyond the limits of the energy group. In transitions to
other energy groups the neutron scattering indicatrix was assumed to be isotropic. The ten-group macro-
scopic constants of the zones and the density of thermal-neutron sources in the zones were determined by
using a procedure expounded in [11]. The function for neutron scattering on water molecules in the thermal
region 0:!s E:5 0.671 eV was calculated by the approximation formulas of [11]. In solving the ten-group system
of kinetic equations we employed an algorithm which largely coincides with the algorithm of the Sn modulus of
the Landysh system [12]. Preliminary methodological investigation made it possible to find the optimal
parameters of the ten-group calculation of the density of the thermal neutron flux in the cell: the approxima-
tion of Ss and the grid from the radial variable r contained 86 nodes with an uneven pitch in the five-zone cell.
In the surface region of the zone of the absorption rod, corresponding to roughly 6-8 mean free paths of the
thermal neutrons (in which flux depression largely occurs), the variable pitch of the grid was a minimum
(0.001 cm).
Results. The results of theoretical and experimental investigations on the temperature effects of reac-
tivity for three assemblies are given in Figs. 2a, b, c. The temperature effect is given in the form of the
temperature dependence of the reactivity difference of the system:
i\p (T) = p (T) - p (20?C),
where p (T) and p (20?C) are the values of the reactivity of the system at a given temperature and at 20?C,
respectively. The dashed curves were obtained by integration of the measured relations 8p/BT=f(T) within
appropriate limits. The results of pulsed measurements for three positions of the shim rods in the assembly
with cadmium rods, given in Fig. 2c in the form of experimental points, show that:
1) the experimental relations obtained by two independent methods are in quite good agreement with each
other, attesting to the reliability of the experimental results;
2) the shim-rod position has practically no influence on the temperature effect of the assembly reactivity
since the experimental points at different shim-rod positions coincide within the limits of experimental errors.
The good agreement between the calculated and experimental relations of the temperature effect is
shown in Figs. 2a, b, c. Theoretical investigation of the temperature effect of reactivity by using the two-
group method with the application of the Sn approximation in determining, the parameters of the thermal group
was also tested for strictly regular and uniform critical assemblies, not containing absorbers, a description
of which is given in [13]. The results of the investigations are described in detail in [14] and presented in
Fig. 3, where good agreement is also observed between calculated and experimental data over a wide range of
235U concentrations (Pn/p5 = 50-600) and temperatures (T = 20-250?C).
The reliability of the experimental data obtained by different methods and systematic computational
investigations, carried out during this study, permit the conclusion that the experimental and computational
procedures presented in the paper can be used in studying regular assemblies with highly blocked absorber.
The authors are indebted to M. N. Lants, V. S. Bykovskii, R. K. Goncharov, V. M. Fedorov, A. F. Zolotov,
A. N. Mezentsev, R. P. Borozdenko, and T. S. Pankratova for participating in the experiment and the calcula-
tions and to V. N. Gurin and G. A. Ilyasova for their useful comments in the discussion of the results.
LITERATURE CITED
1. V. V. Orlov et al., in: Problems of Nuclear Reactor Physics [in Russian], Otd. Nauchn.-Tekh. Inf.,
Fiz.-Energ. Institut (ONTI FEI), Obninsk, No. 1, Vol. 1 (1968), p. 349.
2. The Physics and Power Engineering Institute [in Russian], Atomizdat, Moscow (1974), p. 11.
3. E. I. Inyutin et al., Proc. Third Intern. Conf. on the Peaceful Uses of Atomic Energy, New York, Vol. 3
(1965), p. 23.
4. E. A. Stumbur et al., in: Theoretical and Experimental Problems of Transient Neutron Transport [in
Russian], Atomizdat, Moscow (1972), p. 245.
5. A. I. Nevinitsa, in: Problems of Atomic Science and Engineering, Series "Reactor Construction. Methods
and Algorithms for Nuclear Reactor Calculations" [in Russian], Fiz. Energ. Inst. (FEI), Obninsk, No.
6(20) (1977), p. 73.
6. Sh. S. Nikolaishvili et al., in: State of the Art and Prospects of Work on the Construction of Atomic
Power Plants with Fast-Neutron Reactors [in Russian], Otd. Nauchn.-Tekh. Inf., Fiz.-Energ. Inst. (ONTI
FEI), Obninsk, Vol. 2 (1967), p. 75.
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
7. V. V. Orlov, At. Energ., 4, 531 (1958).
8. S. M. Zakharova et al., Bulletin of the Nuclear Data Information Center [in Russian], Atomizdat, Moscow,
No. 3 (1967), p. 194.
9. S. M. Zakharova, Bulletin of the Nuclear Data Information Center [in Russian], Atomizdat, Moscow,
No. 5 (1968), p. 189.
10. V. N. Morozov, in: Theory and Methods of Nuclear Reactor Calculations [in Russian], Gosatomizdat,
Moscow (1962), p. 91.
11. G. I. Marchuk et al., At. Energ., 13, No. 6, 534 (1962).
12. V. N. Morozov, in: Problems of Atomic Science and Engineering. Series "Reactor Construction.
Methods and Algorithms for Nuclear Reactor Calculations" [in Russian], Fiz. Energ. Inst. (FEI), Obninsk,
No. 6(20), (1977), p. 83.
13. G. A. Bat' et al., At. Energ., 30, No. 4, 354 (1971).
14. V. I. Matveenko and V. N. Morozov, Preprint FEI-694, Obninsk (1976).
OPTIMIZATION OF PHYSICAL CHARACTERISTICS
- OF A HETEROGENEOUS REACTOR
B. P. Kochurov and V. M. Malofeev UDC 621.039.51
By using the method of solving the equations of a heterogeneous reactor proposed in [1] a difference
analog of the initial equations can be obtained which eliminates the long-range interaction and which is formally
similar to the equations for a. homogeneous reactor. However, there is one distinctive feature which is
important for the optimization problem. In the numerical realization the homogeneous finite difference equa-
tions represent an approximation of the differential equations, and the solution of optimization problems may
involve so-called "slipping conditions" [2] which are characterized by extremely irregular behavior of the
control function, which, as a rule, violates the initial assumption made in the homogeneous equations that the
parameters can be averaged, and hampers the physical interpretation of the results. In a heterogeneous reac-
tor the net is fixed with one node per channel, and therefore from the very beginning the difference equations
appear as a system of algebraic equations of finite but rather high dimensionality. For a finite number of
dimensions, slipping conditions do not occur, and therefore the results have a natural physical interpretation,
although the nonlinear nature-of the problems can, as before, lead to such difficulties as slow convergence of
the solution or falling into local minima.
The physical statement of the problem and the notation are the same as in [1]. A heterogeneous reactor
is considered with K cylindrical slugs placed at the nodes of a regular lattice. The vector of extrapolated
values of the neutron fluxes obeys the system of equations:
HN=O; H=Hz-%Ht;
H2 = PV (U) +Ryz (U); (1)
Ht = (PI;'Ko+R) Yt (U),
where P and R are local operators which depend on the properties of the moderator, a is the eigenvalue (the
effective multiplication factor), and Io and Ko are matrices of the values of Bessel functions which are diagonal
in k. -
The channel characteristics y1,2 and V are related to the initial'few-group (G x G, where G is the number
of groups) A matrices by the expressions
A=At-A2; Yt(U)_ -IoC-IA I(U);
Yz (U) IoC-1A2 (U) +OIOC-t; 8 = Pk (8/8pk);
V (U) = I;' FC-1 + K072 (U)].
where C is a matrix which depends on the properties of. the moderator.
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 146-148, March, 1979. Original article sub-
mitted March 13, 1978.
168 0038-531X/79/4603-0168 $07.50 01979 Plenum Publishing Corporation
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
Fig. 1. Optimum values of control and thermal
neutron fluxes.
0
000
0000
00000
00?0000
@@00000
00000000
00?0?00?0000
@@0@@00000
@Y0000@?000
00??00?00?00000
Fig. 2. Geometry of problem No. 2 (slugs with non-
zero concentration of fuel are marked).
0
0000
.8 6 0 @17 C
0000
Fig. 3. Optimum values of control and ther-
mal neutron fluxes for slugs with nonzero
concentration of fuel.
It was assumed in [21 that the properties of the slugs can vary; i.e., the matrix of each slug A(U) depends
on the component of the "control" vector related to such characteristics as the geometry and composition of
the channels.
The optimization problem is formulated as-follows. It is required to find a vector U which satisfies Eqs.
(1), restrictions on the control vector
Umtn
400 keV, completely crossing the cavity; curve 4 and
the unfilled squares correspond to protons with E >400
keV forming inthe cavity; curve 5 andthe unfilled squares
correspondto protons of any energy forming inthe cavity.
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
Fig. 3. Mean-frequency yf and mean-dose
yD events as a function of the neutron energy
En: the continuous curves. give the data of
[15], while the symbols corresponds to cal-
culation; 1) spherical-volume diameter 1 ?m;
2) 5?m.
ulas proposed in [9, 101. The values of the reaction energy are taken from [4]. Data on the retarding proper-
ties of the tissue-equivalent materials for all the charged particles formed by neutrons are taken from [11].
The scatter of the charged-particle energy loss over a section of the track is taken into account as in [2],
except that no account is taken of indirect energy-absorption events in the microvolume (the 6-electron effect).
Such events may make a contribution to the given spectrum in the region of small (- 1 keV) energy liberation,
where the approximation adopted leads to an error exceeding the 6-electron contribution.
Geometry and Calculation Algorithm
The model adopted in experimental microdosimetry is used to calculate the absorbed-energy spectra [12].
The charged-particle tracks present within the microvolume may be divided into four types: crossers, stoppers,
starters, and insiders [13]. Fluctuations of the energy loss are taken into account only for tracks of the first
three types. The coordinates of the neutrons and charged particles in phase space, and also their paths and
energy losses in the converter and the cavity, are random quantities. Their values are chosen from the
general set using tables, in order to achieve the maximum speed of calculation of the neutron histories. Rather
than give a detailed description of the whole algorithm, attention will be directed mainly to the methods used
to reduce the dispersion of the statistical estimates.
A statistical weight is assigned to each point of the neutron trajectory
W = W su' kW p ('i, c/sc). (1)
The first factor is necessary to improve the statistics of choosing the neutrons from the beam. For a plane-
parallel beam, for example, it is equal to the probability that a neutron from the source will fall within an
annular band of width AR within which the neutron distance to the beam axis is distributed according to the
corresponding distribution law. The second factor is introduced to improve the statistics of choice from the
neutron energy spectra and is equal to the probability that a neutron from the source will fall within the energy
group numbered k. The boundaries of the energy groups are chosen in accordance with the 26-group system of
constants adopted in the Soviet Union. The neutron energy is chosen successively within each group in accord-
ance with the shape of the energy spectrum. The reason for the third factor may be explained as follows: the
trajectory of a neutron from the source may cross the converter alone or the converter and the cavity. Let
Si, S2, and S3 be, respectively, the neutron path length in the near (in the direction of motion) wall of the con-
verter, in the cavity, and in the far wall. The method outlined in [14] may be used to model the coordinates of
the points of interaction of the neutrons in the three regions, to give
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WP,j=1-exp{-EjSj}, j=1, 2, 3, (2)
where E j is the total macroscopic cross section for the interaction of a neutron with the converter material
or the internal cavity. In the general case, these first interaction points serve as the initial points of the
tree of neutron trajectories. Successive points of the tree are obtained analogously: each new interaction
point serves as the starting point for no more than three (in the present case) branches of the tree until the
statistical weight becomes less than some value Wo (10-5-10 9). The, neutrons of subsequent generations are
calculated without branching. Capture reactions are taken into account simultaneously using the last factor.
The calculation algorithm for the absorbed-energy spectra may be written in general terms as follows.
1. For each, of the 10 sections of the converter radius in turn the point of intersection of the, neutron
trajectory with a spherical layer is modeled.
2. For this point, the neutron energy in the spectrum is chosen at random from each energy group in
turn.
3. For each neutron of the given energy and entry point, a tree of trajectories is constructed and
analyzed.
After completing the third stage, the second is again carried out. This continues until the trees of all
the energy groups have been analyzed, after which the first stage is again carried out. After considering all
the sections of the layer radius, the neutron history is concluded, and the analysis of the next neutron history
begins.
Results of the Calculations and Discussion
Using the method developed, the functions fl (c) and their errors may be estimated for all types of
particles and tracks making a contribution to the total energy-liberation spectrum. So as to be able subse-
quently to take more accurately into account the fluctuations of the energy transfer on a section of the track
from rebound protons with a path in the cavity much longer than the diameter, which produce tracks of the
first and third types, information is obtained on the energy spectra of such protons and the track-length dis-
tribution in the gas cavity. The characteristic statistical error of the calculated spectra is no more than 5-
10% in the main region (the number of particle histories is - 103). At the edges of the distribution, the error
is - 15-40%.
Results are obtained for a series of monoenergetic neutrons, and also for neutron spectra corresponding
to the fission of the isotope 2 (if and channels P-2 and B-3 of the BR-10 reactor. These data are compared
with the results of [1] in Fig. 2, which shows values of sfi (s) for four values of En of monoenergetic neutrons
and spherical-volume diameters of 1 and 6.5 ?m. In [1], data were obtained without taking into account the fluc-
tuations of energy transfer by protons. Thus, it-may be agreed that the present results in the main part of
the spectrum are in satisfactory agreement with the data of [1]. The explanation for the discrepancy at an
energy liberation of less than 5-10 keV is that in [1] no account was taken of the straggling effect for protons
(which shifts the spectrum. to the left in the region of the maxi mum; for En=5.85 MeV and a sphere of diameter
1?m this shift is 25%), and in the present work no account is taken of the effect of 6 electrons. In Fig. 2C, the
continuous curves 2, 3, and 4 and the filled symbols show the results of calculations for neutrons with En=
3.45 MeV and a sphere diameter of 6.5 pm which were made to elucidate the effect of data on the elastic-scatter-
ing anisotropy of the neutrons. The use of group anisotropy constants increases the mean absorbed energy
from the heavy recoil nuclei (for the given result, by 40-50%) but this has a slight effect on the total spectrum.
The mean-frequency yf and mean-dose YD event magnitudes are shown as a function of the neutron energy.
The discrepancy with the data of [15] is due to disregarding straggling and neutron resonances (for example,
at a neutron energy of 1 MeV) and the approximations in the formula obtained. For a diameter of 1?m, the
accuracy of these approximations may be estimated at 10-20% for yf and 5-15% for D. For a diameter of
5?m, the error is lower, of course.
The program here developed may be used in research on the interpretation of radiobiological effects due
to neutrons of different energies. The calculation of absorbed-energy spectra in spherical volumes of diameter
> 0.5 ?m for'different neutron energies and spectra will form the subject of a future work. -
LITERATURE CITED
1. U. Oldenburg and J. Boaz, Rad. Res., 51, 551 (1972).
2. M. Coppola and J. Booz, Biophysik, 9, 225 (1973).
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
3. H. Paretzke and G. Burger, in: Microdosimetry, EUR-4452, EURATOM, Brussels (1970), pp. 615-630.
4. W. Snyder, in: Radiation Dosimetry, Vol. 1, Proc. of Intern. Summer School on Radiation Protection,
Cavtat, Yugoslavia, September 21-30, 1970, Institute of Nuclear Sciences, Beograd (1971), pp. 160-184.
5. ..Evaluated Nuclear Data File (ENDF/B), Version IV, National Neutron Cross Section Center, BNL, Upton,
New York (1974).
6. Lawrence Livermore Laboratory Evaluated Neutron Data Library (ENDL), University of California,
Livermore, California (1973).
7. N. O. Bazazyants, M. N. Zabrodskaya, and M. N. Nikolaev, in: Nuclear Parameters, No. 8, Part 2, Pro-
vision of Fast-Reactor Calculations [in Russian], TsNHatominform, Moscow (1972).
8. P. Nagaragan et al., A Random Sampling Procedure for Anisotropic Distributions, B.A.R.C.-789,
Bombay (1975).
9. I. Caswell and I. Coyne, Rad. Res., 52, No. 3, 448 (1972).
10. A. M. Baldin, V. I. Gol'danskii, and I. L. Rozental', Nuclear-Reaction Kinetics [in Russian], GIFML,
Moscow (1959).
11. T. Armstrong and K. Chandler, SPAR, A FORTRAN Program for Computing Stopping Powers and
Ranges for Muons, Charged Pions, Protons, and Heavy Ions, USAEC Report, ORNL-4869 (CCC-228),
Oak Ridge, Tennessee (1973).
12. H. Rossi and W. Rosenzweig, Radiology, 64, 404 (1955).
13. R. Caswell, Rad. Res., 27, 92 (1966).
14. N. P. Buslenko, I. M. Golenko, and V. G. Sobol', Method of Statistical Testing [in Russian], GIFML,
Moscow (1962), p. 106.
15. R. Caswell and J. Coyne, "Microdosimetry," in: Proceedings of Fifth Symposium. on Microdosimetry,
Verbania-Pallanza, Italy, Sept. 22=26, 1975, EURATOM, Brussels (1976), p. 97.
ALBEDO OF CONCRETE FOR LOW-ENERGY
GAMMA RADIATION
M. P. Panin and A. M. Panchenko UDC 539.122:539:121.72
Many papers have appeared on the backscattering of gamma radiation. The most complete results with
a detailed analysis of various regularities of the albedo are presented in [1]. The energy range below 100 keV
is considered in only a few papers. Among these the most detailed is [2], but even in it only integral func-
tionals of the field are presented. Recently considerable interest has been shown in low-energy gamma radia-
tion as a result of the spread of low-energy x-ray facilities.
We have used the Monte Carlo method to calculate various current characteristics of the number albedo
aN and the energy albedo aE for incident gamma photon energies from 20 to 100 keV. In addition to integral
functionals we obtained differential angle (daN/dSl) (E0, 00, 0), energy (daN/dE) (E0, 00, E), and spectral-
angle (d2aN/di2?dE) (E0, 60, 0, E) distributions of the number albedo. The component due to single scattering
of the radiation was recorded separately. Angles of incidence 00 were varied from 0 to 89?, and angles of re-
flection 0 from -89? to +89?. Negative values of 0 correspond to scattering in the half plane 9=180?, and posi-
tive values to 9 =0'. Values of the differential-angle albedo in directions not lying in the plane of incidence
were found by using the method of reducing the number of calculations as in [3]. Its applicability for low
energies was checked by random tests. The error did not exceed 6-7%.
Integral values of the albedo were calculated by using the estimate
k
aN =MY, W; exp (- i=) % (n0 ),
10, 1''t >0;
x (t) = t < 0,
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 174-177, March, 1979. Original article sub-
mitted March 6, 1978.
0038-531X/79/4603-0201$07.50 ?1979 Plenum Publishing Corporation 201
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 Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010003-3
),o
pia 48
=I C;
a? c
-30 0
8, deg
0 30 60 90 0 90
0, deg
-30 0
9, deg
Fig. 2.. Angle number albedo as a function of the angle of reflection for initial energies of
a) 60 and b) 20 keV (dashed line denotes data obtained without taking account of electron bind-
ing in atom).
where M is the mathematical expectation; i, number of the scatter; Sk., direction of the gamma photon after
scattering; Ti, optical thickness in the material along the direction 12j; n, normal to the surface; and Wi, sta-
tistical weight of the photon after the i-th scatter.
We are interested in the scattering of low-energy gamma radiation and therefore took account of the
binding of the electrons in an- atom; i.e., we considered both incoherent scattering from bound electrons and
coherent scattering from an atom. At each i-th scatter the estimate for a detector of direction w in the calcu-
lation- of the angle albedo was found from
(D_ Wi_I ( da t
i B (E;-) {ne j IC
(Ei-a, g;-jW) S(4)e-T(E) + na (-- 'd52 )T (ti:-1a)) FZ (4) a (2)
Here (dv /d 7)C and (dQ/di2)T are the differential microscopic cross sections for Compton and Thomson scatter-
ing, respectively; ne and na,. electron and atom densities in the scattering material; S, incoherent scattering
function; F, atomic form factor; q, momentum transfer in scattering from the direction f2i-1 to w for an incident
Fig. 1. Contribution of single scattering to the differ-
ential angle number albedo as a function of the angle
of reflection 0 for initial energies of a) 100 and b) 20
keV.
.30
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0 15 30 45 60 75 80i deg
Fig. 3. Integral values of number albedo as
a function of angle of incidence (dashed line
denotes data obtained without_taking account
of electron binding in atom).
TABLE 1. Coefficients of Semiempirical
Representation Found by the Method of
Least Squares
keV
Eo, I ke V
1,5-4 ?
8,1-5
60
1,4-2
2,2-3
3,3-4
8,3-4
75
2,1-2
5,8-3
2,2-3
1,8-3
100
3,4-2
8,2-3
7,6-3
1,9-3
Eo.
* Read 1.5 .10-4.
gamma photon of energy Ei_1; T (E) and T (Ei_1), respectively, the optical thicknesses in the material for the
energy of a gamma photon after incoherent and coherent scattering; and E, total microscopic interaction cross
section. Calculations were performed in parallel for 13 detectors corresponding to 13 angles 9. The statistical
errors of the differential functionals for the statistics of 103 histories did not exceed 5%.
The results of the calculations, part of which are shown in Figs. 1-3, exhibit a number of special features
which are characteristic of the laws of backscattering of low-energy gamma radiation. One of the most im-
portant of these features is the controlling role of single scattering in the formation of the field of backscattered
radiation. Figure 1 shows that the singly scattered fraction is a complicated function of the angles 80 and 9,
but increases monotonically with decreasing initial energy. This is related to the increase in the photoelectric
absorption cross section. The derivative dET/dcos Os is a measure of the change of probability of absorption
in a single scatter. The cross section for the photoelectric effect ET -En where n-3 [4], and therefore in
scattering through an angle 0s
dE, _ dE2 dE 1 (3)
d cos Os dE d cos 6s E2
At higher energies when the photoabsorption cross section and the derivative (3) are small, the compo-
nents of the field corresponding to various multiplicities of scattering are little different. The somewhat unusual
dependence of the differential angle albedo on the angle of reflection 0 (Fig. 2) is also a result of the low initial
energy. The curves in Fig. 2 show maxima at negative values of 0 forO >0'. This is a result of the increase
in the probability of scattering with a change in the scattering angle 0s from 90? to 180?. The lower the energy
the larger its increase, and in the limit it corresponds to the law 1+ cos2 Os. It is obvious that as E0--0 both
branches of the curves in Fig. 2 would become nearly symmetric for 00 # 90?. However, the effect of electron
binding in the atom distorts this picture considerably. The sharp peak at 0 Ps 80? at glancing angles of incidence
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is formed by coherent scattering at small angles, and is obtained solely as a result of taking account of elec-
tron binding. For comparison Fig. 2 shows results obtained without taking account .of binding. The results
for 60 keV are from [1] for aluminum, and those for 20 keV were obtained by special calculations. The data
presented indicate the range of energies where it is necessary to take account of this effect in calculating the
angular characteristics: for E0 < 60 keV where 00 3 80? and 0 3 60?; for E < 30 keV for 00 3 60? and 0 3 15?.
This effect undoubtedly has a somewhat smaller influence on the integral characteristics of the albedo
shown in Fig. 3. Only for large angles of incidence 00 3 85? and E0 `< 50 keV is there a sharp increase in the
dependence of a on 00. This is a result of coherent scattering becoming important for small-angle scattering.
In order to compare the results obtained by taking account and not taking account of binding the curves for
aN(00) were extrapolated from 00- 75?-85? to 90? by using the extrapolation function
a' (00)=K (2.67-0.5 cos 9o'-cos2 00+1.5 cos3 00+
+3 cos4 0 0 + (2 cos3 00 -3 cos 00- 3 cosfi 00) In [(1 +cos 0o)/cos 00]}. (4)
The coefficient K was chosen to make the functions a' (00) and aN(00) agree in the 00 # 75?-80? range and has
the approximate value
K _- nenr;/2E (E0),
where ro is the classical radius of the electron.
The extrapolation Eq. (4) was obtained from an estimate of the single scattering integral albedo based
on the assumption of Thomson scattering with no change in energy. The extrapolated values are in good agree-
ment with data in [2] for the number albedo. The monotonic dependence of the albedo on the initial energy
shown in Fig. 3 is characteristic of the low-energy region and results from the decrease of the probability of
photoabsorption with increasing energy.
The results for the energy albedo are similar to those for the number albedo. The ratio aE/aN is prac-
tically independent of the angle of incidence 00. This results from the fact that the spectrum of reflected rad-
iation lies within narrow energy limits. For .given 00 and 0 it consists of a single line from single scattering
E, = E0/[1 +(Eo/moc2) (1-cos 08)1 (5)
and is close to the uniform distribution formed by multiple scattering. The boundaries of the distribution are
nearly the same as those of the spectrum of doubly scattered photons:
E, E?
1+[2+V2 (1+cos0.)](Eu/m(.c2) ' 1+[2-Y2 (1+cosOs)1(E,/moc2)
(6)
With a decrease in E0 the singly scattered fraction increases and the single line E1 and the limits of the spec-
trum (6) are shifted toward E0, which means that the spectrum is narrowed.
For E0 = 100 keV a very broad spectrum is observed from the range considered. The spectrum is hard-
ened as 00 is increased, since the average scattering angle is decreased. As a result of all this the ratio
aE/aN at 100 keV does not remain constant but increases somewhat with increasing 00. The angular distribu-
tions of the number albedo can be described by a semiempirical formula which includes an exact analytical
calculation of the singly scattered component
/ daT ( da S (9) n do F2 (9)
dsz ) i (E0i 60, O) = ne \ db2 ) EN E+r' cos O?/cos 0 + a d52 T S (1 +cos 0?/cos 01 (7)
and an. empirically selected representation for the multiply scattered component (the values of the coefficients
Al and A2 are given in Table 71):
(daNld2)m = [A, + 00A21 cos 0;
_ (8)
The errors in % given by Eq. (9) are listed below:
E, key . . . . . . . 0o a 75? O eke-) z 1/3.
These mesons were observed in pN --> r(r') x and e+e- --+ r(r') processes. The honor of the discovery of the
phenomenon (Lederman group, U.S.A.) belongs to experiments of the first type, and the conclusive and detailed
investigation of the properties of the new items (DESY) belongs to the second type of experiments. The unique
interpretation of the new mesons is the hypothesis that they represent bound states of new heavy quarks of
charge -1/3:
(b is the initial letter in the word "beautiful"). For the reader who is familiar with the history of the discovery
of the J/-particle with mass 3.1 GeV, this interpretation is not surprising. History is being repeated in the
well-known sense. It is to be expected, of course, that following the discovery of r, r' the observation will
follow also of particles with a new quantum number of the type (bu), (ub), (bd), (db) .... We note, incidentally,
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that similar expectations in the case of the c-quark (charmed particles) were corroborated. At the present
time, detailed data have been obtained about the spectroscopy of the charmed mesons and their properties.
Without listing the results, we can say that they are all found to be in accordance with theoretical expectations.
Finally, in the table, one of the quarks - the (t)-quark - is labeled with a question mark ("t" from "top").
As yet, there are no direct indications of its existence. This is the expected partner of the b-quark in the
doublet in the Weinberg-Salam model. For the time being, it is difficult to say what is the mass of the particles
containing t-quarks, but there is no doubt that searches for them will be intensive in the high-energy colliding
e}e--beam accelerators which are coming into operation.
Both the quarks and the gluons have not been observed directly. These are the so-called "colored"
particles, which appear only at small distances, and when attempting to isolate them they become (most likely -
infinitely) heavy. Therefore, the confidence in their reality is based principally only on the success of theoret-
ical calculations. The corresponding theory of strong interactions - quantum chromodynamics - is found to be
at the center of attention of many theoreticians and experimentalists. Much attention was paid to quantum
chromodynamics at the conference. Not everything is yet understood. One of the central problems is unsolved:
why colored particles are not observed in the free state. But these unresolved questions, in our view, do not
detract from the confidence and reality of their existence.
We have dealt mainly on the successes of theory and experiments, which obviously answers the objective
state of affairs. The reader might note, however, certain "venomous" questions, with which we have not con-
cerned ourselves. In particular, theory is unable to calculate the spectrum of leptons and quarks. Thus, the
number of elementary particles is as yet taken by theory as a datum, but is not predicted by it, so that this
number is found to be quite large. It is probable that there exists a fusion not only of weak and electromagnetic
interactions, but also of strong interactions. At a higher energy, or at even smaller distances, it Is possible
that a gravitational interaction is joined to them. A theory of such fusion is as yet unknown, although attempts
to discover its structure are being made. These and other questions future experiments, theories, and con-
ferences will have to answer.
ALL-UNION SEMINAR "ELECTRONIC (AUTOMATIC)
METHODS OF CONCENTRATION OF MINERALS"
B. V. Nevskil M. L. Skrinichenko,
and A. P. Tatarnikov
At the seminar, held in Oct. 1978 in Moscow, were heard and discussed for the first time the reports (a
total of 41) of different institutes, establishments and departments concerning the state and prospects for develop-
ing automatic methods of sorting ores of nonferrous, ferrous, and rare metals, coal, and other solid minerals.
An exchange of scientific-technical and production experience was also conducted.
Automatic methods of sorting are based on the use of differences in the physical properties of the individ-
ual lumps or portions of ore. They are sorted in special separators - ore-sorting robots. For this character-
istic by which the lumps are separated, there can be natural or artificial radioactivity, color and luminescence
of the minerals and rocks, their electrical and thermal conductivity, magnetic susceptibility, etc. Accordingly,
different methods have been developed (radiometric, activation, absorption, photometric, luminescent, conducto-
and magnetometric, radiowave, etc.).
Automatic methods have opened up broad new possibilities in solving the complex and varied problems of
mineral-reprocessing technology. They can be applied with great effect to classes of coarseness from 300
(100) mm to 25 (5) mm. Their use allows even in the initial stages of technological schemes withdrawal of a con-
siderable quantity of tailings (up to 20-35% of the original ore) to the dumping ground, and in certain cases sep-
aration of even rich concentrates, without recourse to expensive crushing of the ores and without the expenditure
of reagents.
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 212-213, March, 1979.
- 0038-531X/79/4603-0252$07.50 ?1979 Plenum Publishing Corporation
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The use of these methods ensures a higher efficiency and profit in the extraction and reprocessing of
mineral raw materials. Great attention at the Seminar was paid to the state and development of nuclear-phys-
ical methods of sorting ores, based on the application of different sources of ionizing radiations (isotopes, x-
ray facilities, reactors and accelerators), and also to the radiometric method of sorting radioactive ores.
These problems were reflected in 32 reports.
The radiometric method is widely employed in industry in the Soviet Union and abroad. Part of the meth-
ods have been developed on the basis of the use of isotopic sources. A photoneutron method of sorting beryllium
ores, based on the use of 124 Sb, has been introduced into industry. A gamma-absorption method of sorting iron
and chromium ores is close to introduction or is being adopted, as well as neutron-absorption method of sort-
ing boron ores. The development of an x-ray radiometric method of sorting ores of nonferrous and other
metals is underway, as well as a method of sorting rubble and other structural materials by scattered radi-
ation. Based on the use of x rays, x-ray luminescence sorting of diamond-containing ores has been effected
under industrial conditions. This method is being developed for application to ores of nonferrous and rare
metals. Successes have been achieved in the development of activation methods of sorting minerals. An ex-
perimental neutron-activation concentration facility SO-2 has been built and is operating. The ores before
sorting are irradiated in a neutron multiplier, operating in the subcritical mode. The facility is intended for
the development of a technology of irradiation and sorting of nonradioactive ores, in particular containing such
elements as fluorine, manganese, vanadium, gold, copper, aluminum, etc.
The possibility was noted at the seminar of the widespread use of high-powered large-scale electron ac-
celerators for sorting minerals.
Practice has confirmed the high economic efficiency of the new methods of mineral concentration. With
a sorting cost of 0.5 to 1 ruble per 1 ton of original ore, the annual economic effect to individual establishments,
depending on the specific conditions and scales of application of automatic sorting, usually amounts to hundreds
of thousands to millions of rubles.
The participants in the seminar worked out recommendations for the future development of automatic
methods of mineral sorting, in particular, defined the most promising directions for future work, and acknow-
ledged as advantageous the creation of a special scientific-production amalgamation for the development and
manufacture of ore-sorting plant and instruments.
NINTH RADIOCHEMICAL CONFERENCE
IN CZECHOSLOVAKIA
In the work of the conference, held in Sept. 1978 in Pishtani, more than 140 specialists participated, and
about 90 reports were submitted on sections of extraction, analytical chemistry in the nuclear fuel reproces-
sing cycle, extraction chromatography, physicochemical problems of the nuclear fuel reprocessing cycle, ion ex-
change and sorption, and radiation chemistry.
Three review reports of the Czechoslovakian specialists were devoted to problems originating during the
operation of nuclear power stations: radiation safety, plant decontamination, regeneration, utilization and bur-
ial of waste (liquid, solid and gaseous), protection of the environment, regeneration of spent fuel with a burnup
of up to 30,000 MW ? day/ton, analysis of radioactive effluents, etc.
Part of the reports was concerned with the chemistry of technetium and palladium. In the review report
of A. F. Kuzina (USSR), data on technetium were presented, which can be used for solving certain analytical
pro blems of its concentration and determination, and the composition and properties of -a large number of com-
plex compounds were described. These properties can be used for qualitative and quantitative analysis, iden-
tification of compounds and oxidation state, and also the separation and removal of metals present in solutions
by chromatographic and extraction methods. In some reports of the Czechoslovakian specialists (F. Matsashek
et al.), the extraction of technetium and palladium from nitrate media by solutions of tri-n-octylamine (TOA) and
TBP in different dilutions was considered in detail. Technetium and palladium can be separated quantitatively
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 213-214, March, 1979.
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from fission products by extraction from 0.5-1 M HNO3, and their reextraction is carried out with an aqueous
ammonia solution. It was established that the presence of palladium in a system of 30%TBP-dodecane-nitric
acid (0.5-3M) and an increase of the temperature of the system in its presence, has a significant effect on the
radiolytic degradation of the extractant. Another fission product - molybdenum - does not show any effect in
this case (Z. Novak, Poland). Extractant degradation and the effect of degradation products on the behavior of
certain metals in the chemistry of the fuel element regeneration process was investigated in detail. In part
of the papers, the use of salts of different metals with organic compounds as extractants is described. As
shown in the reports of the Czechoslovakian specialists (I. Rais, M. Kirsh, et al.), cobalt dicarbolide H+C4B18
Hi5C17Co dissolved in nitrobenzene is a selective extractant for the Cs+ ion, which allows this cation to be
efficiently separated from a mixture of fission products. The reagent is very stable to y-radiolysis and the
action of nitric acid.
Reports were interesting, in which the use of tertiary benzyldialkylamines and quaternary salts of benzyl-
trialkylammonia was considered for solving the technologically important problem of the extraction of the rare-
earth elements and americium from nitric acid media (simulators of the water-tailing solutions from fuel ele-
ment regeneration). It was shown that these extractants allow the rare-earth elements and americium to be
efficiently. separated from cesium, strontium, zirconium, iron and other fission and corrosion products. The
extractants studied are stable to y-radiolysis (V. Edinakova et al.). The extraction method of discriminating
and separating the rare-earth elements by means of the new extractant tetra phenyli niidodiphos phonate was
described by specialists from the German Democratic Republic (E. Hermann et al.).
In the section on analytical chemistry in the nuclear fuel reprocessing cycle, interesting reports were
submitted on the .different methods of the quantitative determination of uranium, plutonium, neptunium, etc.
In one of the reports of the Czechoslovakian specialists, the results of work were given on the investiga-
tion of the spent fuel of the A-1 nuclear power station by radiochemical, mass-spectrometric and -y-spectro-
metric methods. In this case, the first two methods were used for the calibration of the nondestructive y-spec-
trometric method, which in future will be used as a control.
In Czechoslovakia, the method of isotopic dilution with mass-spectrometric completion of analysis has
been used successfully. In a joint Czechoslovakian-Yugoslavian report, high characteristics of the quantitative
(not worse than 0.15%) determination of uranium, plutonium and neodymium were given for the analysis of the
A-1 nuclear power station spent fuel, using the Varian TN-5 mass spectrometer. The NBS (USA) standards
were used and 2-5 Mg of uranium and ^-0.1 pg of plutonium or neodymium were taken for the analysis. These
same authors have carried out work on the y-spectrometric determination of 106Ru, 134,197Cs and 144 Ce, using
semiconductor Ge(Li)-detectors (range 400-1300 keV).
I. Feist (Czechoslovakia) reported the results of the use of submersible domestic silicon detectors for
determining integrated a-activity and a-spectrometric measurements. A method of preparation of targets for
a-spectrometric measurements is interesting- (M. Beran, Czechoslovakia). A layer of zirconium phosphate
(-10 p) is applied to a backing of stainless steel; the a-emitter (239Pu, 241Am, etc.) is adsorbed onto it and then
the spectrometric measurements are carried out. Thus, emitters with different sorption properties can be
separated [for example, Pu(IV) and Am (III)].
A precision coulometer has been developed and is being tested (A. Shvets, Czechoslovakia). Its operating
principle is as follows: An electric current is applied to the working detector with a specified frequency and
electrolysis takes place. In the author's opinion, the instrument will allow coulometric analysis to be conducted
with an error of hundredths of one-percent.
Interest was created in a report concerning the determination of microquantities of neptunium by differ-
ential polarography. The neptunium is converted electrochemically to the tetravalent state and is determined
polarographically by a dropping mercury electrode. It can be measured reliably down to a concentration of
5 ? 107 M, the limit of detection is 2 ?10-7 M, and the error is about 2% for 10-5 M and 10% for 10-6 M. The
method is used for both aqueous and organic solutions (TBP+dodecane). Neptunium is determined without pre-
liminary separation from plutonium and uranium with a ratio of M: Np =103 and 5 ?104, but in the presence of
fission products a preliminary separation is necessary
In the section on physicochemical problems of the nuclear fuel reprocessing cycle, reports were presented
which were of interest from the point of view of intensifying concepts concerning the nature of the processes
taking place in solutions of many elements (both actinides and fission products), with which radiochemistry is
concerned: the state of radioiodine in the liquid and gas phase during dissolution.of fuel elements (P. Putrik
et al., Czechoslovakia), the state of trace concentrations of 144Ce in aqueous solutions of inorganic acids (P.
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Benesh et al., Czechoslovakia), physicochemical principles of the separation of individual fission products (in
particular, promethium) for the manufacture of radioactive sources (N. E. Brezhneva et al., USSR), formation
and properties of mono- and di-n-butylphosphates of certain metals which are important in radiochemistry (A.
S. Solovkin, USSR), radiation-chemical reduction of Pu(VI) in nitric acid solutions (M. V. Vladimirova et al.,
USSR) and the effect of complex formation on the rate of reduction of plutonium compounds (A. V. Stepanov et
al., USSR), stability of Pu(IV) and Pu(VI) in nitric acid solutions in conditions of intense a-radiolysis (A. G.
Rykov et al., USSR), and also the electrolytic reduction of Pa (IV) in extraction processes for separating ura-
niumandplutonium(A. Pochinailo et al., Poland). In a recent paper, data were given about the conditions of
electrochemical separation of uranium and plutonium in a counter-current extraction (with TBP) process in
mixer-settlers. The authors have investigated different structural materials. for the. anode and cathode. The
anode is platinum, and for the cathode material gold, tantalum, zirconium, graphite, and pyrographite. can be
used. The acidity of the aqueous phase is 2M HNO3 and the current is 200 mA /cm2. In counter-current condi-
tions, satisfactory results have. been obtained for the separation of uranium and plutonium.
The reports presented at the conference will be published.
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NEW BOOKS
ATOMIC-HYDROGEN POWER GENERATION
AND TECHNOLOGY*
Reviewed by Yu. I. Koryakin
In recent years, considerable attention has been devoted to hydrogen, due mainly to the hope and desire,
by means of its extensive utilization, of overcoming certain difficulties in satisfying rapidly growing power re-
quirements. The use of hydrogen as a secondary energy resource precedes its production. In solving the
problem associated with the considerable costs of primary power, an important'if not decisive role is assigned
to atomic energy, more precisely, to high-temperature nuclear reactors.
The book being reviewed, of which the essence of the contents is well reflected in its title, is perhaps the
first attempt to introduce the reader to the essence of the main questions of the atomic-hydrogen problem. This
attitude and aim of the editorial staff, which is headed by V. A. Legasov, is logically and categorically justified.
An attempt to completely and comprehensively answer the numerous questions of atomic-hydrogen
technique, and technology would "dissolve" the principal key scientific-technical problems, not to mention that
the volume of the book would increase sharply.
The realization of such attitude is not always simple, and especially in this case, when the book is not a
monograph, but represents a collection of papers of a quite large assembly of authors. In this case, one is
frequently involved with the' difficulty of coordination or balancing of the sometimes subjective attitudes of in-
dividual authors in relation to the position and importance of "his" problem and questions on the general as-
pects of the problem as a whole. It is precisely this problem that is solved quite well. The introductory paper
by the President of the Academy of Sciences of the USSR, A. P. Aleksandrov, concerning the prospects of the
use of atomic energy for power generation and the foreward by the editor-in-chief of the book, contribute in no
small measure to the fundamental attitude. Strictly, they also state its principal directive, and define the
problems and the boundaries of the atomic hydrogen problem in all their diversity.
In accordance with this, in 11 of the papers which constitute the main content of the book, the following
principal topics are highlighted: methods and special features of hydrogen production, assessment of a nuclear
reactor as a technical means for achieving this from the position of the necessary transformation or obtaining
temperature, nuclear-physics, and material-study characteristics, and the possible spheres of introduction of
nuclear reactors into power technology.
The editorial staff of the. collection well know that perhaps paramount in the whole problem is the con-
formity of the possibilities of high-temperature reactor techniques with the power-technological requirements,
mainly temperature. Therefore, the account of the principal considerations concerning the feasibility of this
confirmity and the engineering feasibilities is assigned an important place. Hopes of its achievement, obviously
are encouraging and the authors show this, by describing not only the existing experience but also by assessing
the different paths for solving the main problem.
The use of a large list of Soviet and foreign literature references (about 300 entries) relates to the posi-
tive aspects of the data given.
On the whole, it is impossible not to agree with the preface to the book, in which the hope is expressed
that the collection will extend the participants in the solution of the exceptionally important and promising
atomic-hydrogen problem.
*Issue 1, Atomizdat, Moscow (1978), 246 pp., 2 figures, price - 80 kopecks.
Translated from Atomnaya Energiya, Vol. 46, No. 3, pp. 215-216, March, 1979.
0038-531X/79/4603-0256$07,50 ?1979 Plenum Publishing Corporation
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V.
V.
Gonch.arov, N. S. Burdakov,
Yu.
S.
Virgil'ev, V. I. Karpukhin,
and
P.
A. Platonov
ACTION"OF IRRADIATION ON THE GRAPHITE
IN NUCLEAR REACTORS*
Reviewed by A. P. . Si rot.kin
Graphite, as a result of its exceptional properties, finds extensive application in reactor technology. The
book being reviewed is the second monograph, in the Russian language;, and is being issued 10 years after the
first monograph "Nuclear Graphite," by S. E. Vyatkin et al. During this time, many papers, have been pub-
lished,.-devoted to the investigation of the characteristics of. reactor graphite.: Work is continuing on the crea-
tion of new grades. As its properties' depend on the raw materials used: and the special features pf -technology,
then the physicomechanical properties of Soviet reactor graphites under irradiation, given in the book, areof
special-interest..
The book describes the technologies of producing graphite with a density of 1:65 to 1.9 g/cma;. and the:
crystal structure and physical properties are considered, including the -dependence of the rate of oxidation on
the processing temperature, creep, and nonuniformity of properties. The .main attention is devoted to the change
of physical properties during neutron -irradiation.. The principal factors affecting the material during irradia-
tion are considered, as are methods of determining the neutron fluence damaging the,graphite. It is noted that
graphite is one of the most sensitive 'materials to a change not only of the, fluence, but also to the flux density
and the neutron spectrum. Radiation defects and the-degree of change of its properties Tare determined by the
number of displaced atoms, which is.the result of the combined action of both irradiation and annealing. Un-
fortunately, the authors do not make recommendations, beyond that energy to calculate the neutron fluence when
estimating the effect of Irradiation of graphite: above -0.1-8 MeV, -50 keV or with respect to the equivalent fis-
sion neutron flux.
Great attention is paid?to the dimensional deformation of graphite during irradiation the description of ox-
idation, consideration of the design and operating conditions of nuclear reactor stacks, their shielding and ef-
ficiency with the inclusion of experimental data. In this book, which includes a large list of literature refer-
ences, the specific stage of the investigations is summarized. It will be of undoubted interest for designers,
operators and scientific workers - occupied with graphite reactors.
* Atomizdat, Moscow (1978), 272 pp., 3 figures.
Translated from Atomnaya nergiya, Vol. 46, No. 3, pp. 215-216, March, 1979.
0038-531X/79/4603-0257$07..50 ?1979 Plenum Publishing Corporation 257
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A. B. Mikhailovskii
PLASMA IN-STABILITIES IN MAGNETIC TRAPS*
Reviewed by A.M. Fridman
Recent achievements in the heating .and containment of a thermonuclear plasma in tokamakshave involved
special attention to the processes taking place in the plasma The complex geometry of magnetic surfaces in
traps, formed by a system of external and internal currents, determines the diverse and at times nontrivial
physical mechanics of instabilities, the most active of which are Interpreted by collective processes. The
initial stage of the majority of collective processes, as a rule, is associated with-the development of some or
other instability (or several at once). -Therefore, the importance -of constructing a theory of plasma instabilities,
taking into. account the actual geometry of operating facilities., or facilities under construction, is obvious. The
-book being reviewed is devoted to an account of the central divisions of this theory, which have been formulated
in recent .years.
The book describes the theory of the principal plasma instabilities in both open (adiabatic) and closed
(toroidal) traps. The stability of the tokamak plasma is discussed in the greatest detail. The author draws the
--attentionof the readers to the following circumstances. When investigating the.-stability of the tokamak-plasma
_in the approximation of a circular plasma cylinder or by the model of a plane plasma layer in a gravity field,
disregarding the existing effects, the following can be found: shear, magnetic well, bottle effects, effects of
finite orbits, and magnetic particle drift. These effects in some way or other are associated with the curva-
ture of the magnetic surfaces of the tokamak, and are investigated in detail in the book by A. B. Mikhailovskii.
The author has noted and studied the role of Alfv(h waves in the plasma dynamics of the tokamak.
Great, attention in the .book is devoted to the description of the effect of various stabilizing factors: el-
lipticity and triangularity of cross section, and the effects of a finite P. The investigation of the stabilizing in-
fluence of the latter at present is acquiring special interest because of the analysis of the energy balance
carried -out at the I. V. Kurchatov Institute of Atomic Energy. Analysis showed the necessity of having a plasma
in reactor-tokamaks with the maximum possibl< /3 . As mentioned, despite the fact that instabilities represent
-the greatest danger in a low-pressure plasma, and are stabilized in a finite-pressure plasma, the stabil-
izing role of such factors as the temperature gradient, collisions between. particles, the longitudinal cur-
rent gradient (shear), groups of fast particles, and certain other factors, as a rule increases with increase
in Q. Hence, it would be hasty-to draw a conclusion about the stabilizing effect of a finite {3. Following the
logic of the author, we conclude that-increases in plasma stability can be achieved by optimization of the de-
stabilizing factors and not by a reduction of P.
One of the conclusions of the author is given here, which is important for the physicist-experimenter.
In our opinion, other no less easeful conclusions can also be cited.
The urgency of the publication of the monograph is clear. For specialists it will become a reference
book, and it will assist students and graduate students to master new efficient methods of investigating plasma
instabilities.
*Atomizdat, Moscow (1978), 295 pp., 2 figures. Price - 50 kopeks.
Translated from Atomnaya lenergiya, Vol. 46, No. 3, p. 216, March, 1979.
258 0038_531X/79/4603-0258$07.50 ?1979 Plenum Publishing Corporation
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(Onf ULTAf Tf BUREAU-
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Lithuanian Mathematical Journal
Editor: P. Katilius
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