SOVIET ATOMIC ENERGY VOL. 46, NO. 4

• Document Type: CREST
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• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000800010004-2
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• Document Creation Date: December 23, 2016
• Document Release Date: February 12, 2013
• Sequence Number: 4
• Publication Date: April 1, 1979
• Content Type: REPORT

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Russian Original Vol. 46, No. 4, April, 1979
October, '1979
SATEAZ 46(4) 259-350 (1979)
/
SOVIET
ATOMIC
ENERGY
ATOMHAR 3HEPrl1fl
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET Soviet Atomic Energy is a cover:to-cover translation of Atomnay4
Energiya, a publication of the Academy of Sciences of the USSR.
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Applied Mechanics Reviews, Chem-
ical Abstracts, Engineering Index, INSPEC-- -
Physics Abstracts and Electrical and Elec-
tronics Abstracts, Current Contents, and
Nuclear Science Abstracts.
/?
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 thesivality
of the latter. The translation began with the-first issue of the
Pustian journal.
Editorial Board of Atomneye Energiya:,
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. PoOmarev-Stepnoi
I. N. Golovin
V.1. ll'ichev
V: E. Ivanov
V. F. Kaliniri
P. L. Kirilov
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. Vorobsev
Copyright ?1979, Plenum Publishing Corporation. Soviet Atomic Energy partici-
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
October, 1979
Volume 46, Number 4 April, 1979
ARTICLES
Change in the Fuel Component of the Cost of Electrical Energy during a Transitional
Operating Period of a High-Powered Water-Cooled Channel Reactor
(RBMK) ? S. V. Bryunin, A. D. Thirnov, V. I. Pushkarev,
CONTENTS
Engl./Russ.
and V. I. Runin
259
219
Optimization of the Safety Margin to the Critical Load of the Heat-Releasing
Assemblies in a High-Powered Water-Cooled Channel Reactor (RBMK)
? S. V. Bryunin, A. I. Gorelov, V. Ya. Novikov, I. K. Pavlov,
and V. V. Postnikov
262
222
Deformation of an Energy Release Field in a High-Powered Water-Cooled
Channel Reactor (RBMK) ? A. N. Aleksakov, B. A. Vorontsov,
I. Ya. Emel'yanov, L. N. Podlazov, V. I. Ryabov, and B. M. Svecharevskii
267
227
Reproduction Characteristics of Fast Breeder Reactors and their Determination
? V. S. Kagramanyan, V. B. Lytkin, and M. F. Troyanov
273
232
Determination of Stress-Intensity Factor in Reactor Vessel from Models
? V. S. Postoev, N. N. Ryndin, S. N. gigenson, and V. B. Titov
278
236
Neutrons Emitted by Fragments of the Spontaneous Fission of 252Cf and the
Fission of 239PU by Thermal Neutrons ? B. G. Basova, D. K. Ryazanov,
A. D. Rabinovich, and V. A. Korostylev
282
240
Problem of the Optimization of a System of Direct Energy Conversion with
Parabolic Trajectories of Charged Particles ? S. K. Dimitrov
and A. V. Makhin
287
245
Degree of Perfection of Graphite and Changes in its Properties
under Irradiation ? P. A. Platonov, I. F. Novobratskaya, Yu. P. Tumanov,
and V. I. Karpukhin
291
248
Oxidation of (U, Pu)02 and UO2 Pellets ? G. P. Novoselov, V. V. Kushnikov,
Yu. Ya. Burtsev, and M. A. Andrianov
297
254
LETTERS
Neutron-Activation Determination of Oxygen Coefficient of Oxide Nuclear Fuel
? V. F. Kononov, V. I. Melent'ev, V. V. Ovechkin, and V. A. Luppov
302
259
Apparatus for Measuring the Thermophysical Properties of Reactor Materials
at Elevated Temperatures ? S. A. Balankin, D. M. Skorov,
and V. A. Yartsev
304
261
Behavior of Uranium Monocarbide under Low-Temperature Reactor Irradiation
? Kh.g. Maile
307
262
The Possibility of Increasing the "Hot" Neutron Flux in Beam of WV-2 Reactor
with a Rethermalizer ? V. V. Gusev, B. N. Goshchitskii, A. E. Efanov,
M. G. Mesropov, B. G. Polosukhin, and V. G. Chudinov
309
264
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Thermometry of Media with Solid-State Track Detectors ? Yu. V. Dubasov,
CONTENTS
(continued)
Engl./Russ.
V. G. Zherekhov, and V. A. Nikolaev
312
266
Rotational Stabilization of a Spiral Instability in a Plasma with in Immobile Boundary
? T. I. Gutkin? V. S. Tsypin, and G. I. Boleslavskaya
314
268
Fission-Fragment Sputtering of Insulators ? I. S. Bitenskii and S. Parilis
316
269
Calculation of Gamma-Ray Efficiency for a Germanium Detector ? V. A. Kalugin?
V. I. Sedernikov, and 0. N. Tuchkina
318
271
Joint Use of Nuclear and Organic Fuels in a Steam?Gas System ? V. G. Nosach
and O. E; Pushkarev
321
273
New Books Published by Atomizdat in the First Quarter of 1979
323
276
PERSONALIA
In Memory of Dmitrii Ivanovich Blokhintsev
325
277
INFORMATION
Soviet Nuclear Power Station Construction? V. L: Timchenko
327
279
New Heavy-Ion Cyclotron? Yu. A. Lazarev
329
280
SEMINARS, CONFERENCES
Soviet?Finnish Seminar on Norms and Standards for Designing Nuclear Equipment
? E. Yu. Rivkin
331
282
Swedish?Soviet Seminar on Structural Materials ? A. V. Nikulina
333
284
IAEA Symposium on Fuel-Pin Production for Pressurized-Water Reactors
? V. S. Belevantsev, I. G. Reshetnikov, and V. I. Solyanii
334
284
IAEA Conference on Sodium Fires ? V. G. Golubev and B. V. Gryaznov
335
286
INTOR Design ? V. I. Pistunovich
337
286
Soviet?American Conference on Fusion-Application Problems ? N. N. Vasiltev
338
287
Sixth Ml-Union Conference on Charged-Particle Accelerators ? V. A. Berezhnoi
339
288
All- Union Conference on Delayed Consequences and Estimates of Risk from Radiation
? Yu. I. Moskalev
341
289
Corrections and Amendments to ICRP Publication No. 26 ? A. A. Moiseev
343
291
SCIENTIFIC?TECHNICAL RELATIONS
Controlled Fusion Research in France G. A. Eliseev
345
292
BOOK REVIEWS
S. M. Feinberg, S. B. Shikhov, and V. B. Troyanskii ? Reviewed by V. N. Artamkin
348
294
V. V. Rachinskii. Course of Fundamentals of Nuclear Engineering in Agriculture
? Reviewed by R. A. Srapenyants
349
295
The Russian press date (podpisano k pechati) of this issue was 3/26/1979.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ARTICLES
, CHANGE IN THE FUEL COMPONENT OF THE COST OF
ELECTRICAL ENERGY DURING A TRANSITIONAL
OPERATING PERIOD OF A HIGH-POWERED WATER-
COOLED CHANNEL REACTOR (RBMK)
S. V. Bryunin, A. D. Zhirnov, UDC 621.039.517.621.3.016.003.12
V. I. Pushkarev, and V. I. Runin
The presently accepted scheme for taking a high-powered water-cooled channel (RBMK) reactor out of
service into a stationary operating regime involving the reloading of channels with a predetermined degree of
fuel burnup consists in the following. The first fuel load of the reactor is only part (-85%) of the standard
amount. Channels with additional absorbers (AA) make up the remaining part. As the operation of the reactor
continues and fission products accumulate in the fuel, the AA are gradually replaced by heat-releasing assem-
blies (HRA). The burnup of the first channels discharged from the reactor core is less than that projected for
a stationary regime of operation. The burnup gradually increases, reaches the projected value, and for a cer-
tain portion of the channels exceeds the projected amount. After all channels in the initial loading are replaced,
the fuel burnup in the discharged channels becomes equal to the projected value. The stationary operating re-
gime of the reactor also begins at this time.
We can obtain an expression for the fuel component of the cost of electrical energy delivered by an atom-
ic power plant (APP) at a given instant of time t (the time is reckoned from the beginning of operation of the
APP in effective days) from the equation for the balance between cost and expenditures at a given instant of
time
k -1
cnk =Cf AWi? Kka'z,
(1)
where c is the cost per HRA including the cost of transportation to the plant site, nk is the number of HRA used
at the APP from the start of operation up to and including the k-th reloading, cfi is the fuel component of the
cost of electrical energy between the i-th and (i + 1)-th reloading, AWI is the electrical energy delivered be-
tween the i-th and (i + 1)-th reloading, and Kit-z is the value of the active zone of the reactor after the k-th re-
loading.
The left side of the equation gives the expenditures of the APP on fuel from the beginning of operation up
to the present. The first term on the right side represents the total cost of electrical energy delivered by the
APP, taking account of the change in the fuel component of the cost of electrical energy in the preceding period;
the second term represents the value of the reactor core, taking into account the number of HRA in the core
and their partial burnup at the given moment. In this way, the balance equation is based on the principle that
the means expended should be equal to the value of the electrical energy delivered plus the presently available
means in the form of the value of the reactor core at the given moment.
The fuel component of the cost of electrical energy at a given moment can be defined as the ratio of the
value of the reactor core to its energy resources at that instant: i.e.,
Cf k = Kt.Z /Eh,
(2)
where ek is the energy resource of the active zone after the k-th reloading of the HRA. This can be put in the
form
imkg (Pk ? Pk), (3)
where 17 is the net efficiency, mk is the number of HRA in the core after the k-th reloading, g is the uranium
charge in a HRA, and Pk is the projected and current burnup of the HRA in the reactor after the k-th reloading
(averaged over the active zone).
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 219-222, April, 1979. Original article submitted
June 9,1978.
0038-531X/79/4604-0259$07.50 ?1979 Plenum Publishing Corporation 259
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When this is taken into account, Eq. (1) becomes
k - 1
cnh= cfkimkg (Pk? Ph) + E cf
i=o
(4)
From this it follows that the fuel component of the cost of electrical energy after the k-th reloading can be ex-
pressed in the form
cfh= cnh? E cf, AL V/ [Tynkg (Ph? Ph)].
i=o
This expression can be simplified and put into a form which is more convenient for practical calculations.
The sum in the numerator of Eq. (5) (the fuel component of the expenditures on electrical energy delivered up
to the present moment) can be expressed as follows:
(5)
- 1
E
CfAW,=cInh?
(Pk?/Ph)1. (6)
The quantity in the square brackets represents the actual consumption of HRA at a given moment (at a
given reloading), taking into account the fact that the HRA in the core are only partially burned up (proportional
to the relation Pk ? r)k/Pk). Taking this relation into account, the expression for cfk is easily put in the form
Cf = c/rigP h.
If the dimensionality of the parameters appearing in cfk is taken into account, and the expression is trans-
formed from a discrete to a continuous form, we obtain the following expression:
Cf (t) = (100/24) IchigP (t)1 (kopecks/kWh),
(7)
(8)
where c is the cost in rubles of the HRA including cost of transportation to the power plant site, 77 is the net ef-
ficiency (fraction of unity), g is the charge of uranium in the HRA in kg, P(t) is an average over the active zone
of the projected burnup of HRA in the reactor at time tin kW-days/kg, and t is the effective reactor operating
time in days.
As is well-known, there are two approaches to calculating cfk: making no allowance for reprocessing
the spent fuel and extracting plutonium from it ("for disposal"), and taking the latter into account. Expres-
sion (8) corresponds to the first approach. In the second case, the numerator must involve the difference be-
tween the cost of HRA and the cost of the realized uranium with a final content of 235U and the accumulated
plutonium, as well as the expenditures on reprocessing; it does not involve the cost of fresh fuel rods nor the
cost of their transportation to the nuclear power plant. In this connection, the content of 235U in the fuel and
the accumulation of plutonium is determined as the average over the reactor of the projected degree of burnup
at the given instant P(t). This expression does not take into account the cost of AA initially loaded in the re-
actor and gradually replaced by HRA. The increase in cfk (including the cost of AA) can be expressed as
ACP ----- (100/24) (2n AAcAA /iNh T AA)(TAA ?t/ T AA) (kopecks/kWh). (9)
where nAA and cAA are, respectively, the cost in rubles of the additional absorbers loaded initially into the
reactor and the cost of one of them, Nh is the heating capacity of the reactor in kW, and TAA is the time (in
days) from the beginning of the reactor operation to the end of discharge of the AA.
AA
This is a differential expression; i.e., it defines Acf at a given instant. The average (integral) value
of the fuel component of the cost of electrical energy over the preceding time interval from 0 to T can be ob-
tained as follows:
Cf = Cf (t)dt)/T.
0
(10)
However, in practical calculations it is more convenient to use another relation which has the same meaning:
C
C (n (T)? m (T) IP (T) _r, (T)11 P (T))
f (100/24)
11 NhT '
With this expression it is easy to determine the average fuel component for any time interval (calendar
year, quarter, and so forth).
260
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P max
Ps
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T2
t, elf. days
Fig. 1
Fig, 2
1,15
1,05
500 1000 t, eff. days
Fig. 3
Fig. 1. Degree of burnup of HRA unloaded from the reactor.
Fig. 2. Average over the core of the burnup of HRA located in the reactor at a given time.
Fig. 3. Fuel component of the electrical energy cost of an APP using an RI? MK-1000.
It is important to note that the only design parameter appearing in Eq. (11) is P(T). All of the others (the
total HRA outlay n(T), the number of HRA in the reactor m(T), the average over the active zone of the current
burnup of HRA in the reactor P(T), and the average over time T of the nuclear power plant efficiency) can be
calculated at the APP using its actual operating characteristics. The presence in the calculational expressions
of the differential and average (integral) fuel component of the cost of electrical energy P(t) is a necessary
methodological element which is due to the specific use of nuclear fuel. In particular, this consists mainly in
the fact that the cost of nuclear fuel is transferred to the energy produced over a very extended period, while
the outlay to acquire it occurs only once.
The method described here was tested in a calculation of the fuel component of the cost of electrical
energy at an APP plant using an RBMK-1000. For purposes of clarity, the burnup of HRA unloaded from the
reactor was assumed to depend simply linearly on the effective reactor operating time (Fig. 1). In the interval
from 0 to T1, the AA are withdrawn and replaced by HRA; during the time from Ti to T2, the channels of the
initial fuel charging are unloaded (their burnup varies from Pmin to Pmax), and all channels added to the core
are withdrawn with the projected (stationary) burnup Ps during the time interval after T2. In accordance with
these assumptions for the various periods of time, the average projected burnup of the HRA located in the core
at a given time was determined as follows:
t = 0 P = (P x min)/2; (12)
0< t T1 P (t) = I(niax ? Pmin)/21 [(mi int (t)1 P s [(J n(t)dt)/m (0]; (13)
0
Ti 103, the shape of the energy release field in the space of the core has
a clearly expressed tendency to vary spontaneously in the course of time. The solution of the problem of con-
trolling such reactors depends on the specific spatial and dynamic characteristics of the energy release field.
Estimating these characteristics is becoming necessary and is one of the important stages in designing high-
power reactors and their associated control systems. Experience in designing and operating RBA/LK has under-
lined the practical importance of the dynamics of the energy release field and has made it possible to define
more precisely the important aspects of this area and to develop methods for design and experimental analysis.
The distribution of the energy release field in an RBMK has a structure that is complicated by the pres-
ence of irregularities in the lattice of the technological channels (control-and-safety rod channels with ab-
sorbing rods, channels without fuel elements, etc.), and also by the fact that the reactor simultaneously con-
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 227-232, April, 1979. Original article submitted
June 20, 1978.
0038-531X/79/4604- 0267$07.50 ?1979 Plenum Publishing Corporation 267
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tains cassettes with different degrees of fuel burnup. Nevertheless the assembly of the elements which corn-
prise the core has properties which feature a common purpose (criticality, the dynamics of the integral out-
put). The nonstationary deformation of the energy release field belongs to the group of such properties. From
this point of view, the details of the structure of the energy release field do not play an important role, and in
order to study the spatial and dynamic characteristics, it is sufficient to simply describe the "average" be-
havior of the field. A homogenized model of the energy release in the space of the RBMK core is used to de-
scribe the properties of the average field.
In the mathematical model, the dimensional physical variables are reduced to dimensionless variations
in the following way:
4:1)(r, t) =0:1)(r, 0) ? (I) (r, t)0(0, 0).
The dimensional current density [4' (r, 0)] in neutrons/ sec ? cm2 is found from the condition
.S.4)(r, 0) If (r) dr = /V03.1 ? 10i6,
where No is the thermal output of the reactor in MW. The temperature differences between the fuel and graphite
and the coolant are determined, respectively, by the expressions
Of (r, t)= Of (r, 0) 4- Of (r, t) Of (0, 0);
Of (r, t) = Tf (r, t)?t,;
Os, (r, t) = 0 gr(r, 0) t) Ogr (0,0);
ogr= Tgr(r, t)-4,
i.e., assuming the saturation temperature ts is constant with average pressure in the active zone. In this
case
Of (r, 0)/Of (0, 0) = (1:0 (r, 0)11(0, 0).
The variations of the ion and xenon concentrations are found from the relations
I (r, t) J (r, 0) (r, t) J (0, 0);
(r, 0) --- [Vi (r) (1) (r, 0)/Xj];
X (r, t)= X (r, 0) x (r, t) X (0, 0);
(r, 0) Et (r2)? (vxcr-Pvir(D(()r), 0)
+
When the assumptions made are taken into account, the relationship between variations of steam content and
heat flux along the fuel element can be given by the approximate equation
(r,rb Of (0, 0) t, [1 ? sin II) (r) (r, t)dz;
tOn
(r, 0) = x (r, 0)/[17"/?' x (r, 0) (1 ?177')];
(r, 0) = (0.77.10-14/rb) S Ef (r, 0) dz,
Eoff
where kF is the heat-transfer coefficient, F is the perimeter of the fuel element, r is the latent heat of vapor-
ization, G is the circulation flow rate, yt and y " are the density of water and steam, respectively, at the satura-
tion line, x(r, 0) is the stationary mass distribution of the steam content, 4) (r, 0) is the stationary volume
distribution of the steam content, and n (r, t) is the instantaneous deviation of the volumetric steam content.
The boundary of the economizer section 0H is determined by the equation
0.77.10-14 S If (r) 4:120 (r, 0) dz = b (r) (i' ?
The equations which describe the dynamics of the field in the linear approximation (written for the dimen-
sionless deviations of the parameters as defined above) take the form
Ocp (r, t)
/ ? M2 [V2 + (0] q (r, t) +13 [c (r, t) ?
at
268
? cp (r, (r, 0)/(1) (0, 0) [a(prl (r, t)d-
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af0f(0, 0)15f (r, ag,0 gr(0, 0)15 gr(r, t) axx (r, 01;
(1/2) (ac (r, 0/00 = p (r, (r,
Tf (ON (r, 0/00 = [Ef (Oaf (0)1y (r, ?19.f (r, t);
Tgr 1.90gr (r, Wail= [2 f (Oa f (0) } ?r, xj. gr (r, (02bgr (r, 0/0z2);
Ogr(r, 01,0 = 15gr (r, lz=H = 0,
where f3 is the fraction of delayed neutrons, c(r, t) is the dimensionless concentration of delayed neutron
sources, axx(r, t) is the deviation of the multiplication constant, related to the change in the xenon concen-
tration, xi is the coefficient of heat transfer from the graphite to the coolant, and x11 is the coefficient of
thermal conductivity along the graphite unit. The change in the xenon and ion concentration can be written
in terms of dimensionless deviations as follows:
(MA (01(r, t)I at) =[Ef (Oaf (0)] p (r, i (r,
ox(r, t) = Ef ( r)
kx-F xe' (0, 0) at xd-TJ El (0)
0" xa: (0, 0)? s x xcl) (0 , 0)
kx-1- xcl) (r, 0) J (r, t) d- Tx+v, (r, t) kx+0,x0 (r, 0) X (r, t).
With respect to 4. (r, 0) it was assumed that 4, (r, 0)/4)(0, 0) = 1 within a region bounded by the cylindrical
surface r = y (in cylindrical coordinates):
f r = Ri
1 Z1 (BR ? 1). If the 241Pu content of the original fuel is larger than its equilibrium
concentration for the conditions of a stable regime in a fast reactor, BG < (BR ? 1), since 241Pu burnup will
274
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TABLE 1. Values of BR Calculated Ac-
cording to Eqs. (2), (3), and .(7) for a
"Standard" Fast Reactor [9]
Fuel
BR(')
BR (2)
BG
"Pu, 238U
1,24
1,23
0,26
239,240pu*, 238u
1,41
1,39
0,51
2/ 3230Pu, 1/3240Pu.
occur. This is the typical situation when plutonium from thermal reactors is used to maintain the fuel level in
a fast reactor. A comparison of the various definitions of BR shows that BG with the mass coefficients of re-
activity is the most convenient for calculations.
Doubling Time. The methods proposed by many authors for defining the doubling time can be arbitrarily
divided into two groups. The first group includes methods in which the doubling time of the fuel is defined only
on the basis of the fuel balance of an isolated reactor [3, 4, 10]. In this case the indicators of reproduction
depend on the state of the reactor (whose characteristics are estimated), on the isotopic composition of the
plutonium used to reload the active zone of the reactor, and on the choice of plutonium isotopes and their weight-
ing coefficients that is made to calculate the fuel balance. As a result, there may be more than a factor of two
difference between the values obtained for the doubling time for one and the same reactor [5, 10].
The systems approach [2, 5] methods fall into the second group. In our view these are more accurate.
The doubling time must be determined by the conditions of operation of a fast breeder reactor in a system
similar to itself, and then the meaning of this value becomes completely unambiguous. In this case the doubling
time is the time interval required for the output of the system of fast breeder reactors to double. The output
grows because of the excess plutonium produced in the system.
The proposed definition is universal, and makes it possible to give a clear answer to the question as to
whether a system consisting of the breeder reactors being studied can ensure the required rate of growth under
the conditions of a given fuel cycle. Such a definition of the doubling time also makes it possible to get rid of
the many uncertainties associated with a nonsystems approach.
In a developed system of breeder reactors without an external fuel source, a natural equilibrium com-
position of plutonium will become established with its inherent breeder fuel characteristics. As this takes
place, the fuel balance can be determined for any plutonium isotope, since the existence of an equilibrium plu-
tonium composition in a developed system means that the growth rate or the doubling time of the quantity of
every plutonium isotope is the same. In the first approximation, the isotopic composition of plutonium in
equilibrium in a developing system of breeder reactors can be estimated from an analysis of the operation of
a single reactor in a stable regime. It is also necessary to find such an isotopic composition of the plutonium
used for maintaining the fuel level in the active zone in a stable reloading regime, in order that the isotopic
composition of all of the plutonium unloaded from all of the reactor zones be the same as that of the plutonium
used for fuel level maintenance. Any program for calculating the isotopic composition of the fuel in a stable
reloading regime can be used for the iterative calculations.
The equations formulated by L. N. Usachev [2] can be used to obtain an expression relating the doubling
time of the fuel in a system of fast breeder reactors with the reactor characteristics and the fuel cycle. The
balance equation is conveniently represented in a general form for a reactor of unit output which consists of
J zones, each zone j being characterized by its own indicators:
E g iN (t)=-- E q;1? (t? T ? T j) (1 ?
i=1 3=1
(9)
whereN ? is the number of fresh heat-releasing assemblies (HRA) of the j-th type spent at time t for main-
taining the fuel level of the operating reactors and for putting new reactors into service, gj and qi are the quan-
tity of fuel in the fresh and unloaded HRA, respectively, Tj and Trj are, respectively, the average times spent
by the HRA in the j-th zone and the fuel from the j-th zone in the external fuel cycle, yo is the load factor of the
reactor, and ej is the fractional fuel loss in the external fuel cycle (including radioactive decay).
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The solution of the equation is found in the form
N (t) =- A3 exp (cot), (10)
whereis a constant for each type of HRA, which can be determined by taking into account the fact that the
AJ
growth of output of the system is given by the equation
dP (1) N y (t)?N y
at mj
hi which P(t) is the output of the system at time t, and mi is the number of HRA in the zone. Substitution of
solution (10) in Eq. (9) leads to the exponential equation for the fuel balance, from which the characteristic
growth rate co of the system can be found as well as the corresponding doubling time T2 (since T2 = in 2/co):
mg; (1?ei) rum.,
2q) 1 ?exp ( ?(oTi/c) 1?exp(-0)Tiftp) exp[ ? (Ti/ -1- Tr)]
3=1
The value of co found from the exact solution of Eq. (11) can be approximated accurately by the following ex-
pression:
(1? ej) qj ? g j
my
Ty "
i=1
j
2m (1+ _ar)
2 Tj
1=1
(12)
The expression in the denominator of Eq. (12) is the average quantity of plutonium in the fuel cycle of the sys-
tern in a calculation for one reactor of unit output. This value can be interpreted as the specific loading of
plutonium in the fuel cycle:
G2 (v4-20) m,(1+ Trj?Ti).
j=1
It should be emphasized that Gc involves the average quantity of plutonium in all zones of the reactor, including
the shield. The numerator of Eq. (12) is the annual production of excess plutonium in the whole reactor re,
taking into account its operating regime and the loss in the external fuel cycle:
(1 ? sy) qy ? gy
rE=q) mi. (14)
T.;
J=1
Gc and re can be used as independent specific fuel characteristics of a fast reactor in studying the fuel
balance of a system of fast and thermal reactors during the period in which all of the plutonium is for the most
part consumed in the fast reactors. To account for the differences in the isotopic compositions of the plutonium
from the thermal reactors and the natural stable plutonium in fast reactors, these indicators must be expressed
In equivalent amounts of 239Pu, i.e., according to the sum of all plutonium isotopes with appropriate weighting
reactivity coefficients normalized to 239Pu and 238U (8). It is also desirable to use equivalent quantities of 239Pu
to unify the calculations and in defining the doubling time.
Equation (12) can be rewritten in a somewhat different form which is more suitable for comparative cal-
culations by introducing the breeding gain BG, calculated for natural stable plutonium:
(I)(Y BG ? %ie.")
.5=1 (15)
?
Ui [1 + (Tri/Ti)]
3=1
where GQj = qjmj/Ti is the quantity of equivalent plutonium unloaded from the j-th zone per year in tonsAcW(el.) ?
yr), Gj = (qj + 09(2 is the average quantity of equivalent plutonium in a zone in tons AW(el.), and Y is the quan-
tity of fission products formed in the reactor during a year of operation at full power in tons/kW(el.) ? yr). Using
an energy balance of 200 MeV for one fission of a heavy nucleus, we get Y 0.39/n tons/kW(el.) ? yr), where n
is the efficiency of the atomic electric power plant.
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TABLE 2, How Doubling Time Depends
on the Composition of the Plutonium Used
for Fuel Level Maintenance and on the
Method of Calculation
Form of plutonium used I T2, yr
for fuel level maintenance I
1
Plutonium of natural equi-
librium composition
A
10.5 10,5
Plutonium from thermal I 9.2
reactors
14
It should be noted that the use of the weighting reactivity coefficients is justified in determining co (T2)
only when the plutonium has the natural stable composition of a fast reactor.
Table 2 lists the results of a calculation of the doubling time for a large fast reactor (with an active
zone volume of 9 m3) using oxide fuel for plutonium of the isotopic compositions: plutonium with a compost-
tion corresponding to the natural stationary regime of a fast reactor (76% 239Pu, 19% 240pu, 3.5% 241Pu, and 1.5%
2 to 239pu, 20% 240pu, 14% 241p
42PU), and plutonium from thermal reactors (62% u and 4%242Pu). The equilibrium
composition of plutonium in the stationary regime of fuel level maintenance of a fast reactor was determined
in both cases by the method proposed in [11]. Two methods were also used to calculate 1.2: according to
the sum of fissioning isotopes (A) and according to the equivalent quantity of 239PU (B).
It is seen from the data of Table 2 that an error in the value of the doubling time results in the case of
plutonium from thermal reactors when the doubling time is formally defined simply by the sum of the fission-
ing isotopes; in particular, it is reduced in comparison with the true value (10.5 yr) by 20%. Introducing the
weighting coefficients (i.e., using the equivalent quantity of 233Pu) into the calculation increases the doubling
time by 33%. The true value of the doubling time determined for plutonium of natural stable composition does
not depend on the method of calculation.
Conclusions. The study of the reproduction characteristics of fast breeder reactors clearly shows the
need to unify the approach used in determining them. The authors consider it possible to formulate the follow-
ing conclusions and recommendations.
1. From the viewpoint of the reproduction process, the most accurate definition of the doubling time and
the fuel characteristics of a fast breeder reactor is based on the conditions of the reactor's operation in a sys-
tem of such reactors in a stable regime.
2. For calculations of the doubling time and also as an independent indicator it is appropriate to use the
BG [Eq. (7)] defined for natural stable plutonium, rather than the traditional BR.
3. For the purpose of unification, it is preferable to use Eq. (11) and the approximate equations (12) and
(15) for determining the doubling time (characteristic rate of growth).
4. To allow for the differences in isotopic composition of the plutonium, it is good practice to produce
plutonium in thermal and fast reactors, and also to express the load of plutonium in a fuel cycle in terms of
equivalent quantities of 239Pu.
LITERATURE CITED
1. V. V. Orlov et al., At. Energ., 30, No. 2, 170 (1971).
2. A. I. Leipunskii et al., Third Geneva Conference (1964), Report of the USSR No. 369.
3. H. Wyckoff et al., Nucl. Technol., 21, No. 3, 158 (1974).
4. R. Hardie et al., Nucl. Technol., 26, No. 1, 115 (1975).
5. K. Ott et al., Nucl. Set. Eng., 62, 243 (1977).
6. Trans. Amer. Nucl. Soc., 25, 584 (1977).
7. 0. D. Kazachkovskii, Second Geneva Conference (1958), Report of the USSR No. 2028.
8. A. Baker et al., ANL-6792, 329 (1963).
9. A. Baker et al., in: Proc. Symp. "Calculation for a Large Fast Reactor," Pisley (1971), TRG Rep.
2133(R).
10. C. Adkins, Nucl. Technol., 13, No. 2, 114 (1972).
11. G. B. Usynin, At. Energ., 25, No. 6, 466 (1968).
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DETERMINATION OF STRESS-INTENSITY FACTOR
IN REACTOR VESSEL FROM MODELS
V. S. Postoev, N. I. Ryndin, UDC 620.171.5:621.039.53
S. N. Eigenson, and V. B. Titov
The complexity of calculations of the stress state of the connection zone of nuclear reactor vessels with
surface cracks makes research on models very timely. The polarization-optical method of "freezing-in" the
strains has been applied most effectively [1]. The stress-intensity factor for a reactor vessel with surface
cracks in the connection zone was found from a model of optically sensitive material based on ED-16M epoxy
resin, made on a 1:20 scale (Fig. la). The model consisted of the vessel and cover, connected by bolts. The
parts of the vessel (cylindrical shell with connection pipes and bottom) as well as the cover were made by
precision investment casting with subsequent machining. "Large" cracks of 4.4 x 13 mm were inflicted on the
three connection pipes of the upper row and "small" cracks of 3.4 x 11 mm, on the three connection pipes of
the lower row (Fig. lb). The model of the vessel was loaded in a glycerin medium with an internal pressure
p = 0.02 N/mm2 under temperature conditions ensuring that strains would be frozen in. In the loading process
the cracks were in static equilibrium. The nominal stress was taken to be a circumferential stress in the
cylindrical wall of the reactor
= pRav/45 = 0.15 N/mm2, (1)
where (5 is the wall thickness and Ray is the average radius.
Preliminary experiments on a smooth-walled cylinder with a non-through crack, loaded with an internal
pressure, as well as on parts of the model under tension made it possible to determine the internal pressure
with freezing of the reactor-vessel model, in which case the crack does not grow in the highly elastic state.
Once the strains had been frozen in, grooves were filed perpendicular to the plane of the crack (Fig. 2). The
optical path difference at the crack tip was found with a polarizing microscope. In accordance with this method
[2] the thickness of the section was reduced from 2.5-3 mm to 0.8-1 mm in order to make the optical path dif-
ference more precise.
Analysis of experimental data showed that the principal stresses are distributed symmetrically about a
crack. They have their maximum values in planes passing through the middle of the crack. The stresses are
located within a short distance of the crack. Beyond that distance the stress state is the same about all cracks
(Fig. 3). The stresses in Fig. 3 are given in relative units a/o-n as a function of ratio x/d (x is the radius in
polar coordinates, reckoned from the crack tip, and d is the crack-weakened thickness of the connection pipe).
As is seen from Fig. 3b, the circumferential normal stresses ay increase sharply near the crack. The stress
concentration at the tip of a large crack reaches a value 15 times and that at the tip of a small crack, 10.5
times the value of the nominal stresses in the wall of the reactor model. The stress is observed to fall off at
a short distance from the crack tip, 0.1 and 0.06 x/d for the large and small cracks, respectively.
Within the framework of linear fracture mechanics the stress-intensity factor is given by
K=cr VT,/ q) (ail L), (2)
where a is the normal stress, 1 is the crack half-length, and cp is a dimensionless function which depends on
the ratio ai/L of the dimensions of the body. In the given experimental investigations, the stress-intensity fac-
tor for the structure was calculated with allowance for the stress state in the vicinity of the crack, which had
been found in polarization-optical studies by the procedure given in [2]. Two methods of calculation were used:
the first stems directly from Eq. (2), whereas the second is based on the Neuber model of the structure of a
real polycrystalline solid, according to which model the stresses in the vicinity of a crack are averaged over
the experimental curve. Finally, relations of the following form were obtained:
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 236-240, April, 1979. Original article submitted
April 24, 1978.
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a
Fig. 1. a) Position of cracks and b) cross section of model of reactor
vessel: 1) cover; 2) bolts; 3) crack; 4) connection-pipe nipples; 5) cy-
lindrical shell with connection pipes; 6) bottom,
Fig. 2. Bands in frozen-in section of model,
passing through the middle of a large crack
(section vi in Fig. lb).
first method: Ifikr? = Ord (x1d)" 2 (Crykin);
xld
second method: Kilo-n= :1/7/-1/2(x/d)-1/2 $ (cry/an) d (xld).
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(3)
(4)
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1,0
0,8
46
14
/2
10
4004 4008 0,012 0:014
X/d
Fig. 3. Principal stresses in plane passing: a) through
middle of crack in connection-pipe. section and b) near
crack: 1, 3, 5) ay, az, ax about large crack; 2, 4, 5)
for small crack.
440
401 402 403 404 0,05 406
Fig. 4
407 goo 409 x Id?
5000
I 4000
3000
z, 2000
1000
___-500
400' E
200 ;'
100
0 10 20 30 40 50 60 70 80 90 100 h, mm
Fig. 5
Fig. 4. Stress-intensity factorfor model of reactor vessel with: 1) large and 2) small crack in con-
nection-pipe zone; solid and' dashed curves denote calculations by Eqs. (3) and (4), respectively.
Fig. 5. Results of theoretical calculations for reactor vessel with surface crack in connection-pipe
zone.
It is seen from the results of the calculations, as given in Fig. 4; that the values obtained for the stress-
intensity factor by the two methods do not differ at the crack tips. With distance from the crack tip, a con-
siderable difference, 10-25%, is found for large cracks. At a distance of 0.05x/d the stress-intensity factor
for the structure becomes constant. In the case of small cracks the same value is obtained by both methods
of calculation.
' The measurements showed that the maximum circumferential normal stress in a crack-free pipe con-
nection of the model was 0.325 N/rnm2. The stresses can be scaled up to a full-size reactor vessel by the
relation [1]
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TABLE 1. Experimental and Theoretical
Values of Stress-Intensity Factor
Depth of
crack, mm
Mean stress
in connec-
two pipe.
Nimms
Stress-inten-
sity factor
K N/rnmsh
I*
Divergence,
%
85
300
4400-4800*
?
4450j
110
260
4600-5000*
_
4660 1
30
360
3500 ?3700 *
10,7
3125t
50
340
3850-4200*
1,8
4275?
*Solution of [7].
t Experiment.
$ Calculation according to [8].
?fs (Pfs/Pm)arn. (5)
where o-fs, um and pfs, pm are the stress and pressure, respectively, for the full-size reactor vessel and the
model. The highest stress in the pipe connection proves to be a boundary stress; therefore, the use of Eq. (5)
is not at contradiction with modeling technique developed for studying the stress ?strain state of a reactor ves-
sel [3]. The model stress-intensity factor can be scaled up to the full-size reactor vessel by the relation [4]
Kfs = (afskrn) (lfs/lin)1/2 Kra,
1'6)
where ifs//m is the ratio of the lengths of like segments of the full-scale reactor vessel and the model, re-
spectively (modeling scale). The ratio of the stresses at like points of the full-scale vessel and the model is
equal to the operating ratio of operating pressures o-fs/o-m =pfs/pm.
Below we give comparative calculations for a reactor vessel with an internal diameter of 5014 mm with
eight connection pipes, uniformly distributed in one level along a circle [7]. The calculations were performed
by using two versions of the method of finite elements [5, 6] for two non-through cracks with a depth of 40 and
50 mm, on the inner surface of a connection point at the same place as in the experimental investigations de-
scribed above. For the method of calculations from [5, 6] we used the same breakdown into finite elements,
i.e., 178 twelve-point isoparametric elements and 1049 nodes. The results were found to be in good agreement.
Curves 2 and 3 in Fig. 5 show how the stress-intensity factor varies with the crack depth whereas curve
1 shows the variations of the normal circumferential stress in the connection pipe, this stress being perpendic-
ular to the plane of the crack. In the absence of a crack the maximum stress is 400 N/mm2. When there is a
crack the stress falls off with its depth h while at the same time the stress-intensity factor K1 increases. Thus,
with a crack depth of 30 mm, we have K1 = 3500-3700 N/mm3/2 and Uy = 360 N/mm2, whereas with a crack depth
of 50 mm we have IC/ = 3850-4200 N/mm3/2 and ay = 340 N/mm2. Curve 2 was drawn according to the results
of approximate analytic calculation and curve 3 was drawn according to the data from calculations by the Parks
compliance method [6] and the method of finite elements [5]. The results of the calculations by the. last two
methods almost coincide and curve2 gives results which differ by no more than 8% from those of curve 3. The
calculations were carried out with the assumption of elastic strain.
For a comparison of the results of the analytic calculations with experimental data the latter must be
scaled up for the full-scale reactor. As our full-scale reactor we take the one for which calculations are
given in [7]. In shape it is roughly similar to the experimental model given here and has an internal diameter
of 5014 mm. The model has an internal diameter of 200 mm and, therefore, the coefficient of geometrical
similarity is /fs// in =5014/200=25. Model cracks with a depth of 3.4 and 4.4 mm correspond to full-size
cracks with a depth of 3.4 x 25=85 mm and 4.4 x 25=110 mm. The calculated data for such cracks were ob-
tained by extrapolation of curves 1, 2, and 3 from Fig. 5 (shown by dashed lines). The possibility of such
extrapolation was shown in [7]. Scaling up the model stress-intensity factor to the full-size reactor vessel
was done by Eq. (6). The results given in Table 1 indicate that the experimental data are in agreement with
analytic calculation by the method of finite elements. Table 1 gives data from approximate analytic deter-
mination of the stress-intensity factor on the basis of knowledge of the linear fracture mechanics for plates
with shallow surface cracks [8]:
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K1 = Msan. (nalQ)112,
(7)
where Ms = 1 + 0.12(1 - a /c) is a coefficient making allowance for the effect of the crack coming out on a free
surface, a and c are the depth and half-length of the crack, and o-nm is the nominal stress in the connection-
pipe zone near the crack. Parameter Q was found from
Q = = 0.212 (o/aT)2, (8)
where (I) is an elliptical integral defined as a function of the shape of the surface crack and uT is the yield
stress of the material. With the crack cross section weakened by 5-10%, it can be assumed with sufficient ac-
curacy for calculations that the stress in the connection-pipe zone will diminish in proportion to the weakening
(in comparison with the stress in the connection pipe without a crack).
Thus, the investigations carried out made it possible to determine the stress-intensity factor for a reac-
tor vessel with surface cracks in the connection-pipe zone. Scaling up the stress-intensity factors of the model
to the reactor shell yields satisfactory accuracy while maintaining the geometric similarity in the crack di-
mensions. With shallow surface cracks in the connection-pipe zone of a reactor the stress-intensity factor can
be approximated by using available solutions for plates. The agreement between experimental and calculated
results attests to the feasibility of employing the polarization-optical method of freezing-in strains to determine
the stress-intensity factor in constructions with a complex geometry.
LITERATURE CITED
1. A. Ya. Aleksandrov and M. Kh. Akhmetzyanov, Polarization-Optical Methods of the Mechanics of De-
formable Solids [in Russian], Nauka (1973).
2. R. Marloff et al., Exp. Mech., 11, No, 12, 529 (1971).
3. N. N. Zorev et al., At. Energ., 42, No. 6, 465 (1977).
4. F. L. Hesin et al., in: Proc. V. V. Kuibyshev Moscow Civil Engineering Institute, Nos. 125-126, Stroiizdat,
Moscow (1975), p. 56.
5. W. Schmitt, Int. J. Pressure Vessels and Piping, No. 3, 74 (1975).
6. D. Parks, Int. J. Fracture, 10, No. 4, 487 (1974).
7. W. Schmitt et al., Int. J. Fracture, 12, No. 3, 381 (1976).
8. E. Smith et al., Int. J. Fracture, 12, No, 1, 13 (1976).
NEUTRONS EMITTED BY FRAGMENTS OF THE SPONTANEOUS
FISSION OF 252Cf AND THE FISSION OF 239Pu
BY THERMAL NEUTRONS
B. G. Basova, D. K. Ryazanov, UDC 539.173.84
A. D. Rabinovich, and V. A. Korostylev
The investigation of fission fragments which emit an enhanced number of neutrons is of appreciable in-
terest for theory and practical application. It is known that such fragments should have a large nonequilibrium
deformation at the moment-of fission. Establishment of the equilibrium shape of the fragment is accompanied
by a transition of the deformation energy to excitation energy of the fragment nucleus with subsequent neutron
emission.
It has been established experimentally that the dependence of the number of emitted neutrons on the frag-
ment mass v(M) is saw-toothed in nature, indicating a strong nonuniformity in the distribution of the excitation
energy E* between the two fragments [1]. The peculiarities in the behavior of v(M) are explained by the in-
fluence of shell effects in the fragment nuclei [1, 2].
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 240-245, April, 1979. Original article submitted
March 13, 1978.
282 0038-531X/79/4604- 0282$07.50 ?1979 Plenum Publishing Corporation
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It is of interest to clarify how the dependence v(M) varies with a change of another parameter of the
fragments ? the total kinetic energy of the fragments EK (MeV), reflecting the shape of the fragments and
their elongation towards the instant of disruption, which is evident from the relation
EK = 1.44ZLZH/ (RL + RH + d), (1)
where ZL and ZH are the charge numbers of light and heavy fragments, respectively, RL and RH are the maxi-
mum radii of light and heavy fragments, and d = 1-2 F.
Assuming the shape of the fragments to be spheroidal, one can write
/ 2 \
RL-----Ro Lk + 7 PI) RH=-- RoH( I + -} OH) 7
(2)
where h and OH are the deformation parameters of light and heavy fragments and RoL,H = 1.22M2Z3H F.
An enhanced neutron yield is expected for highly deformed fragments with 13L, H a 1 and low values of
EK, in agreement with the energy balance upon fission. One can write the energy balance formula in a form
which is valid for an individual fission event if one identifies this event by the fragment mass M and a specified
value EK
Q (M) = E K(M)? E* (M , EK)= EK(M) v (MEK)(BN(M)+ EN(M)] E
(3)
where BN is the binding energy of a neutron for a fragment of mass M averaged over the charge distribution,
EN is the mean energy of the spectrum of neutrons emitted by a fragment of mass M, E* is the excitation en-
ergy of the fragment, and Ei is the total energy of the y quanta of the fission. The quantities EK(M) and
v(M, EK) in Eq. (3) are specified; the rest vary weakly with a variation of the fragment parameters M and
EK [4].
Thus the simultaneous measurement of M, EK, and the number of neutrons for the fission fragments and
the subsequent calculation of the distributions P(M, EK) and v(M, EK) corresponding to it permits formulating,
in general outline, a picture of the energy distribution in individual fission events.
The main goal of this paper is to obtain the distributions P(M, EK) and v (M, EK) for fissionable 252Cf
and 240Pu nuclei, which differ strongly in their nucleon makeup, as well as to reveal fragments which emit a
large number of neutrons.
Description of the Experiment. The targets were prepared by the method of vacuum deposition of fis-
sionable material onto a film made of A1203 (30 ?g/cm2) covered by a layer of gold (30 pg/cm2). The kinetic
energies of the fragments were recorded by a double ionization chamber with grids filled with a mixture of
gases consisting of Ar + 4% N2 [5]. The fragments were collimated by two diaphragms mounted on both sides
of the target. The mean deviation angle of the fragments from the symmetry axis of the chamber was ?12?.
The moment of fission was fixed with a temporal accuracy of ?10-9 sec with the help of an FEU-30 photo-
multiplier recording the scintillation bursts in the chamber gas caused by the fragments. A plastic scintilla-
tor 175 mm in diameter and 70 mm in thickness served as the neutron detector in combination with the FEU-30.
Separation of instantaneous neutrons and y -quanta of the fission was carried out by the time-of-flight method
on a baseline of 40 cm. An accumulator having 8192 channels and executed on a magnetic drum was used to
record the information. The capacity of each memory channel was 2" discharges. The accumulator memory
was divided into two equal parts. Double coincidences (64 x 64) in the coordinates "kinetic energy?kinetic
energy of coincident fragments" F(Ei, E2) were recorded in one part, and triple coincidences between two
fragments and a neutron in these same coordinates ? N (Ei, E2) ? were stored in the other part [6]. The average
number of neutrons for each fission event (E1, Ei) was calculated from the relation
N (E E j)
v (E1, L) = (Es, E,i) IF (E? N (E E1)], (4)
where t(E1, Ei) is the efficiency of recording neutrons emitted by fragments in a fission event with the co-
ordinates (E1, Ei).
The procedure of calculating the efficiency and the procedure for processing the measurements are de-
scribed in detail in [7]. We briefly note that the algorithm for calculating Ei) was constructed on the basis
of the model of neutron evaporation from completely accelerated fragments with account taken of the neutron
spectra in the center-of-mass system of the fragment, the dimensions of the neutron detector and its sensitivity
of neutrons of different energies, and the angular distribution of coincident fragments and the velocities of the
fragments.
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4,5
3,6
2,7
1,6
0,9
V?
5,20
4,55
;90
3,25
75 90 105 120 135 150 165 117 mass units
70 85
100 115
440
3,85
3,30
2,75
2,20
120 145 160 11, mass units
Fig. 1 Fig. 2
Fig. 1. Dependence of the neutron yield on the mass of the fragments for 252Cf. ?) yield of
fragments and ?) total number of neutrons from two fragments; the number of neutrons per
fragment is from the sources: 0) this paper, A) [8], and 0) [4].
Fig. 2. Dependence of the neutron yield on the mass of the fragments for 235Pu + nth: ?1
yield of fragments and.) total number of neutrons from two fragments; the number of neu-
trons per fragment is from the sources: 0) this paper and 0)110].
,As a result of experiment 7.84 ? 106 events of spontaneous fission of 252Cf and 2.83 ? 105 neutrons emitted ,
by fragments were recorded. For the fission reaction of 239Pu by thermal neutrons 1.28 ? 106 fission events
and 2.9 ? 104 neutrons corresponding to them were recorded.
Results of the Measurements. The dependence v(M) for the spontaneous fission of 252Cf is shown in Fig. 1
in comparison with the data of [4, 8] obtained with the help of a large liquid scintillator (LLS) with dissolved
gadolinium and by the time-of-flight method with application of a plastic scintillator. One can note the good
agreement of the data obtained by different methods. The structural peculiarities of the distribution v(M) at
ML 90-100 mass units and MH r-t1 140-142.156 mass units are appreciable, which was pointed out in [9].
Also shown in Fig. 1 is the variation in the dependence of the total neutron number from two fragments on the
mass of the heavy fragment vn(MH). The increase in P11(MH) upon fission of the nucleus into fragments of
equal mass draws attention to itself.
The dependences v(M) and vn(MH) for the fission of 239Pu by thermal neutrons are shown in Fig. 2 in
comparison with the data obtained with the help of an LLS with dissolved cadmium [10]. The difference in the
methods .of measuring the number of neutrons appeared more strongly at the edges of the dependence v(M).
Notwithstanding the difference of 12 nucleons between the fissionable nuclei and the differences in the
mass distributions, one can note general features in the behavior of v(M) and vn(MH) for the fission of 252Cf
and 239Pu. As has already been noted, the dependence v(M) is produced by the properties of the fragments [1,
2, 4]. Fragments with masses ML ;z-, 80-90 mass units and MH ?=-: 130 mass units are distinguished by a large
rigidity and are stable to a change in their shape due to a "magic" number of nucleons making up closed shells
in nuclei with M = 82 (N = 50, Z = 32) and M = 132 (N = 82, Z = 50) [2, 11]. Fragment nuclei of mass 150-170
and 105-120 mass units and with the number of nucleons differing strongly from the known magic numbers thus
obtain a supply of deformation energy which changes into a number of emitted neutrons.
Consideration of the experimental data on v(M) for 233U and 23511 upon fission of the indicated isotopes by
thermal neutrons [10] and of the fission of 23811 and 226Ra by protons [12, 13], together with the data presented
in Figs. 1 and 2, permits concluding that fragments of specified mass emit the identical number of neutrons in-
dependently of the type of fission and the kind of fissionable nucleus. Thus the mass distribution of the frag-
ments determines in a decisive way the average number of neutrons T formed upon fission. We note that such
a relation of v(M) and the mass distribution of the fragments can be used for a more or less successful predic-
tion of i; for a number of heavy and superheavy nuclei [14].
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4
3
2
1
0
4
3
2
0
4
1
0
4
3
2
4
2
1
0
4
3
2
0
165 MeM. .1,
...T ;??
ei ?K.::????:
.., ,4 ,
. ... .#1:-?4?i-f.
' ,.. 1., ?e?
?4li .: .iii .:11
150 .,. 1
_e?
145 ,
?????t:' 4'4 .1..1
.:1 .? *#1.
?4' ? ?
? 4.1.
140 I..
??:?4?? ??? 41 ?
-
81 96
111
a
4
3
2
0
4
2
0
4
2
0
4
3
2
1
0
4
3
2
4
2
_ 2075,
-
-
?
_?2"-N-1-'44.???1 ; ?
-202,5
i
_200
-
_
_
.4
:4 ?.
_195
_
-
-
..."
.
..
.4. ?
?
?
_
_
- :
.
:
?
l'
?
- 175
-
-
-
.?
1
i
. .
ri?
126 141 155 171 81
21, mass units
95
III
126
141 156 17/
?7
4
2
4
1
4
3
2
1
4
3
2
4
3
2
1
0
4
3
2
162 MeV
A AL.
152 .
.: ? ? ?
. ?'' '
..41.61 A
?
147
."
, .4.:??-...A*
7
1..
-
142
. i. ? ..{....-i.:.
:..
1:4'.. ?'. i? if ? ..."
.. .?
137
{....7. :. ? ..
...
4
3
1
4
3
2
4
2
1
0
4
3
2
0
4
3
2
1
3
2
1
0
_192 I
_ t
, Ia\ Lti
_187
_ i
_ 182 "K
_
- .? ? 1.1.
?
-177 1
_
_ ?
?
-172 ?
_ . ?
.
- ? ???????..4
_
- .
- ?
-. 4.. ?
?
?
75 90 105 120 135 150 165 75 90 105
21, mass units
120 135 150 165
Fig. 3. Dependence of neutron yield (*) on the mass of the fragments (? is the yield
of fragments) for the specified values of the total kinetic energy (a) upon the spontane-
ous fission of 252Cf and (b) upon the fission of 239PU by thermal neutrons.
Let us consider more detailed information in the form of the dependences v(M) for fixed values of EK
(Fig. 3). Here are given the corresponding mass distributions of the fragments. As was pointed out earlier,
the parameter EK is important from the point of view of the energy balance upon fission and the effect on the
shape of the fragments [see Eqs. (1) and (2)].
A characteristic feature of the results presented is the large and stable yield of neutrons from light frag-
ments in the mass range 110-126 mass units for 252Cf and 105-120 mass units for 239PU over almost the entire
range of variation of EK. The function v(M) for a heavy fragment demonstrates a strong decrease of v as EK
increases, which can be explained by the preferential yield of a narrow group of masses with MHF',1 130-134
mass units (spherical fragment) for 252Cf and 239PU. The maximum number of neutrons (v 5) are emitted
by fragments with ML?-?=1 120 ? 5 mass units and EKc?-', 185 MeV for 252Cf and fragments with ML ,??-?? 110 mass
units and EK 167 MeV for 239Pu. The corresponding heavy fragments with MH = A - ML (here A is the mass
of the fissionable nucleus) almost do not emit neutrons. In both cases there are fission events with extremely
different deformabilities of the fragments [11]. We also note that as EK increases fission events with greatly
different masses of the light and heavy fragments (highly asymmetric fission) are characterized also by a large
difference in the deformability of the fragments. In this case the heavy fragment emits a large number of neu-
trons: for 252Cf MH 164, EK 150-165 MeV, and v ??=: 5; for 23913u MH r=: 156, EK 137-147 MeV, and v r=:, 4.
In this case the light fragment with (A - MH) = ML 82 is a rigid nucleus of almost spherical shape, due to the
effect of the shell structure.
Let us estimate the deformation parameters f3L and 3H for the indicated fission events on the basis of
Eqs. (1) and (2). The values of the charges ZL and ZH are determined from the assumption that the charge
density in a fissionable nucleus is identical to that in the fragments (one can include direct experimental data).
For a heavy fragment with MH 130-134 mass units it is natural to take 13 = 0. Then we obtain h = 1.0 for
252Cf with ML 120 mass units and EK = 185 MeV and /31., = 1.17 for 239Pu with ML 1=?? 110 mass units and EK =
167 MeV.
Having assumed )3 0.1-0.2 for a light fragment with ML 82 mass units, we obtain SH = 0.9 for 252Cf
with MH?????? 164 mass units and EK = 155 MeV and )3H = 1.0 for 239PU with MH P-1 156 mass units and EK = 147
MeV. It is evident that upon fission fragments can be formed with very appreciable initial nonequilibrium de-
formations. An estimate of the excitation energy from the formula
E* c(32 (5)
2
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4
3
2
2
a
0 00 00 I? 00000?40o
0 00 0, 0
00} 000f00
-
?? 0 104.00
0
0
0 0?0000
00
0
130
155 180 205 Ex, MeV ?
Fig. 4. Dependence of the neutron yield
on the total kinetic energy for specified
masses of the fragments with: a) ML =
MH = 126, b) MH = 132, and c) ML=
120 mass units: 0, ?) neutron yield
and fragment yield, respectively.
(here c = 120 MeV), which corresponds to the liquid-drop model, gives an exaggerated value of E* for highly
deformed fragments in comparison with the experimental data.
Returning to Fig. 3, we turn our attention to the appreciable yield of neutrons from fragments of sym-
metrical fission, which is more and more clear as EK decreases right down to EK = 140 MeV for 252Cf and
EK 137 MeV for 239Pu. In view of the fact that the yield of events of symmetrical fission is small and sub-
ject to the effect of instrumental errors, corrections are introduced into the data of Fig. 3 for the background
of random double and triple coincidences, scattering of fragments at the collimator edges, and other factors.
A correction was not introduced for the mass resolution, which is equal to 3.5 mass units. The dependence
of the neutron yield on EK for the spontaneous fission of 252Cf is shown in Fig. 4 for three selected masses of
the fragments. At ML = MH = 126 v(EK) is a weakly growing function with decreasing EK. There are fission
events in which both fragments are strongly deformed by neutron-rich nuclei, emitting 3-4 neutrons each, which
is in agreement with the energy balance formula (3). An estimate of the deformation parameter gives the value
13H 1.29 at EK = 145 MeV. The yield of such events is small (10's for spontaneous fission of 252Cf),
and they have no appreciable effect on the average number of fission neutrons -v.
Let us consider a pair of fragments with MH = 132 mass units and ML = 120 mass units. The neutron
yield from them is shown in Figs. 4b and c as a function of EK. At EK 170 MeV the light fragment emits an
appreciable number of neutrons, and consequently, it is more highly deformed in comparison with the heavy
fragment. However, at EK < 170 MeV the number of emitted neutrons is redistributed in favor of a fragment
with MH = 132 mass units, which indicates the possibility of strong deformation of a fragment with the magic
number of nucleons. It has been shown theoretically [3] that a definite set of deformed states is observed for
a fragment with a specified nucleon makeup (Z, N). For strong deformation of the nucleus the property of the
magicness of 132 nucleons is destroyed, i.e., for a quantitative estimate of the neutron yield from fission frag-
ments it is necessary to know not only the mass distributions of fragments but also the deformed states of frag-
ments up to the moment of separation.
LITERATURE CITED
1. J. Terrell, Phys. Rev., 127, 880 (1962).
2. R. Wandenbosch, Nucl. Phys., 46, 129 (1963).
3. B. Wilkins, E. Steinberg, and R. Chasman, Phys. Rev., 14, 1832 (1976).
4. H. Nifenecker et al., in: Proc. IAEA Third Symp. on the Physics and Chemistry of Fission, Rochester,
13-17 Aug. 1973, IAEA-SM-174/207.
286
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010004-2
5. B. G. Basova et al., Prib. Tekh. Eksp., No. 4, 46 (1975).
6. B. G. Basova et al., Preprint NHAR P-269, Dimitrovgrad (1975).
7. B. G. Basova, A. D. Rabinovich, and D. K. Ryazanov, Preprint NIIAR P-262, Dimitrovgrad (1975).
8. H. Bowman et al., Phys. Rev., 129, 2133 (1963).
9. J. Boldeman and R. Walsh, in: Proceedings of the Conference on Neutron Physics [in Russian], TsNII-
atominform, Moscow (1976), Ch. 5, p. 210.
10. V. F. Apalin et al., in: Proc. IAEA Symp. on the Physics and Chemistry of Fission, Vienna (1965), Vol. 1,
p. 587.
11. V. A. Rubchenya, lzv. Akad. Nauk SSSR, Ser. Fiz., 36, No. 1, 212 (1972),
12. E. Cheifetz and Z. Fraenkel, Phys. Rev. Left., 21, No. 1, 36 (1968).
13. H. Schmitt and E. Konecny, ibid., 16, No. 22, 1008 (1966).
14. V. P. Zakharova, Preprint IAE-2738, Moscow (1976).
PROBLEM OF THE OPTIMIZATION OF A SYSTEM OF
DIRECT ENERGY CONVERSION WITH PARABOLIC
TRAJECTORIES OF CHARGED PARTICLES
S. K. Dimitrov and A. V. Makhin UDC 621.039.6
A suggestion was made in [1] for the direct conversion of the energy of reactor ion beams by using a sys-
tem with parabolic trajectories of the ions or a system of tapered diaphragms (STD). The simplicity and high
efficiency (-90%) of an STD for sufficiently dense ion beams (d/rdi 0.2, where d is the beam diameter at the
entrance to the deceleration zone and rdi is the Debye ionic radius) may prove to be decisive factors in con-
nection with the selection of a specific regenerator design for a thermonuclear reactor. It is possible to use
an STD in the injection system of tokomaks; however, it is necessary in this case to apply compensation of the
ion space charge by electrons [2].
A method is given in [1] for calculating the optimum parameters of the system (slope angle of the dia-
phragms a opt, lengths of the deceleration zone Aopt, and maximum efficiency n max). The optimum angle of
a section of the diaphragms i3opt is assumed to be found from the condition
tg popt = 2 tg aopt,
(1)
or flopt 2aopt for small a opt, i.e., the edges of the collecting electrodes coincide with the line of the vertices
of the parabolic trajectories of the ions.
A method of calculating the optimum angle of the section is assumed in this paper which takes account of
secondary emission from the diaphragms. The trajectories of charged particles in the STD are shown sche-
matically in Figs. la and b. The beam energy W is such that the vertices of the parabolas lie between the N-th
and N + 1-th diaphragms. As experiments have shown, the current in this case flows mainly towards the N-th
and N ? 1-th diaphragms if the beam is not very dense and wide. The dashed line shows the trajectories of
secondary electrons. It is necessary in the case of regeneration of negative ions or electrons to exclude in-
cidence of the beam on the diaphragms from the direction of the entrance aperture of the system, since failure
to do so leads to a loss in efficiency due to secondary emission only if a > 1, where a is the secondary emis-
sion coefficient, which depends on the energy of the particles incident on the diaphragms, i.e., on the discrete-
ness of the plate arrangement (see Fig. la). It is possible to write this condition mathematically in the follow-
ing way:
x, I (aopt+ 0/2)xN
from which
2a opt ? ? d/rd
P opt= dlrd.
1---(1/1dpird)112
We will discuss the direct conversion of the energy of a beam of positive ions in two aspects.
1. Mode without Compensation of the Ion Space Charge by Electrons. In this case it is necessary to achieve
the absence of a current of secondary electrons from the diaphragms, since secondary electrons will be ac-
celerated along the direction towards the next diaphragm, which will result in a loss in efficiency (see Fig. lb).
The condition for finding gopt can be written as follows:
xi jr,N (ocopt? 0/2)..>-xN+ d, (6)
from which
opt? 2a?13t ?112 diird "1/- d/rd
(7)
1+ (112 dp/rd)1 2 1 --V dp/rd
One should note that the estimates made will be valid for beams which are not very wide and dense; other-
wise a significant redistribution is observed in the current among the diaphragms. In addition, for wide and
dense beams of charged particles (d/rd > 0.2 and d/ A. Opt > 0.1) the efficiency of the system may be insuffi-
ciently high even in the optimum case. As computer calculations have shown, the field in the STD is already
distorted at d/rd:=?-?-: 0.3 by the beam so much that it loses its ability to deflect particles effectively. The posi-
tion of the beam in the deceleration region and a picture of the equipotentials with space charge taken into ac-
count (the method of large particles was used) are shown in Figs. 2a and b. It is advisable in this case to apply
a mode with compensation of the ion space charge by electrons.
2. Mode with Compensation. The system is placed in a weak transverse magnetic field, such that the
ion trajectories do not differ too much from parabolas (see Fig. lb); the secondary electrons drift from one
edge of the diaphragms to the other, compensating the space charge of the ion beam. The optimum angle is
that at which a maximum part of the beam is incident on the N-th diaphragm, where the ion energy is a mini-
mum.
It is possible to write the conditions for g opt as follows:
xi luiv_ @opt
x2I?N (c?opt ?0/2) d.
Condition (8) excludes incidence of the beam on the N ? 1-th diaphragm from the direction of the input
aperture of the system, and condition (9) does the same for a beam incident from the direction of the N-th
diaphragm. Thus the angle 10 opt should satisfy the following inequality:
2a opt -1-0 < 2aopt ?0 d/rd
- Popt
1+ (2 "Ii2dp/rd)012 (ildpird )1/2 1 --17 dp/rd
This inequality is always satisfied for thin parallel beams (d/A.
opt ? 1 and 9 = 0), and in this case
opt '' 2ctopt? (1 -I- 0) a opt (0 dp/rd)1/2.
In the general case one should take an "average" angle gopt:
aopt +0/2d/ (-1(2. rd)
Popt? a opt? 0/2
1+(2-0.dp/rd)1/2 + 1+ CV-5 dp/r01/2 1-1 / cipird ?
(8)
(9)
(10)
(12)
The difference between gopt and 2aopt amounts to 10%. Experiments have shown that such a deviation from
optimality is accompanied by a drop in efficiency of 4-5% on the average.
The proposed method of calculating gopt was checked experimentally in an STD with regeneration of the
electron beam (Fig. 3). A beam of electrons from a Pierce gun (d/rde = 0.05, W = 5 keV, and 9 = 2.5?) was
289
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I. A
5 11 14 11 13, deg
Fig. 3. Layout of the experimental setup:
1, 2) cathode and anode of the beam, 3) col-
limation diaphragm, 4) collector of sec-
ondary electrons, and 5) system of tapered
diaphragms.
Fig. 4. Dependence of: a) the current of secondary particles and b) the regener-
ation efficiency on the section angle of the collecting diaphragms [0) experiment].
decelerated in a system of 10 diaphragms of overall length 10 cm. The optimum parameters of the system
calculated from the relations in [1] are as follows: a opt = 8.6?, ltopt = 8 cm, and %/lax =95%.
A secondary-electron collector (SEC) mounted immediately beyond the collimating diaphragm (CD) was
used to measure the current of the particles flying out of the system. The diameter of the central aperture of
the SEC is somewhat larger than the diameter of the central aperture of the CD in order to exclude the incidence
on it of electrons from the direction of the beam anode. This method permits tracing qualitatively the course
of the dependence of the secondary electron current on the different parameters of the system. In this ex-
periment the energy of the electrons incident on the surface of the diaphragms is ?0.5 keV, i.e., a = 1.5.
The dependence of the current at the SEC on the section angle g , with the other parameters being op-
timum, is shown in Fig. 4. It is evident that gopt = 14? and 2a opt = 17.2?. When 13 < gopt, the current at the
SEC increases strongly due to secondary emission. 1113 > f3ot,.the current at the SEC increases insignificant-
ly by virtue of the returning electrons which have not hit the diaphragms. A significant increase in the current
from the intermediate diaphragms occurs simultaneously. The dependence of the conversion efficiency n on
g is presented in Fig. 4b. The maximum efficiency is %max = 92% at gopt = 14?. Calculations according to
Eq. (3) for a > 1 also give gopt = 14?. In a control experiment nmax = 88% at 13opt = 16? when a = 10?, which
is in agreement with the calculated value.
Thus the proposed method of calculating the optimum angle of the diaphragm section with account taken of
losses due to secondary emission is well confirmed by the experimental data. A maximum efficiency of direct
conversion is achieved in the optimum case (92 ? 3%) with a calculated value of 95% for a beam with d/rde =
0.05.
LITERATURE CITED
1. 0. A. Vinogradova et at., At. Energ., 33, No. 1, 586 (1972).
2. 0. A. Vinogradova et al., ibid., 42, No. 5, 411 (1977).
290
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DEGREE OF PERFECTION OF GRAPHITE AND CHANGES
IN ITS PROPERTIES UNDER IRRADIATION
P. A. Platonov, I. F. Novobratskaya, UDC 621.039.532.21
Yu. P. Tumanov, and V. I. Karpukhin
The development of nuclear power reactors has been responsible for an increase in the production of
graphite and the use of different starting materials; this explains the interest in the technology of the produc-
tion of structural reactor graphite.
An important stage in the technological cycle for obtaining graphite is that of high-temperature treat-
ment. The transformation of carbonaceous material into crystalline graphite proceeds gradually with a rise in
the graphitization temperature. For a material with a different processing temperature in the range 1300-
2800?C there exist structures characteristic of both the turbostriated and graphite states, as well as mixtures.
The perfection of the structure of the carbon?graphite material is usually characterized by the degree of
graphitization y [1]. For turbostriated structures, we have y = 0, whereas for ideal single crystals y = 1. It is
well known that the degree of perfection of graphite has a substantial effect on a change in its linear dimen-
sions under irradiation [2, 3] and on the working capacity of graphite, especially at an elevated temperature.
Characterizing the behavior of graphite under irradiation, we can arbitrarily isolate several temper-
ature and fluence ranges within which the variations in the linear dimensions are of a common nature for vari-
ous grades of graphite [4-6].
1. In the temperature range up to 300?C swelling is observed to occur at a rate which falls with a rise
in temperature.
2. Over a narrow temperature range (300-400?C) changes in the dimensions take place at a slow rate up
to a fluence of more than 1022 neutrons/cm2. In this case the character of the deformation (shrinkage or swell-
ing) depends on the type and anisotropy of the graphite.
3. At a temperature of 500-800?C shrinkage occurs at a rate which depends on the temperature; in the
fluence range ?1022neutrons/cm2 shrinkage gives way to swelling. The fluence at which this process takes
place decreases with a rise in temperature.
4. At a temperature above 850-900?C the behavior of graphite does not differ qualitatively from that at
500-800?C, but the transition from shrinkage to swelling shifts sharply to low fluence values (4-6)? 1021 neu-
trons/cm2 and the shrinkage rate rises substantially.
The character of the change in the linear dimensions of GMZ graphite is shown in Fig. 1. Although the
fluence corresponding to the transition to the region of 'secondary swelling" has not yet been attained here, it
is seen clearly that the shrinkage rate diminishes at an irradiation temperature of 500-600?C and approaches
an extremum (Fig. la). It is precisely for this temperature range, which is of greatest interest in respect of
the use of graphite as a moderator in channel-type reactors, that we studied the effect of the degree of per-
fection on some properties of GMZ graphite.
Specimens with a diameter of 30 mm and a height of 40 mm, cut from an annealed block parallel to the
axis of extrusion, were heat-treated for 2 h at 1300-3000?C in a nitrogen atmosphere and at 2300?C and higher,
in an argon atmosphere.
Table 1 gives the structural parameters characterizing the specimens studied. It should be noted that
from a heat-treatment temperature of 2300?C, when the interplanar distance practically does not change, the
crystallite size increases considerably. Since the temperature in the graphitizing furnace may differ at dif-
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 248-254, April, 1979. Original article submitted
December 14, 1977; revision submitted April 17, 1978.
0038-531X/79/4604- 0291$07.50 ?1979 Plenum Publishing Corporation 291
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Declassified and Approved For Release 2013/02/12 : CIA-RDP10-02196R000800010004-2
TABLE 1. Structural Characteristics of
Graphite of Different Degrees of Perfection
Temp. of
heat treat-
ment, ?(
Lattice con-
stant, A
Degree of Crystallite
graphitiz., ji
rel. units
1300
6,96
60
1500
6,89
75
1800
6,88
,
120
2000
6,87
0,06
150
2300
6,76
0,7
200
2800
6,74
0,82
1000
3000
6,74
0,82
*Found from formula of Selyakov [1].
2 4 6 8 10
F, 104 neutrons/cm2
14
2 4 6 8 10 12
F. 1021 neutrons/cm2
14
Fig. 1. Change in linear dimensions of GMZ graphite specimens, cut a) perpen-
dicular and b) parallel to the extrusion axis at different irradiation temperatures:
? , 0) experiment.
ferent points of the specimens by 300-400?C [3], even in one batch of graphite with practically the same lattice
constant the crystallite sizes of the various specimens may differ.
Variations in the electrical resistivity during the heat treatment are correlated with the structural trans-
formations of the carbon?graphite material (Fig. 2). It has been proposed [3] to use the value of the electrical
resistance as a parameter for checking ready graphite blocks. As the heat-treatment temperature is raised
there is also a decrease in the modulus of elasticity (Fig. 2). The linear relation between the strength and the
modulus of elasticity allows the change in the strength after irradiation to be assessed from the change in the
modulus of elasticity.
Specimens with varying degrees of graphitization were irradiated in the hot channels of the MR reactor
at 500?C. The maximum neutron fluence was 6.8 ? 1021 neutrons/cm2 (E> 0.18 MeV). The temperature was
monitored with thermocouples and diamond indicators [7]. The neutron fluence in the hot channels was cal-
culated from the energy production of the fuel in which the irradiation was performed and of the three chan-
nels nearest to it and was also found with the aid of threshold indicators. The graphite specimens were ir-
radiated in hermetic ampuls (in which the medium was nitrogen or helium). The linear dimensions, the modulus
of elasticity, the electrical resistivity, and the structural characteristics of the material before and after ir-
radiation were measured in accordance with techniques described earlier [8].
It follows from Fig. 3 that the shrinkage rate increases substantially as the degree of perfection of the
material diminishes. For carbon?graphite material heat-treated at 1300?C, a transition from shrinkage to
secondary swelling is observed at a fluence of 3 ? 1021 neutrons/cm2.
The change in the modulus of elasticity of the specimens at various heat-treatment temperatures shows
that the higher the degree of structural perfection (Fig. 4), the greater the difference between the moduli of
elasticity before and after irradiation. The dependence of the modulus of elasticity on the fluence has a maxi-
mum at a fluence of 2 ? 1021 neutrons/cm2, after which for specimens heat-treated at a temperature above 2000?C
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6,9
6,8
0,4
6
1000
1500 2000 2500
Fig. 2
C.
- 600
-6400 ,z)
- zoo
T,oc
4 6
F, 1021 neutrons/ cm2
Fig. 3
Fig. 2. Effect of heat-treatment temperature on changes in the properties of carbon?graphite ma-
terial.
Fig. 3. Dimensional changes in graphite with different degrees of perfection as a function of the
neutron fluence at an irradiation temperature of 500?C (here, as in Figs. 4 and 5, the specimens were
cut parallel to the axis of extrusion; the numbers next to the curves are the heat-treatment temper-
atures).
(E/E01-1
A
?
?
?
1500
01800
3000?C
.2800
? 0 2300
2000
4 5
F, 1921 neutrons/cm2
Fig. 4. Modulus of elasticity of graphite with different degrees of
perfection as a function of the neutron fluence .at an irradiation
temperature of 500?C.
the curve of this dependence gradually becomes flat and for specimens heat-treated at 1800?C or lower the
modulus diminishes steadily, even going below the initial value for the specimen treated at 1300?C.
The maximum on the plot of the modulus of elasticity against the fluence for specimens with a parallel
cut [5] is attributed to the overlapping of stress fields caused by complexes of radiation-induced defects. This
effect can, however, be given another explanation.
It is characteristic of most materials that the contribution of radiation-induced defects to the change in
properties under irradiation diminishes with a rise in the concentration of structural imperfections in the ini-
tial state. Most frequently, this is due to the fact that the initial Structural imperfections, being sinks for ra-
diation-induced defects, intensify the annihilation of the latter. In the process, part of the initial imperfec-
tions should vanish as the result of absorption of radiation-induced defects. Such an effect is probably ob-
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(P/P0)-1
2
1
4 5 6
F, 1021 neutrons/ cm2
Fig. 5. Change in resistivity of graphite with different degiees of
perfection as a function of the neutron fluence at an irradiation tem-
perature of 500?C.
,
_Fig. 6 ___ ,
_ _ . Fig. 7, r
Fig. 6. Overgrowth of oriented xnicroporosity and formation of a network of cracks in imperfect
graphite under irradiation: a) original si)ecimen; b) after irradiation (Tirr = 500?C, fluence 5 ?
1021 neutrons/cm2). . 4
Fig. 7. Cracking inside coke particles in iniperfect graphite (Tin; = 500?C, flitence 5 ? 1021 neu-
trons/cm2).
served during'irradiation of iraphite heat-treated at 1300?C, ag is 'expressed by a drop in resistivity at the on-
set of irradiation-(Fig. 5). The most chai?acteristic aspect of the change in resistiviti is its 'sliarp gi?owth after
a fluence of 3 ? 1021 neutrons/cm2,rfor_less perfect graphite, which correlates well with the change in the mod-
ulus
of elasticity.. The growth of the resistivity begins,at the same fluence as the transitiondrom shrinkage
to swelling for the material treated at 1300?C.
The latter unambiguously demonstrates that the "secondary swelling," growth of resistivity, and decrease
in the modulus of elasticity of the graphite below the initial value are all caused by the same process, i.e.,
the intensive formation of porosity. The character and nature of the porosity formation are evident upon exam-
ination of the Change's in the structure of specimens in the secondary swelling stage.
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Fig. 8. Cracking (typical cracks are indicated by arrows) at filter?binder interface in imperfect
graphite as a result of irradiation: a) original specimen; b) after irradiation (Tirr = 500?C, flu-
ence 5 ? 1021 neutrons/cm2).
The structure was studied with electron and optical microscopes. To avoid structural imperfections
during the preparation of thin sections, the specimens were impregnated with epoxy resin, then ground, polished
on paper with diamond paste, and subjected to cathodic-vacuum etching (Figs. 6-8). It is seen from Fig. 6 that
the oriented pores (Mrozowski cracks [9]), which are characteristic of unirradiated graphite, are practically
closed in the irradiated specimen while at the same time a large number of microcracks are oriented across the
basal plane. It is likely that precisely the formation of such cracks, which do not lead to any .significant swell-
ing, is the reason why the modulus of elasticity decreases after reaching a maximum value. Verification of
the assumption requires more detailed electron-microscopical studies of graphite in the range of fluences up
to 5 1021 neutrons/cm2.
In addition to the microcracks detected during electron-microscopical investigations, the structure of
graphite in the secondary swelling stage is characterized by many larger cracks (which, for convenience, can
henceforth be called macrocracks),which are visible at lower magnifications.
The crack shown in a coke particle in Fig. 7 extends across the basal plane. The region shown is highly
characteristic: in coke a striated structure envelops, as it were, a long segment in Which the orientation of the
crystallites differs from the external layer. In the course :of shrinkage tensile stresses should develop in the
outer striated layer, and the maximum stress should be in the region of maximum curvature, in which place
cracking occurred. Figure 8 shows cracks at the filler?binder interface in a direction perpendicular to the
largest axis of each coke particle. Among the cracks we can see wedge-shaped cracks which are the result of
grain glide over their boundaries. Thus, the pores formed constitute cracks with a wide range of sizes.
The experimental results allow a qualitative picture to be given of radiation-induced damage in graphite
in the range of elevated temperatures. As is known, graphite single crystals experience growth along the c
axis and compression along the a axis. In the polycrystalline material, which synthetic graphite is, the crys-
tallites interact with each other during irradiation, causing deformation which leads to a gradual, closed Mro-
zowski crack and other pores in the region of compression. In this case the crystallites prove to be compressed
along the c axis and elongated along the a axis. When the stress reaches a critical value, depending on many
factors (the modulus of elasticity, the size distribution of pores, the surface energy, the coefficient of creep,
the size of the crystallites and coke particles, the anisotropy coefficient, etc.), micro- and macrocracks begin
to form. The formation of cracks (especially microc racks) probably begins somewhat earlier than when complete
covering of the oriented porosity occurs, but a pronounced growth of stress and intensive cracking begin after
the maximum possible compression. In accordance with this hypothesis, a qualitative analysis can be made of
the relation between the individual factors and the fluence at which maximum compression is attained.
if c denotes the relative deformation of the crystallites along the c axis until the pores closed, (d/dF) ?
(LOCc/Xe) and (d/dF)(AXa/Xa) are the rates of change of dimensions along the c and a axes, respectively,
a c and Ea are the mean coefficients of thermal expansion of the graphite single crystal along the c and a axes,
respectively, and T is the temperature, then the fluence up to the moment that maximum compression is reached
can be written in simplified manner as
r d I AXc d AX?
I 1 ?
Pmax= 8 ? (ac aa) L dF 1 xe dF xa /J
The numerator of this relation is the relative total "width" of the pores in the specimen heated to a tem-
perature T (the pores close in part because of thermal expansion), and the denominator is the radiation-induced
deformation of crystallite.
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Thus, elevation of the temperature on the one hand reduces the total deformation until maximum com-
pression is attained because of the partial closing owing to the thermal expansion of the crystallites. On the
other hand, as follows from experimental data [7], after reaching a minimum at a temperature ?500?C the
rate of change of crystallite size again grows with a further rise in temperature, i.e., raising the temperature
above 500?C simultaneously causes the numerator in the relation to diminish and the denominator to increase
and results in a decrease in the fluence corresponding to the maximum compression. Moreover, with a rise
in irradiation temperature the radiation hardening decreases and, consequently, cracking is facilitated. There-
fore, the higher the irradiation temperature, the greater the probability of cracks forming before the maxi-
mum compression is reached. In other words, the maximum shrinkage during transition to secondary swelling
should decrease with a rise in the irradiation temperature, as is confirmed by many experimental data [5].
If it is assumed that the transition to secondary swelling for most grades of graphite at 500-600?C is
observed at a fluence (1-1.5) ? 1022 neutrons/cm2, then upon comparing these data with the results obtained
for a specimen heat-treated at 1300?C, we can conclude on the basis of the formula given above that the rate of
change of crystallite size in this specimen should be three to five times that in well-graphitized material. In
actual fact, this rate may be somewhat lower if it is borne in mind that in the specimen heat-treated at 1300?C
the oriented porosity is less pronounced than in the well-graphitized material. The estimate made here is in
agreement with the data on the rate of change of crystallite size of pyrocarbon [10] with crystallite sizes com-
parable with those in Table 1. The ideas considered here correlate with the results and data of other research-
ers. A more detailed consideration of the mechanism of the transition from shrinkage to swelling requires ad-
ditional experimental data.
Thus, our investigations of carbon?graphite material with various degrees of perfection permitted the
following conclusions to be drawn.
1. If the degree of perfection of graphite decreases, the shrinkage rate of the graphite rises and the tran-
sition from shrinkage to secondary swelling is shifted to the region of lower fluence. A qualitative correlation
is observed between the shrinkage rate and the crystallite size.
2. The transition from shrinkage to swelling of the graphite at an elevated temperature is due to the ap-
pearance of micro- and macrocracks caused by stresses generated by radiation-induced deformation of crys-
tallites. The stress apparently reaches a critical value when the oriented porosity is closed. The cracks are
oriented primarily in a direction perpendicular to the basal planes.
3. The transition from shrinkage to swelling is accompanied by a sharp rise in resistivity and a decrease
in the modulus of elasticity below the initial value. Since the resistivity correlates with the thermal conduc-
tivity and the modulus of elasticity correlates with the strength, the character of their changes at the same
time denotes a drop in the thermal conductivity and strength. The latter indicates that additional factors limit-
ing the lifetime of graphite products, along with the intensity of swelling after maximum shrinkage has been at-
tained, are the drop in strength and thermal conductivity.
In view of these limitations, it must be admitted that, apparently, the lifetime of graphite only slightly
exceeds the fluence at which the graphite goes from shrinkage to swelling since in the region of secondary
swelling the graphite structure suffers quite rapid degradation; under actual conditions, this degradation may
be accelerated by the existence of cyclic thermal stresses, an increase in the temperature gradients, and in-
teraction with other elements of the reactor structure.
Consideration of the results obtained leads to the indirect conclusion that, other conditions being equal,
grades of graphite with a higher strength prove to be radiation-resistant with respect to secondary swelling.
LITERATURE CITED
1. S. E. Vyatkin et al., Nuclear Graphite [in Russian], Atomizdat, Moscow (1967), pp. 41, 48.
2. H. Yoshikawa et al., in: Proc. IAEA Symp. "Radiation Damage in Reactor Materials," Vienna (1969), p.581.
3. P. A. Platonov et al., in: Graphite-Based Structural Materials [in Russian], No. 8, Metallurgiya, Moscow
(1974), p. 105.
4. R. Henson, A. Perks, and J. Simmons, Carbon, 6, 789 (1968).
5. J. Cox and J. Helm, Carbon, 7, 319 (1969).
6. G. Engle, Carbon, 9, 539 (1971).
7. V. I. Karpukhin and V. A. Nikolaenko, Temperature Measurements with Irradiated Diamond [in Russian],
Atomizdat, Moscow (1971).
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8. P. A. Platonov et al., At. Energ., 35, No. 3, 169 (1973).
9. S. Mrozowski, in: Proc. Conf. Carbon, Baltimore (1956), p. 33.
10. J. Bokros and R. Price, Carbon, 5, 301 (1967).
OXIDATION OF (U, Pu)02 AND UO2 PELLETS
G. P. Novoselov, V. V. Kushnikov, UDC 621.039.542.342:66,094.3
Yu. Ya. Burtsev, and M. A. Andrianov
Gaseous discharges during regeneration of spent nuclear fuel must be decontaminated in order to protect
the environment [1, 2]. It is expected that oxidation of the fuel may resolve this problem quite effectively since
this will make it possible to isolate Kr, Xe, 3H, 14C, I, and other highly volatile fission products (FP) during
preparation of the fuel for reprocessing. However, the conditions have not yet been found for a sufficiently
complete isolation of the radioactive noble gases and iodine from the fuel during its oxidation. The published
data on the behavior of these FP are contradictory [3-12].
The objectives of the present paper are, first, to ascertain the rate of oxidation of unirradiated briquettes
of a solid solution of uranium dioxide and plutonium (U, Pu)02, briquettes of UO2, and the same briquettes after
thermal stripping of the fuel elements (melting off the cans) [13-15] and, second, to study the conditions for
obtaining powdered U308 with particles of a certain size.
Results and Discussion. In our investigations we used unirradiated pellets of a solid solution of (U, Pu)02
and UO2 which are used in fuel elements for thermal and fast reactors [16]. The phase composition of the
powders obtained at different stages of oxidation of the pelletized fuel and the reduction of the oxidation prod-
ucts were monitored by the x-ray method (RKU-86 camera for Co radiation). The granulometric composition
of the oxidation products was determined by sieve analysis and microscopic examination under an MBI-11 mi-
croscope (x1000).
The briquettes were oxidized at a temperature ranging from 350 to 550?C and a continuous flow of air
(or commercial oxygen) at a linear velocity of 0.2-0.3 cm/sec or under static conditions in air. The powdered
U308 was reduced with dried and purified hydrogen at 600?C for 7 h.
The rate of the process of oxidation of the ceramic fuel and reduction of the powdered U308 was studied
on continuously weighing scales with a coil wire of OVS alloy [17, 18], the change in the mass of the specimens
was found with a KM-6 cathetometer, and the temperature was measured with an accuracy of ? 10?C.
Uranium Dioxide. Oxidation of UO2 briquettes proceeds according to the reaction
3UO2 ? 02 U308 + 25 kcal/ mole
(I)
through stages of formation of intermediate oxides and at a temperature above 300?C ends with the formation
of U308 with a rhombic structure [19]. An attempt has been made to describe this process with a system of
differential equations and to provide a theoretical explanation for it [20].
The efficiency of the oxidation process is affected by a number of factors. Thus, high linear velocities
of the oxidant (>25 cm/sec) are employed with "fluidized-bed" apparatus. We proposed oxidation in a "vibro-
fluidized" bed which permits operation with an air supply at a lower linear velocity [21] and considerably re-
duces the demands on dust-collecting and gas-purification systems. It is well known that the rate of oxidation
of pelletized fuel is affected considerably by the temperature, fabrication technique, quality of the sintering, the
specific surface of the initial powder used to make briquettes, the presence of fission products, and axial melt-
ing of the core of the fuel elements [22].
Studies on the oxidation of UO2 briquettes showed that for some time they remain "inactive." The length
of this period depends on the temperature and other factors. Figure 1 shows the plots of the completeness (a)
of the reaction of oxidation of UO2 briquettes. (The term "completeness of oxidation," which has been borrowed
from [22], denotes that fraction of the substance which has reacted in wt.% of the initial quantity.) It follows
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 254-258, April, 1979. Original article submitted
January 30, 1978.
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ct.wt?To
100
90
80
70
60
50
40
30
20
10
10 20 30 40 50 60 70 80 90 100 t, min
Fig. 1
log v
-1,2
-1,3
-14
-1,5
-1,7
-1,8
1,9
?
?
?
1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 (1/7)103
Fig. 2
Fig. 1. Completeness of reaction of oxidation of UO2 pellets as function of time at various tem-
peratures under static (- - -) and dynamic (--) conditions: 0) initial UO2; ?) UO2 after thermal
opening of fuel elements; 1-5) 500?C; 2, 4, 6, 8) 450?C; 3 and 7) 400?C.
Fig. 2. Temperature dependence of mean rate v of oxidation of UO2 and (U, Pu)02 pellets under
static (- - -) and dynamic (?) conditions: 0) initial UO2; ?) UO2 after thermal stripping of
fuel elements; 0) (U? Pu)02.
from Fig. 1 that as the temperature rises, the process of UO2 oxidation becomes shorter (curves 1-3 and 5-7),
with the oxidation ending more quickly under dynamic conditions than under static conditions (curves 2, 4 and
6, 8). The curves have three segments characterizing different stages of oxidation. In the initial stage after
the induction period the rate of oxidation increases insignificantly. A further change in the completeness of
the oxidation reaction is characterized by a rectilinear segment; then the oxidation products form a protective
layer and the reaction rate falls off. Oxidation of UO2 briquettes after thermal stripping of the fuel elements
(curves 1-3) ends more quickly than does oxidation of the initial briquettes (curves 5-7) at the same temper-
ature: after thermal stripping the briquettes have a large specific surface because of micro- and macrocracks.
From the curves given in Fig. 1 we calculated the mean rate of uranium oxidation in UO2 briquettes at
various temperatures (Fig. 2). The value of the apparent energy of activation of the process for UO2 briquettes
under static conditions was 5.7 kcal/mole, with the oxidant moving with a linear velocity of 0.2-0.3 cm/sec the
value was 5.3 kcal/mole, i.e., even a slight increase in the velocity of oxidant flow in the reaction zone in-
creases the oxidation rate.
It is known that the particle size and the stability of the granulometric composition of U308 or (U, Pu)30'8
solid solutions are the principal factors determining the rate and completeness of fluoridation of U308, e.g., in
apparatuses of the flame type. Moreover, the size of U308 particles determines the degree to which the FP
and their chemical compounds are stripped as well as how completely the gaseous and volatile FP are re-
moved from the fuel [23]. The particle size is controlled by selecting the optimal oxidation temperature, the
gaseous medium, the rate of oxidant flow, and the execution of cyclic operations of oxidation and reduction.
The optimal U308 particle size was not established. In view of this, we studied the conditions for obtaining
powdered U308 with a particular granulometric composition (Table 1). Analysis of the data of Table 1 shows
that with a lowering of the oxidation temperature, the proportion of fine fractions in the powder increases. At
350?C in an atmosphere of air all of the powdered U308 consisted of particles under 50 pm in size. The explana-
tion usually given for this is that, along with the formation of finely dispersed powder, there is sintering of
this powder at a rate which is inversely proportional to the particle size and directly proportional to the tem-
perature [24]. Replacement of air by oxygen increases the oxidation reaction rate and the quantity of heat re-
leased and this also results in the growth of the particle size. With the oxidation conditions indicated above,
U308 is the principal phase in the oxidation products, regardless of the size of the powder particles.
Microscopic examination of fractions with a size :5100 pm, obtained by oxidizing UO2 briquettes, made
it possible to find the distribution of particles ranging from 5 to 100 pm in size inthese fractions andto deter-
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Fraction, wt.5
TABLE 1. Granulometric Composition of U308 Powder after Oxidation of UO2
Briquettes with Air and Oxygen, wt.%
Temp., ?C
Fraction, p
+200
- 200+ /00
-100 +63
-63+ 50
-50
oxygen
air
oxygen
air
oxygen I air
oxygen air
oxygen
air
500
49,42
17,82
11,82
4,25
18,70
35,15
2,24
60,6
450
46,73
18,42
6,95
2,16
11,63
19,14
16,27
78,7
400
36,43
22,59
14,58
1,80
15,86
18,20
10,54
80,0
350
100,0
70 20 30 40 50 60 70 80 90 100
Particle size, ?
Fig. 3
cx,Ift.ob
80
80
70
60
50
40
JO
20
10
0 10 20 JO 40 50 60 t, nain
Fig. 4
Fig. 3. Effect of temperature of oxidation process on granulometric composition of U308 at
0) 350?C and .)450?C.
Fig. 4. Time-dependence of completeness of oxidation rate of pellets of (U, Pu)02 solid so-
lution at temperature of: 1) 550; 2) 500; and 3) 750?C under dynamic conditions.
mine the mean size of U308 particles (Fig. 3): 18 pm (rmia=5 gm, rmax =42 pm) at 350?C and 53 pm (rmin =
6.6 um, rmax = 98 pm) at 450?C. Moreover, it was found that the particle distribution over the fractions
depends on the temperature in different ways.
(U, Pu)02 Solid Solutions. The rate of oxidation of the solid solution affects the Pu02 content in it [5, 22].
The investigations were carried out in a solid solution containing 15 wt.% PuO2 (Fig. 4). The oxidation rate in-
creases with the temperature. The relation shows that the briquettes are inactive at first and the oxidation
rate begins to grow after some time. The curves have three segments characterizing the different stages in
the oxidation process. They are less steep for the solid solution than are the analogous curves for UO2, in-
dicating a longer process of transformation of UO2 to U308 in the solid solution. The data of Fig. 4 were used
to calculate the mean rate of oxidation of 1302 in briquettes for (U, Pu)02 solid solution at various temperatures.
The apparent activation energy of the process (see Fig. 2) for the given conditions (linear velocity of
oxidant 0.2-0.3 cm/sec) is 5.8 kcal/mole, i.e., the apparent activation energy of the oxidation process for
briquettes of (U, Pu)02 solid solution is somewhat higher than for UO2 briquettes. Data on the granulometric
composition of the oxidation products of the solid solution are given in Table 2. Just as for UO2 briquettes,
the granulometric composition of the oxidation products of the solid solution depends on the temperature of
the process. The appearance of particles with a size exceeding 200 pm at 450?C maybe the result of the in-
completeness of the oxidation of briquettes of the solid solution. Microscopic examination of the powder frac-
tion smaller than 50 pm in size revealed the distribution of particles with a size ranging from 6.4 to 48 pm (Fig. 5),
and made it possible to establish that the mean particle size was 29.2 pm.
The oxidation products of the solid solution consist mainly of 13308 with plutonium dissolved in its rhombic
lattice. Comparison of the x-ray photographs of U308 and the (U, Pu)308 solid solution revealed that, in the x-ray
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TABLE 2. Granulometric Composition of
Oxidation Products of (U, Pu)02 Solid Solu-
tion at Various Temperatures, wt.%
:Temp. of
process. *C.
Fraction, ?
+200
-200+100
-100+50
-50
450
3,68
0,27
96,05
500
100,0
550
0,16 ?
12,84
87,00
110 20 JO 40 50 60, 70 80 50 100
Particle size,.?
Fig. 5. Variation of granulometric composition of
oxidation products of (U, Pu)02 solid solution in
course of: 0) first and ?) second cyclic oxidation?
reduction operation.
photograph of the latter, lines corresponding to large reflection angles 0 are displaced noticeably towards
smaller angles, which is indicative of an increase in the dimensions of the crystal lattice of the (U, Pu)308
solid solution as the result of part of the uranium atoms in the U308 lattice being replaced by plutonium atoms.
Analysis of the x-ray photographs, however, did not show the oxidation products to contain the Pu02 phase
whose presence in similar products was noted in [23]. It is possible that in the oxidation products of the studied
solid solution containing 15% Pu02, the amount of the Pu02 phase was small ( 1 MeV), an empirical relation is proposed, de-
fining the change of the yield point o- = a() + A(4304/11. The irradiated zircalloy was found to be sensitive to
surface defects, and failure occurred even after the smallest plastic deformation. As a result, maximum per-
missible dimensions of surface defects were established, for which the reliable operation of the zircalloy
cladding is still guaranteed.
Corrosion tests of shortened fuel element claddings of alloys of zircalloy-2, zirconium-1% Nb, and Zr-
1% Cr-0.08% Fe were conducted in the R2 reactor in boiling water at 286?C and with a neutron flux intensity of
(4-9) ? 1043-neutrons/cm/. sec (E > 1 MeV). We studied the effect of surface workings, thermal stresses,
and time lag on the corrosion resistance of this alloy. The values for the oxidation rates of these alloys is
as follows: Zr- 1% Nb, and Zr- 1% Cr- 0.08% Fe are respectively 0.2-0.7, 1.8-2.5, and
6-8.7 mg/dm2. day. However, traces of nonuniform oxidation were found only in zircalloy-2 claddings
(maximum thickness of oxide was 24 12).
When calculating the yield curves for recrystallized tubes of zircalloy with two different textures, it is
necessary to take account of triaxial deformation, which occurs by means of prismatic slip and twinning, in
view of which a set of values of the critical reduced shear stresses for different crystallographic slip systems
were used. Consideration of the deformation of zircalloy tubes, taking account of the anisotropy of the me-
chanical properties of the material, has permitted different types of tests used for determining the plasticity
of the claddings to be assessed. Low-cyclic fatigue of recrystallized tubes of zircalloy-2 under conditions of
flexure at a temperatures of 20, 250, 300, 350, and 400?C follows the Coffin-Manson law. Irradiated samples
were tested at 20 and 300?C. The lifetime of the irradiated samples at 20?C was less than, and at 300?C was
equal to that found by the Coffin-Manson curve for unirradiated samples. Experiments on the deformation
at a temperature of -300?C of flat polycrystalline samples of zircalloy-2, for which the axis c of the majority
of grains is oriented approximately parallel normal to the surface, showed the absence of twinning and permitted
the assumption that slip along the {101-1} planes is the cause of breakdown of the oxide film, responsible for
the initial stage of corrosion cracking in the iodine atmosphere. In flat samples of zircalloy-2, the effect was
also studied of the texture and thermal processing on the plasticity and sensitivity to corrosion cracking under
stress, in the case of tests at 300?C in air and in an argon medium with iodine as impurity. By comparing the
set of prereactor properties of 15% Cr-25% Ni and 19% Ni and 19% Cr-25% Ni steels, the advantage of steel
containing 15% chromium, as applicable to the operating conditions of the fuel element claddings of fast reactors,
was shown, in relation to both stability of the microstructure and phase state, and also to creep resistance.
An automatic system has been developed for the multiparametric analysis of nonmetallic inclusions in
metals which permits about 500 inclusions with respect to area, perimeter, diameter, coordinates, and chemi-
cal composition for 5-15 elements) to be analyzed in 1 h.
The firm ASEA-ATOM has developed a set of programs for calculating the fuel cycle and designing
light-water reactors. The set includes the following problems: neutron physics of fuel element assemblies
and lattice, microscopic neutron physics, hydraulic and heat transfer, calculation of the fuel cycle, dynamics
and 'reactor control, emergency cooling system of the core, shielding from neutron and y radiation, design
of fuel elements, and analysis of structures.
Translated from Atomnaya Energiya, Vol. 46, No. 4, p. 284, April, 1979.
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In conclusion, the specialists of both countries stressed the advisability of closer collaboration in the
field of development of reactor materials, especially zirconium alloys.
IAEA SYMPOSIUM ON FUEL-PIN PRODUCTION
FOR PRESSURIZED-WATER REACTORS
V. S. Belevantsev, N. G. Reshetnikov,
and V. I. Solyanyi
This symposium was held in Nov. 1978 in Prague (Czechoslovakia) and was attended by about 250 par-
ticipants from 30 countries and three international organizations; papers were presented on the national pro-
grams on fuel-pin manufacture for pressurized-water reactors by representatives of Belgium, the United King-
dom, India, Italy, Canada, the USSR, the USA, France, the Federal German Republic, Czechoslovakia, and Japan.
In all there were 41 papers, which were concerned with four major topics.
Effects of Production Processes on Working Characteristics. Papers from producer organizations stated
that fuel reliability is ensured in part by all-round quality control for the fuel in particular and the process as
a whole at all stages, along with on-going analysis of working results.
Belgian workers reported interesting results on the production of mixed uranium-plutonium oxide fuel
for light-water reactors at the Belgonucleaire plant. This produces 18 tons of fuel per year as tablets having
92-95% of the theoretical density and an 0/M ratio of 1.998 ? 0.001. It was observed during the discussion
that the sizes of the Pu02 inclusions in the finished tablets were less than 30 /A. Some of the papers on oxide
fuel emphasized the need for strict monitoring of the density, grain size, and porosity distribution. A state-
ment from the Federal German Republic indicated that the addition of U308 can provide control of these charac-
teristics. The materials produced atKraftwerkunion(KWU) plants contain less than 0.2 mass % of impurities.
The fluorine content is less than 0.0005 mass %, while the water content is below 0.0005 mass %.
Interesting information was presented on heat-resistant UO2 tablets in one of the French papers. The
method of production was outlined as follows: pressing the initial powder at high pressures, production of
granules from the pressed powder, tablet pressing from the granules, and sintering. Reactor tests have been
performed at a linear power output of 465 W/cm up to a burnup of 4000 MW ? day/ton U with 43 thermal cycles;
tablets made in this way are readily moved undamaged from the fuel rods, whereas ordinary ones break up.
Two papers from Denmark and the United Kingdom dealt with improved fuel-rod reliability arising from
Improved working characteristics in the fuel; data were presented on a modified design of fuel core, which re-
places the form commonly employed at the present time. A two-layer (duplex) tablet was suggested, in which
the outer layer consists of UO2 and the inner layer of depleted material. The two ways of producing these
tablets were discussed: separate production of the outer and inner layers, with combination directly before
loading into the sheath, and pressing blanks for the outer and inner parts, which are combined by sintering.
British workers consider that these duplex tablets can be used in conjunction with control of gas release from
the fuel, with the latter provided by the addition of oxides of titanium, magnesium, niobium, and chromium,
along with grain-size monitoring.
Research and development in the area of granulated fuel was also reported for the production of vibra-
tionally loaded fuel rods not only for high-temperature reactors, but also for light-water ones, as well as for
fast reactors; these aspects were discussed in a paper from Western Germany.
Working Characteristics of Zirconium Alloys. Some of the papers dealt with the characteristics of zir-
conium sheaths and welded joints; it was stated that careful all-round quality control of sheaths at all stages of
manufacture is essential. A British paper dealt with the causes of various flaws in fuel-rod sheaths and the
behavior of these in a pressurized-water reactor. Criteria were presented for extracting fuel-rod assemblies
containing faulty rods, and it was suggested that one should neglect the activity excursions arising from shut-
down, startup, and power cycling.
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A Canadian paper dealt with researches on zirconium?niobium alloy sheaths, including welded joints;
Zr?Nb alloys have been compared with alloys of zircalloy type in iodine vapor at 300?C. The resistance to
iodine corrosion under stress of the zircalloys is somewhat better than that of zirconium?niobium ones.
Aspects of Reactor Operation Relevant to Fuel-Rod Production Specifications. It is generally considered
that the working reliability of the rods in a pressurized-water reactor is now reasonably high and that the
probability of failure is in the range 0.01-0.05% of the total number of fuel rods per reactor-year. This level
of reliability has been attained by attention to the following features: design, technological improvement (par-
ticularly the elimination of failure due to deposition, hydrogenation, and sheath buckling), reduction of the
maximum thermal loading at the fuel rods while retaining the mean thermal output from an assembly unchanged
(this has been attained by changing the dimensions of the fuel rods, increasing the number of rods, and suitable
distribution of the fuel enrichment over the height and radius of an assembly), and improvements designed to
ensure stability and to meet all the technical specifications for fuel-rod manufacture.
The papers show that fuel-rod reliability in pressurized-water reactors may be improved further by
means of various improvements in the design of the fuel and sheath, as well as in the manufacturing technology.
For the near future, nuclear power stations must work with peak loading, and it is generally considered
that this can increase the probability of fuel-rod failure on account of mechanical interaction between the fuel
and sheath, along with chemical effects arising from fission products and technological impurities. Some im-
provements are being made in order to prevent such forms of failure, and some of these have already been
checked out in reactors: spaces at the ends of fuel tablets, initial excess gas pressures in BWR fuel pins, and
graphite lubrication between the fuel and sheath in HWR.
Some very promising design improvements have not yet been checked out on commercial reactors, but
American workers consider that the most promising of these are as follows: duplex tablets, lubrication in the
fuel-sheath gap (LWR), and coatings (Cu, Zr) on the inside of the sheath.
It was pointed out during the discussion that the working reliability has become the basic parameter,
while economic aspects have receded very much into the background. One American paper therefore dealt
with the economic aspects of the various design improvements. It was shown that although the contribution to
the cost of 1 kWhfrom the manufacture of fuel pins and assemblies is not much more than 1%, improved
techniques can nevertheless result in a marked economic gain. For example, if the manufacturing cost is un-
changed, the returns from increasing the burnup from 33,000 to 45,000 MW ? day/ton and from using spacing
grids made of zirconium alloys would be, respectively, one million and 800,000 dollars per year for a reactor
of electrical output 1000 MW.
IAEA CONFERENCE ON SODIUM FIRES
V. G. Golubev and B. V. Gryaznov
This conference was held in Nov. 1978 at Caderousse, France. The participants were drawn from Britain,
Italy, the Netherlands, the USSR, the USA, France, the Federal Republic of Germany, and Japan; there were 24
papers presented.
The purpose of the meeting was to survey accumulated experience on the combustion of sodium coolants,
including fire-fighting techniques, with the special purpose of defining unsolved problems in this area.
The participants visited experimental and test systems at the Caderousse nuclear research center as well
as the Phenix fast reactor at Marcoule.
Recommendations were drawn up on the following research aspects.
Sodium Ignition (Fires). The mechanisms involved in sodium ignition and combustion are now reasonably
clear. Physical and chemical models have been formulated, although these require further experimental evalua-
tion. Sodium cannot burn in ordinary air at temperatures below its melting point, but it can ignite spontaneously
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at room temperature in the finely divided state, and in that way can cause a general fire. The ignition of sodi-
um is also favored by high atmospheric humidity. More experimental researches are required in this area.
As yet, the precise effects of the area and depth of the sump and the volume of the reactor shield on the igni-
tion have not been established. These parameters should be the subject of immediate research. Fires due to
sodium sprays are just as predictable as sump fires. It has been observed that the results from spraying
single drops are not the same as those from a series of drops.
Computer programs have been written in several countries to predict the combustion rate in a sodium
fire in a sump, and also to predict the corresponding temperature and pressure. Experiments are planned to
check these programs. An urgent task is to write programs to predict fires arising from sodium sprays, since
the exact relationship between ignition and droplet size has not been established. Models for sodium fires
should be evaluated by defining criteria, which in particular should be used to evaluate the accuracy of the com-
puter programs. A further task is to develop and check out models for occurrences of simultaneous ignition
of sodium in a sump and on account of sprays.
Prevention and Extinction of Sodium Fires. The discussions indicated that successful prevention of
sodium fires can come from the design of sensitive and reliable systems for detecting sodium leaks. None of
the existing systems is satisfactory in this respect.
It is anticipated that good results will be obtained from a program of research on sodium leaks through
the reactor containment, but more experiments in this area on different scales are required. A recent ad-
vance in extinguishing sodium fires is provided by the development of extinguishing mixtures such as Graphex
SK23 and Marcalina, which are effective in sodium fires of all types. Research is needed on the consequences
of sodium fires in which new materials are employed. A further object for research concerns the effects of
possible fires and of extinguishing agents on the design of reactors and reactor equipment.
Methods of extinguishing sodium fires with nitrogen gas were discussed; it is desirable to dilute the ni-
trogen with about 5 vol.% of carbon dioxide, since this raises the ignition temperature of the extinguished sodium.
Portable and mobile powder extinguishers were demonstrated, along with fire vehicles carrying up to 2000
liters of extinguishing agent.
Aerosols. Considerable progress has been made in some countries on the filtration of finely divided
sodium aerosols; successful tests have been performed with industrial systems such as cyclones, wet scrubbers
of various types, and Brink filters. Future tests will be concerned with Venturi scrubbers and electrostatic
precipitates. Complete characteristics of aerosols for various working conditions are required in filter testing.
Research is also needed to optimize the various filtration systems, particularly for use with higher reactor
powers and larger loads.
General Recommendations. The reactions of sodium with concrete (in reactor shielding) were not dis-
cussed. It was decided to discuss this aspect at the next conference, which is to be held in four years' time.
A decision was also taken on further research on the chemical behavior of aerosols, particularly damage effects.
There were many favorable comments on the good organization of the conference and the warm welcome
offered by the French delegation, which was headed by George Malet,
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INTOR DESIGN
V. I. Pistunovich
The first meetings of the steering committee of the International Working Group on the design of the In-
ternational Tokamak Reactor was held in Nov. 1978 in Vienna; the committee decided to present a report to the
International Fusion Research Council at the end of 1979 in collaboration with the International Working Group,
which is to contain recommendations on the purposes and major characteristics of a large thermonuclear
tokamak-type system, which is to be constructed by international collaboration. The meeting laid down the
purposes of the working group, the membership, the scheduling of various tasks, the invitations for the first
session, and various physical and engineering aspects that must be discussed under the INTOR project.
The steering committee decided that the IlitC report should include an evaluation of the plasma-physics
and engineering aspects of the design, as the system might be begun now or in the early 1980s; the recommenda-
tions were to be included on the general design in consistency with the physical and engineering principles and
purposes, including various alternatives. The report should also identify the main uncertainties that need to
be elucidated before the construction can be initiated, along with the researches required for full program def-
inition. Further, the requirements for the most important materials must be defined along with the plan for
detailed design and construction of the reactor. Recommendations must also be made on the engineering and
scientific feasibility of such a reactor, which should be working in the late 1980s or early 1990s.
The composition of the working group was agreed upon at the meeting. Each side (the USSR, the USA, the
Euratom countries, and Japan) will be represented at the meetings of the International Working Group by not
more than four delegates. Also, the steering committee or particular members may invite experts to parti-
cipate in the meetings of the working group.
The timetable for the working group envisages three or four meetings in Vienna during 1979 in conjunc-
tion with various tasks to be carried through by the members between meetings in accordance with the agreed
program.
The IFRC laid down the purposes of INTOR as follows: to make the largest reasonable forward step in
fusion research in order to define the scientific, technical, and engineering aspects of the feasibility of pro-
ducing electrical power from a pure DT reactor, to incorporate the major components and systems character-
istics of commercialfusion station, and to provide for testing equipment, components, and materials for a com-
mercial reactor.
The steering committee laid down the technical purposes of lNTOR as the attainment of a power amplifica-
tion factor in the plasma Q> 5 from the D?T reaction, the definition of technologies appropriate for the reac-
tor, development of methods of creating and sustaining a plasma appropriate for a reactor, and definition of
devices for testing prototype blanket modules and the scope for electrical power production.
The first meeting of the International Working Group was held in Vienna in February 1979.
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SOVIET ? AMERICAN CONFERENCE IN FUSION-APPLICATION
PROBLEMS,
N. N. Vasil'ev
This conference was held in Nov. 1978 in Moscow and discussed the prospects for using fusion reactors
to produce high-grade technological heat and synthetic fuel. Research in this area has been performed in
various laboratories and firms in the USA as well as at the Institute of High Temperatures, Academy of Sci-
ences of the USSR, and at the Kurchatov Institute of Atomic Energy.
The heat produced in the blanket of a fusion reactor can be utilized in coal gasification, production of
hydrogen from water by thermochemical or electrochemical means, and fixation of atmospheric nitrogen; the
advantage here is that the working component (water, air, etc.) is heated directly in the blanket. No heat ex-
changer is required, and the working medium can therefore be heated to 1200-2000?C, which very much sim-
plifies the thermochemical aspect of producing synthetic fuel, while much of the energy can be supplied as heat
in electrothermochemical decomposition of water. However, it is clear that the decomposition products in that
case will be radioactive, either from direct activation of the working body or as a result of entrainment of
blanket materials (A1203, MgO, and Si02). Some designs envisage an additional heat exchanger to transmit the
heat to the working body, in which case the temperature of the latter falls to 1000-1200?C, which approaches the
level adopted in the design of high-temperature nuclear reactors.
Many of the papers dealt with the definition of blanket structures in which much of the heat will be ex-
tracted at high temperatures while providing a tritium breeding factor greater than 1. This appears possible
if the high-temperature heat accounts for 0.4-0.7 of the total reactor output. In that case, the blanket would be
made of ceramic materials. The blanket would have to be changed once or twice a year, or alternatively finely
divided ceramic materials might be circulated continuously through the blanket zone.
Much attention was also given to preliminary economic analysis. Two types of system were considered:
a pure fusion reactor, in which the product is synthetic fuel, and a hybrid reactor, in which the high-tem-
perature zone in the blanket is accompanied by a zone for the production of nuclear fuel (Pu or 233U). In the
latter case, the reactor would be a dual-purpose one, which might reduce the final cost of the products. The
cost of producing synthetic fuel with a fusion reactor is comparable with similar costs in systems based on
coal (about 3.5 dollars per 2.52 ? 105 kcal, or 2-3 times current prices for fossil fuels). The cost parameters
of fusion reactors are based on designs intended for electricity generation. It has been found that pure fusion
reactors will produce synthetic fuel at a cost twice that for a coal-based system, whereas a hybrid system would
involve costs comparable with those of a coal-based system at reasonable prices for the nuclear-fuel component,
and it is possible that the costs might even be lower. The potential advantages of pure fusion reactors might
then be related in the main to the lower environmental pollution, which was not incorporated into the economic
analysis.
On the whole, the discussion showed that pure fusion reactors may have advantages over other types of
power system in the production of synthetic fuel only if the working body can operate at temperatures above
1500?C, which will require very considerable development and research on materials and blanket design. In
that respect, hybrid reactors appear economically more attractive, while the technology and materials will be
much more similar to those used in high-temperature graphite reactors.
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SIXTH ALL-UNION CONFERENCE ON CHARGED-PARTICLE
ACCELERATORS
V. A. Berezhnoi
This conference was held in Nov. 1978 in Dubna; the participants were drawn from the Soviet Union and
eleven other countries. Two plenary sessions dealt with designs for new large accelerators, at which surveys
were presented.
Considerable interest was shown in reports on the design of a system drawn up at the Institute of High-
Energy Physics for accelerating about 6 ? 101' protons to an energy of 3 TeV, in addition to the Tevatron pro-
ject and the planslor a 500-GeV accelerator at the Fermi National Laboratory in Batavia, USA, as well as
progress in the design of superconducting magnet systems (Experimental Physics Research Institute). Other
papers dealt with a design for colliding e-e+ beams, the scope for using electron cooling in accelerators de-
signed for ultrahigh energies, and the state of development on the commissioning of the VEPP-4 storage rings,
as well as on the existing and future systems with e-e+ colliding beams (Institute of Nuclear Physics, Siberian
Branch, Academy of Sciences of the USSR).
Attention also centered on reports on a system for accelerating ions of all elements up to energies rang-
ing from hundreds of MeV to several GeV per nucleon (Kurchatov Institute of Atomic Energy, Joint Nuclear
Research Institute, Institute of Experimental Physics, and Moscow Electronics Institute, Academy of Sciences
of the USSR), as well as the use of heavy ions at high energies in controlled fusion (USA). The last session
dealt with what have now become traditional papers on current problems in high-energy physics and the specifi-
cations for the next generation of accelerators (Institute of Theoretical and Experimental Physics and Institute
of High-Energy Physics.)
The session on heavy-ion accelerators was concerned with various research lines, and papers were given
on problems in extending these systems, Including the U-400 heavy-ion isochronous cyclotron, which was com-
pleted at the Joint Nuclear Research Institute in Dec. 1978. When this is brought up to its design parameters,
it will provide heavy-ion beams of very high intensity ranging up to xenon. Interesting data were also presented
on the upgrading of the cyclotron at the Kurchatov Institute of Atomic Energy and on the Saturn-2 synchrotron
in France, as well as on the development of a source for producing highly charged ions (Belgium). Results
were presented on optimization of the accelerating structure in a compact linear accelerator for heavy ions
(Technical Physics Institute, Academy of Sciences of the Ukrainian SSR), and also data on the parameters of
the heavy-ion injector for a proton synchrotron at the Institute of Theoretical and Experimental Physics. Re-
searches were also reported on the acceleration of heavy ions with a wide charge spectrum (Experimental
Physics Research Institute and Institute of Theoretical and Experimental Physics). Most of the papers at the
session were concerned with cyclic machines.
The colliding-beams session dealt with electron cooling and optimization of stochastic cooling. Beam-
cooling techniques have now become basic to pi-) colliding-beam systems. Much interest was aroused by papers
on a new design for e-e+ colliding-beam systems (see above), which lead one to hope that an energy of 2 ? (100-
300) GeV might be obtained with an accelerator of length 2 (1-3) km and an effective aperture of ?1032 cm-2 ?
sec-1; this led to a discussion of the production of energy increments of about 100 MeV/m, etc. One of the
papers dealt with a method of producing an energy resolution comparable with resonance-peak widths in e-e+
colliding-beam systems, particularly those characteristic of the 4) particle family. The session also discussed
results obtained with the VEPP-2M system (Institute of Nuclear Physics, Siberian Branch, Academy of Sciences
of the USSR).
High-intensity cyclic and linear accelerators were considered in a special session; here considerable in-
terest was aroused by papers on the current state and future development of the Triumph accelerator in Canada,
as well as on prospects for upgrading high-energy high-current cyclotrons (Nuclear Physics Research Institute,
Moscow University). Some of the papers dealt with designs for high-current linear accelerators with lithium
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targets, which provide intense neutron sources for materials research related to fusion (Institute of Theoreti-
cal and Experimental Physics, and also in the USA). There was an interesting communication on the use of
electrostatic focusing in the central part of the synchrocyclotron at Leningrad Nuclear Physics Institute,
Academy of Sciences of the USSR, for operation at 1 GeV, which has increased the internal-beam current by a
factor 3.
A central place was taken at the session on new acceleration methods by papers from the Joint Nuclear
Research Institute dealing with a prototype collective heavy-ion accelerator, where a decaying magnetic field
has been used to accelerate nitrogen ions to 2 MeV/nucleon over a length of 0.5 m while producing ?(5-6) ? 1011
ions per cycle, while checks have been performed on the scope for accelerating argon and xenon. Researches
on electron injection have been completed with the PUSTAREX system in Western Germany, as well as on
beam generation and extraction. Considerable interest was aroused by papers on collective ion acceleration in
a system with an isolated anode (Nuclear Physics Research Institute, Tomsk Polytechnical Institute). Some of
the papers dealt with multicycle injection systems and nonadiabatic processes in electron-ring production (Insti-
tute of Theoretical and Experimental Physics), along with research on the nonlinear stage in the cyclotron-
focusing instability (Moscow Electronics Institute). The second meeting during this session discussed the de-
sign of small high-current linear accelerators for use as injectors in collective accelerators (Kurchatov Insti-
tute of Atomic Energy, Nuclear Physics Research Institute at Tomsk Polytechnical Institute, and Institute of
High Temperatures, Academy of Sciences of the USSR), as well as the interaction of high-current beams with
various resonator systems (Joint Nuclear Research Institute and Moscow Electronics Institute). Another dis-
cussion concerned ring storage of high-current relativistic electron beams (Nuclear Physics Research Insti-
tute at Tomsk Polytechnical Institute). The results presented at the session and the discussions showed that
these researches are very promising.
An impressive picture of accelerators applied for practical purposes was presented at the sessiononac-
celerators in applied research. A particular place was taken by papers on the development of accelerators
for industrial and medical purposes (Experimental Physics Research Institute) and on researches at the Nuclear
Physics Institute, Siberian Branch, Academy of Sciences of the USSR on electron accelerators for industrial
purposes. Papers presented by the Experimental Physics Research Institute, the Institute of Nuclear Physics,
Siberian Branch, Academy of Sciences of the USSR, and the Nuclear Physics Research Institute at Tomsk Poly-
technical Institute showed that it has recently become possible to build various highly efficient and reliable sys-
tems providing high electron-beam power levels that meet industrial specifications. Accelerators are being
used on an increasing scale for many industrial purposes.
The session on synchrotron radiation dealt with sourcs and uses. There were papers from the Institute
of Physics Problems, Academy of Sciences of the USSR, and the Institute of Nuclear Physics, Siberian Branch,
Academy of Sciences of the USSR. Considerable interest was shown in a paper on a design for a synchrotron-
radiation source based on an electron storage ring operating at 2.5 GeV (Erevan Physics Institute). Some of
the papers dealt with research on undulator radiation (Physics Institute, Academy of Sciences) and research
on synchrotron-radiation sources at other research centers in the USSR, and these included an interesting paper
on the limiting power output of an optical klystron (Nuclear Physics Institute, Siberian Branch, Academy of
Sciences of the USSR). Synchrotron radiation appears to have many research applications, which accounts for
the importance of researches in this area, including those designed to provide coherent sources.
The session on particle dynamics in accelerators and stores dealt with research designed to improve
existing systems and to define methods for designing new ones. Particular attention was attracted by papers on
the acceleration of polarized particles (Institute of Nuclear Physics, Siberian Branch, Academy of Sciences of
the USSR) and on correction of the vr-vz resonance coupling in the proton synchrotron at the Institute of High-
Energy Physics. Some of the papers dealt with advances in the theory of particle motion in accelerators. There
were interesting communications on preliminary tests on a superconducting container for the VE PP-3 storage
ring and on a method of calculating the characteristics of beams in stores with any form of coupling between
oscillations in all the degrees of freedom (Institute of Nuclear Physics, Siberian Branch, Academy of Sciences
of the USSR).
Future progress in accelerator engineering is dependent on advances in electronic and radio systems
used in accelerators. The sessiononthese aspects discussed a report on the Nuclear Physics Institute, Siberian
Branch, Academy of Sciences of the USSR, which stated that automatic controls for accelerators employing mini-
computers or larger machines have been built at accelerator centers in the USSR. Interest was aroused by re-
ports on a system for measuring the equilibrium orbit parameters of the beam in the VEPP-4 store (Institute
of Nuclear Physics, Siberian Branch, Academy of Sciences of the USSR) and on remote-sensing methods of
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measuring beam parameters in high-energy accelerators (Moscow Electronics Institute). The session also
discussed the design of the accelerator systems for the new machine being built at the Institute of High-Energy
Physics and the upgrading of these systems in the U-70 accelerator (same institute).
r There was a lively discussion on a paper concerning laser ion sources (Moscow Physics Research Insti-
tute) at the session onion sources and superconducting UHF systems. It was pointed out that this type of source
is promising for the production of highly charged ions. Considerable interest was also aroused by papers on
prospects for using superconducting uhf systems in accelerator engineering (Nuclear Physics Research Insti-
tute at Tomsk Polytechnical Institute) and on an electron-beam source of highly charged ions (Nuclear Physics
Institute, Siberian Branch, Academy of Sciences of the USSR). It is to be expected that new types of sources
will substantially extend the performance of heavy-ion accelerators in the near future.
The session on magnet systems (including semiconducting ones) discussed the design of magnet systems
and the definition of magnetic cycles in charged-particle accelerators, particularly for high energies. Many of
the communications dealt with the design of superconducting dipole magnets for the new system at the Institute
of High-Energy Physics, and these studies have been performed at that institute, the Joint Nuclear Research
Institute, and the Institute of Experimental Physics.
The session on efficiency in accelerator use in physics experiments (targets and beam transport) dis-
cussed the stable acceleration of about 4.5 1012 protons/cycle with the synchrotron at the Institute of High-
Energy Physics. Important results have been obtained with the synchrophasotron at the Joint Nuclear Re-
search Institute, where the magnet system has been upgraded along with the beam-diagnosis unit. The second
group of papers dealt with some practical results and new concepts on accelerator-beam handling. In par-
ticular, there was a paper on lithium lenses for focusing secondary-hadron beams at high energies (Institute
of Nuclear Physics, Siberian Branch, Academy of Sciences of the USSR), while there was a rather different
but interesting paper on the prospects for using single crystals in accelerators (Institute of Technical Physics, -
Academy of Sciences of the Ukrainian SSR).
The papers presented at the conference reflect the substantial progress that has been made in accelerator
science and engineering. The papers are to be published.
ALL-UNION CONFERENCE ON DELAYED CONSEQUENCES
AND ESTIMATES OF RISK FROM RADIATION
Yu. I. Moskalev
This conference was held in Oct. 1978 in Moscow and was attended by about 200 participants from various
research institutes throughout the country. The organizing, committee received 112 abstracts, which were made
available as a booklet before the conference opened. During the three days of the meeting, 31 papers were
read and discussed, including 7 reporter papers that surveyed 32 communications on the biological effects of
241Am, 252cf, 228Th, 147pm, 3?.xi, 137
various compounds of 239PU, --Cs, "Sr, 75Se, 35, and 1311 alone or together with
damage by radiation and other sources.
The conference was opened by L. A. Iltin, who emphasized the practical significance of research on re-
mote consequences and radiation hazards. Valuable report papers were presented by A. V. Fedorova, N. A.
Koshurnikova, S. V. Stepanov, T. A. Norets, L. N. Burykina, et al. These papers contained new and important
data on delayed radiological effects from external and internal radiation sources, including effects on the hema-
topoietic, immune, neuroendocrine, cardiovascular, and gastrointestinal systems, in addition to those on sex
glands, skin, and eyes. Much attention was given to malignant and other remote pathological effects, including
the evaluation of the tumor risk in various areas of the body, as well as ways of applying animal data to man.
Some of the papers dealt with the treatment and prophylaxis of delayed effects, combinations of external
radiation with ingested radionuclide damage, and combinations of radiation with chemical compounds, the latter
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including carcinogens. Interest was aroused by new evidence on biological effects of 1251, 14C, 252ct 239pu,
30Sr,30Y, and 3H, along with information on delayed consequences in man from therapeutic use of radiation.
Research on delayed consequences and radiation risks constitutes a major division of radiation hygiene,
since it makes it possible to define measures for reducing morbidity and for prophylaxis of delayed effects,
as well as for the definition of scientifically sound recommendations on acceptable levels for various types of
ionizing radiation. The radiation damage responsible for delayed effects is persistent; structural and functional
changes occur at various levels in biological systems. A biological object after local or acute irradiation
shows an increase in the number of possibly pathogenic factors. Ionizing radiation is not only a carcinogen but
also may enhance the sensitivity of an irradiated tissue to other carcinogens. Radiation is therefore one of the
agents that enhance the blastomergenesis risk. Aleksandrov (Central Radiation Research Institute, Leningrad)
considers that the changes responsible for delayed radiation damage are of a potentially but not essentially ac-
cumulated to show that it is possible to offset some late effects. The view that the changes responsible for
delayed effects are only conditionally irreversible is the basis for the search for effective means of offsetting
such effects.
When ionizing radiation is combined with ultraviolet light, chemical carcinogens, or cancer viruses, it
it is usual to find that the carcinogenic effect is enhanced; it seems that this is due to the fact that all physical
and chemical agents of this type damage DNA and interfere with the repair mechanism. Combination of radia-
tion and carcinogenic viruses may mean that this damage can facilitate the incorporation of exogenous viruses
into genes or can activate endogenous oncogenic viruses. DNA damage is also important in radiation aging
(M. M. Vilenchik, Institute of Biological Physics, Academy of Sciences of the USSR, Pushchino).
Improvements in radiotherapy techniques and the use of high-energy sources are constantly increasing
the numbers of cures of malignant tumors in various body areas. However, any radiotherapy patient requires
prolonged followup, since such patients constitute an elevated-risk group as regards radiation-induced cancer,
as was demonstrated by A. S. Pavlov et al. oncology Center, Academy of Medical Sciences of the USSR, Mos-
cow). The main way of treating cancer of the uterine cervix, and the most effective one, is radiotherapy. The
specific conditions here are such that the small intestine is irradiated, and this gives rise to malignant tumors
and other changes 5-26 years after elimination of the cervical tumor. Extended research is needed on cancer
epidemiology for population groups in the USSR exposed to radiation on account of radiotherapy and diagnostic
procedures, as well as from the use of radiation sources in industry.
A major task of experimental research is to evaluate the tumor risk arising from various forms of ion-
izing radiation. This risk is dependent on the dose, the form of radiation, the area administered, and the dose
pattern. Radiation of high LET (a particles or neutrons) as a rule has a much larger blastomergenic activity
than does radiation of low LET 6 particles, y rays, x rays).
Rats receiving y -ray doses of 100 or 200 R at various stages during fetal development (at 7, 14, or 19
days) show increased incidence and increased growth rates of various neoplasms in the early postnatal stages
and during adult life. The irradiated animals have more organs involved in the neoplastic process than do
controls, while tumors are induced that are rare or very rare in controls (leukemia, lung tumors, and bone
tumors, as well as mammary-gland tumors in males). There are no substantial differences in frequency and
spectrum for the tumors observed in animals irradiated at various stages (V. N. Strel'tsova et al., Institute of
Biological Physics, Ministry of Health of the USSR, Moscow).
Considerable practical significance attaches to observations on the occurrence of malignant tumors in
bone and lung when small amounts of transuranium elements enter the body. Experiments show that these
tumors arise only in long-lived rats, namely in ones whose life spans are greater than the average for the con-
trol rates. The cumulative doses to the lungs and skeleton in such animals have been 3-100 rd. It has also
been found that prolonged exposure to radiation of low LET results in a tumor risk less by a factor 2-4 than
that from a single exposure to a radiation of high LET giving the same total dose.
The participants stressed the need for periodic conferences of this type (every 3 or 4 years), which should
include contributions from researchers on viral and chemical forms of carcinogenesis.
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CORRECTIONS AND AMENDMENTS TO ICRP PUBLICATION No. 26
A. A. Moiseev
In January 1977 the International Commission on Radiological Protection (ICRP) approved the final word-
ing of the text of new recommendations in the realm of radiation protection (Publication No. 26), which ex-
pounds the principal concepts of the ICRP on this subject and presents recommendations concerning the choice
of optimal conditions for ensuring the radiation safety of professional workers and the population, and the or-
ganization and implementation of radiation monitoring. The recommendations were published in Russian in the
USSR in 1978 (Radiation Protection, ICRP Publication No. 26. Translated from the English. Edited by A. A.
Moiseev and P. V. Ramzaeva. Atomizdat, Moscow (1978), 88 pp.). At a meeting in Stockholm, Sweden, in May
1978 the ICRP reexamined the recommendations presented in that publication and made the following statement.
Assessment of Radiation Risk. The risk factors which the Commission presented in Publication No. 26
(Sections 36-60) are based on the data of the ICRP Committee 1 on Radiation Effects. They are in agreement
with the data given in the scientific literature and with information given in the 1977 report of the U. N. Scien-
tific Committee on Atomic Radiation.*
On the basis of a continuous, careful analysis of available epidemiological and radiobiological data on
the risk of the effects of ionizing radiation on man, the Commission believes that the data published up to May
1978 on these subjects do not provide a basis for a review of the numerical values of the risk factors. These
values are very realistic estimates of the effects of radiation at low annual equivalent doses (within the limits
of the permissible equivalent dose recommended by the ICRP).
To estimate the probability of stochastic effects from the action of ionizing radiation, the Commission
(Sec. 105, Publication No. 26) recommends that weighting factors be used to sum up the equivalent dose indif-
ferent organs and tissues. The Commission noted that it did not propose to include the wrists and forearms,
feet and ankles, the skin, and the crystalline lens of the eye among the so-called "other organs." Therefore,
EWTHT should not be taken into account in the calculations. To preclude nonstochastic effects the Commission
recommends that the appropriate maximum doses indicated in Sec. 103 be extended to these tissues.
In assessing the damage due to the irradiation of various groups in the population, one must take account
of the low probability of deaths as the result of skin cancer caused by irradiation, e.g., in the case of the overall
irradiation of the skin with low-energy 13 radiation. In this case a risk factor value of 10-4 should be used for
a dose of 100 rem, averaged over the total skin surface of the body. This value will correspond to the coeffi-
cient WT - 0.01.
The maximum dose for occupational exposure, as established by the Commission for all persons working
with sources of ionizing radiation, are based on the average values of the risk factor for men and women. The
variations of the risk level to persons of both sexes and of various ages under irradiation, mentioned in Sec.
38 of Publication No. 26, are discussed in greater detail in Publication No. 27 "Problems Arising in the Elab-
oration of an Injury Index." This publication also considered the principal data which formed the basis for the
selection, for Publication No. 26 (Sec. 60), of a mean value of the genetically significant fraction (0.4) for occupa-
tional exposure and the mean value of the risk factor for death from cancer (10-i rem-l) for persons of both
sexes and various ages.
Effective Equivalent Dose. The Commission recommends that the sum ZWTHT (see Sec. 104, Publication
No. 26) be called the effective equivalent dose (denoted by HE).
* This refers to the report of the U. N. General Assembly's Scientific Committee on the Effects of Atomic
Radiation with the appendices "Sources and Effects of Ionizing Radiation." United Nations Organization, New
York (1978). The report was published in English, Russian, French, and Spanish.
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Some Changes in the Wording of the Text of Publication No. 26. The Commission believes that the follow-
ing changes inthe wording of Publication No. 26 will permit the sense of the recommendations to be expressed
more clearly.
Section 38. The fourth and fifth sentences should read:
"Therefore, for the purposes of protection one and the same value of the maximum effective equivalent
dose can be used with sufficient accuracy for all workers, regardless of age and sex. This value is based on
the mean values of the risk level, given below for various organs or tissues."
Section 79. The first sentence should read:
"The maximum values of the equivalent dose established by the Commission for workers are intended
for estimating the sum of the equivalent dose due to external radiation accumulated over a one-year period and
the expected dose due to the entry of radionuclides into the human body in the course of that year."
Section 79. The following should be added at the end of this section:
"Similar principles underlie the use of maximum equivalent doses established for individuals from the
population."
Section 89. In the third sentence delete "... intended for the use of the management in planning, and,
therefore..." Further as in the text.
109).
Section 93. In the first sentence delete "...intended for the purpose of planning and .../
Section 107. The end of the last sentence should read:
"...notably, the maximum depth and surface dose indices Hid and 111,5 (see Sec. 108) and PGP (see Sec.
Section 108. The last part of the first sentence should read:
". . . it is possible to estimate the maximum value of the equivalent dose which will be produced at a
depth of 1 cm or more in a sphere of diameter 30 cm (depth dose index Further as in text.
Section 108. The following should be added at the end of the paragraph:
"Moreover, the equivalent surface dose index (the maximum value of the equivalent dose in a layer at a
depth of 0.07 to 10 mm in a sphere of diameter 30 cm) should not exceed 500 mZv to ensure the protection of
skin covers. The annual equivalent radiation dose for the crystalline lenses of eyes with such limits for the
indices of the equivalent depth and surface doses should in practice not exceed 300 mZv."
Section 110. This section should have the following wording:
"With a combination of external and internal irradiation the dose limits recommended by the Commission
will not be exceeded if the following two conditions are satisfied simultaneously:
d/HE, 2 (1,/I.", L.) I and HI, s/Hsh, L1,
where HIA and 1-11,5 are the annual indices of equivalent depth and surface doses, respectively, HE,L is the
annual limit of the effective equivalent (50 mZv), Hsk,L is the annual limit of the equivalent dose for skin (500
mZv), Ij is the annual intake of radionuclide j, and Ii,L is the annual limit of the intake of radionuclide j.
Section 113. The second sentence should be worded as follows:
"In such cases extetnal irradiation and the intake of radioactive substances into the human body may be
permitted provided that the sum of the equivalent dose from the external irradiation and the expected equiv-
alent dose due to the intake of radionuclides into the body does not exceed the corresponding doubled annual
limit for any single event and not more than five times for the entire lifetime."
Section 187. In the first statement the term "limits of equivalent dose" should be replaced by the
term "system of dose limitation."
344
Section 238. In the last sentence the third line should read:
"...articles of mass consumption, they were studied or monitored..." Further as in text.
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SCIENTIFIC ?TECHNICAL RELATIONS
CONTROLLED FUSION RESEARCH IN FRANCE
G. A. Eliseev
A delegation of the USSR State Committee on Atomic Energy visited France in Nov.-Dec. 1978, in order
to study the present state of research on controlled thermonuclear fusion withinthe frameworkofthe long-term
Soviet?French program of scientific and technical cooperation. During the visit the delegation saw the thermo-
nuclear laboratories at the scientific centers in Fontenay-aux-Roses and Grenoble of the Commissariat
litnergie Atomique of France and the plasma theory and physics laboratories of the *toole Pol3rtechnique. The
delegation became thoroughly acquainted with experiments based on the main thermonuclear devices and stands
and the prospects for the further development of work on controlled thermonuclear fusion in France. Some
aspects of the organization of joint work in forthcoming years were discussed.
The Department of Plasma Physics and Controlled Fusion at Fontenay-aux-Roses comprises more than
200 workers. Half of them are on the staff of the TFR facility. Moreover, there are laboratories (groups)
working on plasma theory, ion sources, and methods of rf heating of plasma, as well as a group engaged in de-
signing the next generation of TORUS II tokamaks. About 40% of the department budget is provided by Euratom.
The TFR facility is a classical tokamak with a circular cross section and closed iron core (major torus
axis 98 cm, maximum magnetic field at chamber axis 6 T). The facility was put into service in 1973 (the TFR-
400 modification). In this version, the chamber had a copper shield inside it and the current in the plasma was
400 kA. The TFR-400 was used for experiments on heating plasma by the injection of beams of fast atoms at
small angles; ion temperatures exceeding 2 keV were attained during these experiments. In 1977, the facility
?was reconstructed to become the TFR-600 modification. The copper shieldwas eliminated, its function of
ensuring the equilibrium of the plasma column now being performed by a system of external feedback conduc-
tors. The inner diameter of the chamber was increased from 30 to 50 cm. The cross section of the iron core
was also increased, thus making possible operations with a current of up to 600 kA in the plasma. Because of
the imperfections of the feedback system, however, the maximum current has thus far not surpassed 300 kA.
At the present time the power and speed of the feedback system are being increased, which will apparently make
it possible to increase the current in the plasma to the design value. Inconel was used as the material for the
TFR-600 chamber. The chamber cleansing technology (heating plus Taylor discharge) was optimized. As a
result it was possible to substantially reduce the impurity content in the plasma. Thus, under conditions with a
discharge current of 250 kA at a mean plasma density n ? 7 ? 1013 cm-3 the effective charge Zeff does not ex-
ceed 1.2-1.5. The energy lifetime of the plasma in this case is about 25 msec.
Two injectors have been set up in the TFR-600 at the present time and each has five duopigatron ion
sources arranged vertically. Because of the change in the design of the connecting pipe of the chamber it was
possible to increase the injection angle to 15?. The sources were tested under operating conditions with 40 keV,
10 A, which warrants the assumption that a stream of fast atoms with a power of PL? 1.5 MW (witha pulse
duration of 50 msec) can be introduced into the plasma. At present it is operating at 20 keV and 5 A with PL =
600 kW. It has been established that the ion temperature of the plasma rises in proportion to PL. It is ex-
pected that with the injection operating at full power (PL = 1.5 MW) an increment of Ti ? 2.5 keV will be ob-
tained in the ion temperature.
The TFR is to undergo another reconstruction to permit further development of the injector program.
The main objective of this modification (TFR-604) will be to study plasma equilibrium and stability with tan-
gential injection in the ion-temperature range up to 5 keV. By replacing several coils in the solenoid of the
toroidal magnetic field and some alterations to the chamber, eight beams of fast atoms with a total power of up
to 4 MW are to be introduced into the plasma tangentially to the axis of the plasma filament. Ion sources of
the periplasmatron type, each with a power of 0.5 MW, have already been developed for these injectors. A 1-
MW source of this type, is being developed for JET, which is under construction in Gt. Britain. The project
for the TFR-604 modification has been drawn up but its implementation will not begin before the end of 1980.
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 292-294, April, 1979.
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Fig. 1. Tokamak TER-600 (France).
Traditionally, much attention has been paid in Fontenay-aux-Roses to rf methods of plasma heating. An
experiment on ion-cyclotron heating of a mixture of deuterium (80-90%) and hydrogen (10-20%) was carried out
on the TFR-600. The plasma had 200 kW of rf power fed into it at double the ion frequency for deuterium. The
average plasma density was (2-3) ? 1013 cm-3, the magnetic field was 4.3 T, the rf-generator frequency was
66 MHz, and the rf-pulse duration was 20 msec. The average ion temperature rose from 600 to 800 eV. The
electron temperature was also observed to rise, by ATe ? 400 eV. No satisfactory explanation has as yet been
provided for this effect. The power injected into the plasma is to be raised to 500 kW in 1979 and 3 MW in
1980. Plans for rf plasma-heating systems for the large-scale tokamaks JET and TORUS II are being drawn
up in parallel.
The Plasma Theory Laboratory at Fontenay-aux-Roses has a staff of about 20. Attention is being fo-
cused on the development of an adequate theoretical model for tokamak plasma (as supplied to TFR). The nu-
merical code MAKOKOT has been constructed and continuously improved on the basis of this model. Long-
term research has recently been given comparatively less attention, but in this case as well results of a very
high caliber have been attained.
Investigations are being actively pursued on various methods of rf plasma heating in the Ionized Gases
Laboratory at the Nuclear Research Center in Grenoble. Some 60 scientific workers and engineers work in the
laboratory, many of them being specialists from the Institute of Plasma Physics at Garching (German Federal
Republic). Research is being done on plasma heating by magnetic time-of-flight magnetic pumping (TTMP),
by Alfven, ion-cyclotron, and electron-cyclotron waves, as well as at a low-lying hybrid resonance (LH). The
laboratory has in recent years concentrated its efforts on the development of LH- and TTMP-methods of plasma
heating. Experiments are being conducted on two intermediate-sized toroidal machines, the tokamak PETULA
and the tokamak-stellarator WEGA. In PETULA the ion temperature was raised from 200 to 250 eV (average
plasma density (1.2-4) ? 1013 cm-3)by TTMP heating at a frequency of 150-200 kHz and an rf-power level of 16
kW. The machine is used to study rf heating in the region of low-lying hybrid resonance. Up to 125 kW of rf
power at 500 MHz is delivered to loop antennas placed inside the chamber. The ion temperature rises in pro-
portion to the rf power without reaching saturation under the conditions of the experiment. Projects are being
elaborated in Grenoble for high-power units for rf heating by the TTMP and LH methods for the JET and TORUS
II tokamaks; their construction will obviously depend on the results of experiments on increasing the efficiency
with which the rf energy is utilized. For this purpose, in particular, it is proposed to reconstruct the PETULA
and WEGA machines. Note should also be taken of the work being done in Grenoble on a steady-state source of
deuterium atoms and a source of negative ions with recharging of a xenon target.
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It was with interest that the delegation became acquainted with the plasma physics research conducted at
the Ecole Polytechnique, the oldest school of higher education in France engaged in training specialists in science
and engineering. A new complex with well-appointed laboratories was recently built for it 30 km from Paris.
Plasma physics research is being done in the Laboratory of the Physics of the Condensed State, which has some
50 specialists on its staff. The principal areas of work are: nonlinear waves in turbulent plasma, the inter-
action of high-power laser radiation with dense plasma, the formation of negative ions, etc. The Laboratory
has several experimental plasma apparatuses, including the Q-machine GALIE and EPAL, the PARADIE
ap-
paratus with a magnetic multipole grid, a generator of relativistic electrons with parameters of 500 keV, 125
kA, and 60 nsec, as well as a CO2 laser with a beam energy of 15 J. Some Work is being done under a contract
from the Commissariat a l'Energie Atomique of France. The apparatuses are provided with modern diagnostic
equipment to an even greater extent (this is characteristic of the thermonuclear laboratories at Fontenay-aux-
Roses and Grenoble). The theoretical laboratory of Prof. G. Laval has been working successfully on problems
of the hydromagnetic stability of plasma and simulation of the compression of the plasma sheath.
The prospects of further development of research on controlled thermonuclear fusion in France are linked
today with the construction of a national thermonuclear center in Cadarache. In particular, this is to be the
site of a tokamak of the next generation, TORUS II. The plans for this facility have been drawn up at Fontenay-
aux-Roses. The principal parameters of TORUS II SUPRA are: major radius of torus 2.25 m, minor radius
0.75 m, magnetic field at axis 4.5 T, current in plasma 1.7 MA, and duration of current plateau 10 sec. The
facility will have a superconducting magnetic system with NbTi superconductor cooled to 1.8?K. Superfluid
He II will be used as the coolant. The maximum field in the superconductor will be 9 T. A model of the coil
on a scale of 1:2 has been built for strength and cryogenic tests. The complex for supplementary plasma heating
includes a system for injecting fast atoms with a power of more than 10 MW and an rf-heating system with a
total power of 5-6 MW. The expected plasma parameters: ion temperature 5 keV, density 5-10 cm-3, and
energy lifetime 0.1-0.2 sec. It is envisaged that TORUS II will be put into service in 1983-1984. The final de-
cision on the construction will be made in July 1979.
The reception given the delegation was well organized by the French and took place in a businesslike and
friendly atmosphere.
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BOOK REVIEWS
NUCLEAR REACTOR THEORY, VOL.
S. M. Feinberg, S. B. Shikhov,
and V. B. Troyanskii
Reviewed by V. N. Artamkin
It is useful to quote from the preface to the book by two of its authors: "The textbook 'Nuclear Reactor
Theory' is based on a course given by Professor SaveHi Moiseevich Feinberg over a period of 30 years at the
Moscow Engineering Physics Institute.... We tried to preserve the manner of presentation and the essential
features of the original manuscript of SaveHi Moiseevich Feinberg and we hope that this textbook will to some
degree fill the void caused by the death of its author, who is remembered with great sentiment by a large number
of former students of the Moscow Engineering Physics Institute who attended his lectures and teachers who
learned from those lectures." Familiarity with the book warrants the statement that the objective has been
achieved. The book can be perfectly justifiably considered a weighty contribution of Savelii Moiseevich to
Soviet reactor engineering for which he did so much in his lifetime. The coauthors of the book (S. B. Shikhov
and V. B. Troyanskii) have managed in the pages of the book to recreate the style and line of thought of the
course given by S. M. Feinberg, who focused his attention on the comprehension of the physical foundations of the
processes considered.
Most of the books published in recent years on nuclear reactor theory assume the use of computers to
realize the algorithms considered and this reflects a manifest tendency to exclude analytical methods from the
practice of nuclear reactor design, methods whose role at all stages of the design process can scarcely be
overestimated. Against this background the book under review differs favorably not only by its detailed descrip-
tion of the traditional methods of reactor physics but also by its graphic demonstration of the capabilities of
these methods in the consideration of some physical prossess or other. The book will undoubtedly be conducive
to the development of appropriate habits in students and young specialists. It is to them that this book is pri-
marily addressed.
Bearing in mind that this book is a textbook, we must particularly emphasize the clarity of exposition,
accuracy of formulation, and the now classical consistency. The text has been conveniently divided according
to degree of importance (main text, text in fine print, and appendices to each chapter). Note should be taken
of the large number of well- chosen exercises, a large proportion of which have detailed solutions.
There are some slips, however. Although the terminology employed in the book does, on the whole, con-
form to the established usage, the deviations that do appear are hardly justified. Thus, the equilibrium spec-
trum of reactor neutrons should not have been referred to as "fission spectrum" (p. 18), especially since almost
right after that (p.22) the "fission-neutron spectrum" is construed in the usual sense. For some unknown rea-
sons the nuclear fuel which remains in a reactor at the end of a run is called the critical mass (Exercise 1 on
p. 379). The same exercise gives a definition of the conversion ratio which not only contradicts the definition
introduced earlier (p. 364) but also runs counter to common sense (the conversion ratio cannot have the dimen-
sion of time:). Unfortunately, ambiguous statements can also be found. Thus, on p. 337 contrary to Eq. (8.1.20)
the book states that "neutron capture by fission fragments is not taken into account" (in actual fact what is
meant is that in the approximation under consideration the concentration of fission fragments does not change
under absorption of neutrons by these fragments). A dubious recommendation is given on p. 54: if the reac-
tivity (of a critical reactor) is to become positive, it is necessary to "move the rod to position 2 in which the
neutron flux is smaller." Such action will assuredly lead to the desired result only if a pointabsorbing element,
(there are no such elements, alas) and by no means a rod, is used, not to mention the fact that for a rod of
finite dimensions the concept "flux in position 2" (or any other position) requires definition. It is difficult even
for a well-prepared reader to imagine what is meant when an enumeration of isotopes found in raw materials
has the words "and so forth" after 232Th and 238U (p. 18).
*Atomizdat, Moscow (1978).
Translated from Atomnaya Energiya, Vol. 46, No. 4, pp. 294-295, April, 1979.
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Typographical errors have not been avoided. Thus, the screening factor (7.3.3) for a slug has been re-
produced incorrectly. This is all the more disappointing since the authors omitted the entire derivation (p. 291)
so that not every student will know how to reproduce it. Generally speaking, the authors should not give all the
derivations. References to materials which are inaccessible to the students, however, are scarcely justified;
e.g., a reference to the general theory of Feller (p. 110).
The trifling details mentioned above are unavoidable flaws in the creation of a textbook such as that re-
viewed here. Nevertheless, it is appropriate to express the hope that the second volume prepared for publica-
tion by the authors will, while preserving the advantages of the first volume, be as free as possible of these
errors which separate a good textbook from a very good one.
COURSE OF FUNDAMENTALS OF NUCLEAR ENGINEERING
IN AGRICULTURE*
V. V. Rachinskii
Reviewed by R. A. Srapenyants
The book under review expounds in rigorously scientific style the theoretical and methodological funda-
mentals of nuclear engineering in biology and agriculture. The first edition was published in 1974 in a quite
limited printing. Therefore, the second edition in a large printing is a welcome event at a time when the de-
mand for scientific and educational-instructional literature on the use of isotope and radiation techniques in
agriculture has not waned.
In the general part the author presents the theoretical foundations of radiation physics, radiometry, and
dosimetry of ionizing radiation, Isotope chemistry, general radiobiology, and health physics. The second,
specialized, part of the book is of an applied character. It gives the methodological fundamentals of the applica-
tion of isotope and radiation techniques in biological research, in agrochemistry, soil science, and ameliora-
tion, mechanization, and electrification of agriculture. The author devotes particular attention to agricultural
radiobiology and radiology (radiation protection in agriculture). The exposition is logical, and is written in
rigorously scientific language, without vulgarisms and simplifications. The book points out that nuclear en-
gineering is a new, still little-used resource for the intensification of agriculture. In addition to this and in
combination with mechanization, chemicalization, and amelioration, nuclear engineering provides enormous
potentialities for intensification of all branches of agriculture, including individual stages of agricultural tech-
nology.
The new edition brings slight terminological corrections and gives numerical data. The author has re-
written the chapter on health physics in view of the introduction of new standards for radiation safety (NRB-76).
The chapter on agricultural radiology has been supplemented with valuable material about the radiation en-
vironment in the country.
In the next edition the author might be advised to devote more attention to the presentation of nuclear-
physics methods of ultimate analysis of agricultural objects. Substantial changes are now occurring in radio-
metric techniques. Microelectronic and minicomputer techniques are being introduced on a broad scale. Radio-
metric techniques are being automated. It is therefore necessary for specialists working in the field of applied
isotope techniques and biology in agriculture to become familiar with the new technology.
The second edition of this book by an eminent specialist on nuclear engineering in agriculture will un-
doubtedly be welcomed with great interest.
*University textbook, Second, revised and enlarged edition. Atomizdat, Moscow (1978).
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0038-531X/79/4604- 0349 $07.50 ?1979 Plenum Publishing Corporation 349
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Lithuanian Mathematical Journal
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Editor: P. Katilius
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An international medium for the rapid publication of the latest.davelopments,in mathematics, this new quarterly keeps
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Subscription: Volume 12, 1978 (4 issues)
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Litniti-ng Poisson Processes.in Schemes for Summation Of Independent IntegerNalued Processes?R. Bemis
Formal Differentiation in SpaCes of Geometric Objects?R. V.'Vosylius. ; "
Scalar Products 'of Hecek L-Series of Quadratic Fields-E. Gaigalas -r
Characterization of Stochastic Processes with Conditionally Independent Increments?B..Gri'gelionis
, Limit Theorems for Products of Random Linear Transformations on the Line?A. K. Grincevicius
One Limit Distribution for a:RanclOrn Walk On,the Line?A. K. Grince,vicius ,-- ,
' Estimate Of. Remainder!" Term. in Local ,Limit Theorems fpr Number of Renewals in the Multidimensional Case-7
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Solvability of a Differential Equation in a Subspace?B. Kvedaras '
ModellingPf a NonlinearitY by a Sequence of Markov Chains?V. V. Kleiza - ,
Density Theorems for Sectors and Progressions?F. B. Kovarchik , ,
Mathematical'MOdelling of the Combustion 'Process in the Chamber of a Liquid Propellant Rocket Engine?J. Kolesovas
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HUMAN PHYSIOLOGY
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SOVIET JOURNAL OF BIOORGANIC CHEMISTRY
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SOVIET JOURNAL OF COORDINATION CHEMISTRY
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THE SOVIET JOURNAL OF GLASS mysics
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Fizikai Khimiya Stekla
Devoted to current theoretical and applied research on three
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Volume 4, 1978 (6 issues) $125.00 '
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LITHUANIAN MATHEMATICAL JOURNAL
Litovskii Maternaticheskii Sbornik
An international medium for the rapid publication of the
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configurations. Among the many areas reported on in
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Carlo method, the "innovation theorem," and the Martin-
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PROGRAMMING AND COMPUTER SOFTWARE
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