SOVIET ATOMIC ENERGY VOLUME 21, NUMBER 1
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,r
Volume 21, Number 1
July, 1966
SOVIET
ATOMIC
ENf RGY
ATOMHAfl 3HEPfYIfI
(ATOMNAYA ENERGIYA) `
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU
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SOVIET
ATOMIC
ENERGY
~ , . ~ .
Soviet Atomic Energy is acovertocover translation of Atomnaya
Energiya, a publication, of the Academy of Sciences;of the USSR.
An arrange~ment~witf~"`Mezhdunarod`naya Kniga, the Soviet book "
export agency, makes available both advance copies of the Rus
Sian journal and original glossy .photographs and artwork. Thais
serves to decrease the necessary tune lag between' publication
:of the original arld publication of the translation and helps to im= ~ `
prove th?e,quality of the latter,"theltranslation began with the first ,
issue of,the Rus'sia:n journal ~ ~ ~ '
. .~
1
Editorial Board of Atomnaya Energiya:
f
,?, , j .
.Editor; M: D: Millionshchikov . ,~
Deputy Director, Ihstitute of; Atomic Energy
? ? ? irr{eni I. V. Kurchatov'
Acadefny of.Sciences~of the USSR
., tvloscow, USSR ,
,/ ,
s ,
Associate Editors: N. A. Kol"okol'tsov,,~
. N._A.?Vlasov
A. I. Aiikhanov
A. A. ?Bochvar 1 sec, 0.5 < ~ < 1 and, consequently, l /Tt ~13< 10'2 .
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aA[1Re~(jw)](1 ~ oe?a cos?c~)}[wImcU(jw)](w~e?a sin ?w) a 1cos w 0
[1Re~()w)I2I[wImcD(Iw)]2 + ?6( !a ) ~ (17)
aA [1 Re ~ (ice)] (~fie?a sin ?w) [wIm ~ (iw)l (1fve?6 cos ?ca) + w + e?Q Sin ?w = 0,
where the real parameter w takes all positive values, from 0 to infinity. In. addition to the Dcurve (17~ the Dsub
division itself includes the singularcurve  ~? ??  . ? ~ .
corresponding to the value w= 0.
It is obvious that the singular curve lies outside the region a > 0, ? >_0, since in this region 1 + a e?? > 0.
We shall show that the Dcurve is also located outside this region: Let us consider Eq. (17). Depending on the
actual values of ?, a and w, four cases are possible:
w { auQ s in ?w ~ 0. }
In view of expression (15), 1Re~(jw) > 0 and, consequently, it is not possible to satisfy Eq. (17) simultaneously in
any of the four cases. This means that if the inequalities (19) have identical sense, the first. equation of (17) will
not be satisfied; if the inequalities of (19) have opposite sense, then the second equation of (17) will not be satisfied.
Thus, neither the singular straight line (18) nor the Dcurve (17) lies in the region of? >_ 0, a > 0. Consequently,
for proof of the stability of the unit, it is sufficient to show that all the roots of the characteristic Eq. (14) have
negative real parts at any single point of the' region ? >_ 0, a ,> 0. We choose as an example the point with the
coordinates ? = 0 (a is some positive number). In this case, the characteristic Eq. (14) will have the form
P~1cD(P)
Let us assume the contrary: suppose that Eq. (20) has roots with a positive real part and that p = u + j u is one of
these roots (Rep = u > 0). We substitute p = u +jv in Eq. (20) and we separate the imaginary and real parts. As
a result we obtain the system of identities:
where
U=aA u{1Re~(u{jv)
[u~1Re @ (uf1v)]2~[vImp (u~Iv)]2 ,
V=aA vfIm~(u{jv)
[u{1Re ~ (u} jv)]2+[vImcp (u+jv)]2 .
According to inequality (16), U > 0 and, consequently, the lefthand sides in Eq. (21) are always positive. This
latter shows that whatever be the signs of v and V, it is not possible to satisfy simultaneously the identities of (21 ).
Consequently, the characteristic Eq. (20) has no root with a positive real part and. the point of the ? , a plane which
we selected belongs to the region of stability. Thus, stability over a small region is proved.
Reactor without Delayed Neutrons
The resulting (nonlinear) system in this limiting case has the form:
~1 . dt _
dz
di =zinz}=ay.
It is easy to demonstrate here the stability of the unit being considered in relation to arbitrary deviations of
the variables from the equilibrium state, i. e., overall stability. We compile the transfer constant G(p) from power
to reactivity, taken with the reverse sign. To an accuracy of up to constant positive coefficients
G (P) = 1
p {1 cD (P)
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According to the VeltonSmets criterion [10], it is sufficient for. stability of the reactor that
Re G (jw) ~ 0 for all values of c,~ ~ 0.
After substituting p = jw in Eq. (24), we obtain
Re G (~ 1Re ~ (jw)
(1 )=[1Re~(I~)l2![c~lrrcQ~(j~)]2>O
by virtue of Eq. (15). Consequently, overall stability is proved.
The author thanks N. A. Zheleztsova and E. F. Sabaeva for critical comments and interest in this work.
(25)
1. W. Ergen, J. Appl. Phys., 25, 6, 702 (1954).
2. W. Ergen and A. Weinberg, Physica, 20, 7, 413 (1954).
3. J? Fleck, BNL357 (1.955).
4. R. Figueuredo, Report No. 1815, presented at the Second International Conference on the Peaceful Uses of
Atomic Energy [Russian translation] (Geneva, 1958).
5. Yu. R. Kharper, Basic principles of fission reactors, Chapter 10 [in Russian], Moscow, Gosatomizdat (1963).
6. M. A. Schultz, Control of nuclear reactors and power plants, McGrawHill (1961).
7. B. N. Devyatov,. Dokl. AN SSSR, 130, 68 (1960).
8. A. B. Vasil'eva and V. F. Butuzov, in the collection "Numerical methods of solving differential and integral
equations and quadrature formulas [in Russian], Moscow, Nauka (1964).
9. Yu. I. Neimark, Stability of linearized systems [in Russian], Leningrad Air Force Engineering Academy,
Leningrad (1949).
10. H. Smets, J. Appl. Phys., 30, 1623 (1959).
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The aircraft Kanchenjanga crushed on the slopes of Mt. Blanc on January 24 of this year. There were no.
survivors.
Several days earlier the renowned Indian physicist Homi Jehangir Bhabha, on his way to a meeting of the
scientific consultative council of the International Atomic Energy Agency, had changed his ticket from a January
22 flight to a January 24 flight ... Who is capable of predicting his own fate ? Homi Bhabha was among the
victims of the tragedy occurring on the slopes of Mt. Blanc.
News of his death profoundly moved all of us who had the pleasure of becoming acquainted with this out
standing man, talented physicist, prominent organizer of India's atomic science program, consistent fighter for the
peaceful uses of atomic energy,. and profound and able connoisseur of literature, sculpture, and music.
The mutual acquaintance of Soviet physicists and Homi Bhabha was by written word at the beginning. In
1937 he published, jointly with W. Heitler, work on the cascade theory of electronphoton showers in cosmic rays
[13]. This theory became the basic theory for understanding the behavior of the soft component of cosmic radiation.
Other contributions by Homi Bhabha dealt with a topic of high current interest, the theory of mesons and particles
with higherorder spins [46]. He was the first topoint out the fact that a moving meson has a longer lifetime than
a meson at rest. The famous "twin paradox" of Einstein's relativity theory was carried over from the realm of
theoretical abstraction to phenomena observed in reality.
Only very recently, physicists of the Joint Institute for Nuclear Research returned to a work of Homi Bhabha [7]
in their study of the structure of the meson, to gain insight on the scattering of particles of spin t/2 by particles
of spin 0.
The scientific achievements of Homi Bhabha were given their due when he was elected member of the
British Royal Society (1941), and honorary member of the Royal Society of Edinburgh (1957). He was awarded the
Adams prize (1942) and the Hopkins prize (1948).
In the postwar period, Homi Bhabha distinguished himself as an outstanding organizer of Indian atomic
science and engineering. This was a turning point in the development of physics when the scale of physical experi
ment underwent a transition from the scale of the laboratory bench to the scale of modern reactors and accelerators,
and the staffs of physics institutes expanded from several dozen members to many hundreds and even thousands.
Homi Bhabha correctly evaluated the significance of this turning point and was convinced that his own home
land was capable of playing its part creatively in the contemporary scientific and technical revolution.
When one of the public officials responsible for atomic science attempted to prove the impossibility of the
developing countries mastering atomic science and engineering before traditional and older stages of science and
engineering had been developed, Homi Bhabha protested .vigorously against this variety of shortsighted snobbism.
The Institute of Fundamental Research was founded in Bombay in 1945 on the initiative of Homi Bhabha.
Characteristic traits of the initiator of the institute are manifested in the style of the institute. The institute is not
only equipped with modern instrumentation, but is embellished with modern literature and sculpture in a delicate
and tasteful manner. Art and science, combined here by the deliberate design of Homi Bhabha, serve to create an
atmosphere of intellectual culture on a high level.
Not far from Bombay Homi Bhabha founded a second center, the atomic center of Trombay, which he viewed
as providing a foundation for the development of India's nuclear power program.
In this "Sturm and Drang" period of postwar atomic science and inc]ustry, I had the opportunity to become
personally acquainted with Homi Bhabha who twice visited the World's First Nuclear Power Station at Obninsk
following the visits of Jawaharlal Nehru and Indira Gandhi. In 1955, Homi Bhabha chaired the first international
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 78, July, 1966
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conference on the peaceful uses of atomic energy at Geneva,
where the leading nations informed the world of their achieve
ments in the development of atomic power. It was then for the
first time that the veil of secrecy surrounding the work of atomic
scientisu was lifted arid that these scientists, already grown
accustomed to lack of communication with each other, found to
their surprise that scientific truth, like gold, is the same no
matter in what part of the earth it is mined.
At that time Homi Bhabha represented a country in which
most of the necessary power was furnished by human labor
and buffalo.
What was it that placed Homi Bhabha in the chairman's
seat at the famous 1955 conference? My. feeling is that the basis
for the deep respect accorded to Homi Bhabha was his profound
faith that the great conquest of human intellectthe mastery of
the fission chain"reaction in uranium and plutoniumwill be
used only for the welfare of mankind, and not for war, destruction
and annihilation.
Homi Bhabha remarxed more than once that India "has the knowhow to make an atomic bomb, and has the
necessary materials, but will not use them for this purpose."
Even at the first Geneva conference, Homi Bhabha expressed his conviction that in the not too distant future
mankind will be in possession of an almost inexhaustible source of energythe energy of thermonuclear fusion. Now
we are less optimistic about that, but work is proceeding ahead, the search is being continued, and it would be
incorrect to think that these hopes must be abandoned.
Homi Bhabha's profound faith in the high purpose of science, his conviction in the triumph of reason, clearly
flowed from the fortunate combination Hof high level of scientific culture and the traditional spirit of Indian wisdom,
a humanistic and peace loving wisdom which gave birth to the famous "Panch sila" principles.
Homi Bhabha had a deep understanding of the fact that the end does not justify the means. There are bounds
beyond which the means will destroy the very essence of the end. The use of atomic weaponry is just such a means,
no matter how "important" or how "noble" the ends.
Homi Bhabha took an active part in the work of international organizations. He was a member of the scientific
consultative council of the International Atomic Energy Agency (IAEA), where he actively defended the interests
of the developing nations.
For several years he headed the Presidium of the International Union of Pure and Applied Physics (IUPAP).
As President of this body, Homi Bhabha exercized great tact in combining the interests of persons representing
different nations, different political systems, and different races. It was always a pleasure to me to see in him.
the prototype of the man of the future, with a deep understanding of the interests of mankind and a capability of
standing above the temporary but tragic bounds which separate mankind today.
We shall always retain a shining memory of Homi Bhabha.
This article was reprinted from Uspekhi fizicheskikh nauk 89, No. 1, 173
(1966).
1.
LITERATURE CITED
H. J. Bhabha and W. Hettler, Proc. Roy. Soc., A 159, 432 (1936).
2.
H. J. Bhabha and S. K. Chakrabarty. Proc. Ind. Sci., A15, 464 (1942).
3.
H. J. Bhabha and S. K. Chakrabarty, Phys. Rev., 74, 1352 (1948).
4.
H. J. Bhabha, Proc. Roy. Soc., A166, 501 (1938).
5.
H. J. Bhabha, Rev. Mod. Phys, 17, 200 (1945).
6.
H. J. Bhabha, Phil. Mag., 43, 33 (1952).
7.
H. J. Bhabha. Proc. Roy. Soc., A164, 257 (1958).
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A function is derived from the kinetic equations of nuclear reactors that can be used in the deter
mination of the variation of the multiplication coefficient if the variation of the neutron density is
known, and also in the derivation of the law of variation of the multiplication coefficient that will
yield a given variation of the neutron density.
It is known [1] that the dynamics of the processes taking place in nuclear reactors are governed by the
kinetic equations
N
do Keff 1Keff n ~,?c?
at  t +~i = =+S~
i=1
dtL = ~z Keff n ~tct (i =1, 2, 3, ... , N),
where n (t) is the neutron density, ci (t) and ~i are the concentration and decay constant of the radiators of delayed
neutrons of the ith group, i; Bi is the field of the delayed neutrons of thei.thgroup, is S and ~ Si is the total
i ,
field of delayed neutrons, l is the mean life of prompt neutrons, Keff is the effective multiplication coefficient of
the neutrons, and s(t) is the strength of extraneous neutron sources.
The kinetic equations are usually solved to determine the law of variation of neutron density if the multiplica
tioncoefficient varies according to a given law, i. e., a functional n {Keff (t)} is found. It is of interest to find the
functional Keff {n(t)} which can be used: 1) for 'the determination of Keff when the neutron density is known for
all preceding times; 2)in the planning of optimum systems of automatic control tofind the law of variation of Keff
for which n(t) varies according to a given law ns(t); 3)in the determination of the characteristics of the executive
mechanisms and of the absorbing rods ensuring a. given law of variation of the neutron density.
The problem of finding the functional Keff { n(t)} is posed and solved in [1] for linearized kinetic equations.
In [2] this problem is solved for a special case (considered below), but the method used cannot be employed to find
the desired functional for l = const. In the present work we give a complete solution of the problem.
We consider a reactor controlled by influencing the absorption or dissipation of neutrons. In this case, as
shown in [3], Z is not constant but depends on Keff
Z = AKeff
where the generation time A is constant. The values of A and l are identical in the critical case.
If this expression for l and the reactivity
Keff 1
~ Keff '
are used, relations (1) and (2) yield
N
do e~ n + ~1 ~i~Z ~ s~
at  A L
ati  ~i n  7~ici (i =1, 2, 3, ... , N).
W e assume that the reactor is in equilibrium fort < 0, i. e.,
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 913, July, 1966. Original article submitted
November 20, 1965; revised February 2, 1966.
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0,025 plt) 0,75
 0,05 0,5
0,075  0,25
/zrt~
' n 4
there is in general no analytic solution,altho.ugh we can find a solution with any desired degree of accuracy. Numer
ical solution is not required in practice, however, since if we use the fact that S ? 1 we can determine the
functional analytically with sufficient accuracy.
Infact, if we neglect terms of the order of S compared with unity in (16) and (1,7), we can obtain the.,relation
N t
4K (t)= n(t) ~l ~ dt S/ ~"~ ~t ~ dr exp[7~i(t~c)]di~
i=1 0
after some transformations,
To find the next term in the expansion in powers of S> we leave out the constant component and introduce
a correction function. This operation yields an expression for ~ (t) with a precision up to terms of the order S:
N
~ (t) ? (1 + ~) S (t) . ~ ~,~t exp [ =7~it]. (21)
i=1
Formulas (19) and (21) coincide in the singlegroup approximation.
Substituting the expression (21) for ap(t) in (17), we obtainthe following formula with the same accuracy:
N t'
.,K (t) = n (t) ~l (1~ ~) ~ at  s) ~ l ~' ~~~t ~ s (i) exp [  ~i (t 'c)] d~c
i=1 0
t N N
+ ~ d~ { ~ ~t exp [ 7~L (t z)] [ 1} ~~r~t (tt)~ ~k ~k+~a ta;i ] }d~r
0 i=1 k~i
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N
+ ~ (1 + Tito)
{1exp [  \~i
t
+ o/tiJ~
X exp [  ~i (t = ti) l ,
i=1
t < 0;
OGt TK, then the resultant rate of condensation is given by
formula
b'm = fi 1 (nr)y~  n1oo (TH) l + 2 f2 (n2)y=0  n2oo (TK)
IL 2nm 1 4nm
~kT x ~k7 Ec
ft =~2aai fz= )zaaz (see [6, 7]) (14')
In the particular case when al = 1 and a2 = 0, we have f t = 2; f 2 = 0, and
i+
qm=2
lnm
kT'rc
In the derivation of (14), (14") and (32) (vide infra) we assume for simplicity that (T~ ~ ,/ TK . If gm?gm max?
the error due to this approximation is small. Diatomic vapor molecules, brought to the condensate surface by con
vection currents in the vapor. are reflected from the condensate surface and diffuse in the opposite direction to the
convection current. The concentration of diatomic molecules in the vapor therefore decreases with increasing
distance y from the condensate surface, and when y > ~ it tends to the equilibrium concentration n2~ (Tn?o), which
depends on the temperature of the saturated vapor at an infinite distance from the condensate surface. (Fig. 2). The
concentration of diatomic molecules near the condensate surface is higher than the equilibrium concentration n2~
(Tn,~, and therefore endothermic dissociation of diatomic molecules will take place in the vapor phase, causing
supercooling of the vapor.
During evaporation, the concentration of diatomic molecules in the vapor increases with increasing distance
from the liquid surface, tending towards the equilibriui concentration n2~ .Since the concentration of diatomic
molecules near the liquid surface is lower than the equilibrium value, dimerization must occur in the vapor near the
evaporating liquid. The heat liberated by this reaction superheats the vapor. Thus, in the scheme adopted, there
must be a positive temperature gradient in the vapor during evaporation. As shown by the solution to the diffusion
problem which we shall give below, the dimensions of the region in which the main concentration and temperature
changes occur depend on the temperature of the saturated vapor and the direction and magnitude of the resultant
mass transfer flux qm. For example, for sodium with saturated vapor at 773? K and evaporation rate qm = 1.5 ? 1020.
atoms/cm2 ? sec (thermal flux q = 233 kw/m2), the. size of this region is of order 10 cm. Note that the boundary
conditions are not used in the derivation of this size. It is therefore independent of the absolute value of a2.
The distribution of the diatomicmolecule concentration can be found by solving one of the differential
equations
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t i~ i
D1 d2 2 ~ wl do ~ do ~~
dy dy dt
d2nz dnZ dnz
Dz dy2 ~ wz dy ~ dt  0
using the condition that the total pressure is constant at all points in the vapor phase:
Po = Pi I Pz = n1kT { nzkT = nokT = const,
n! ~ nz = no = const.
The lower (minus) sign attached to the convective term in (15).and (16) refers.to the case of evaporation. Hence
we find dnt _ dnz
dy dy (18)
Substituting from (18) into (15) and remembering that ~T1=  2 dz , we find that
D, `~ry? _~ w, `Gay } 2 ~dt = 0. (l s)
Let us now write down the boundary conditions for (16). When y = 0 there is no resultant flux of diatomic molecules
through the phase interface, because the coefficient of condensation of diatomic molecules a2 = 0. It follows that
the convective flux of diatomic molecules must, when y = 0, be equal to the diffusion flux of diatomic molecules
flowing in the opposite direction, i. e.,
dnZ1
I w2 (nz)y=o . Dz dy Ju=o? (20)
The convection velocity wz is found from. the condition that the resultant mass flux qm (atoms/cmz ? sec) is constant
for all points in the vapor space,
? D, ~yi f 2Dz dy { wlnr ~ 2wznz = q,~ = const. (21)
Using (17) and (18), and remembering that Dl = 2Dz and that wt = 2wz, we can simplify (21 ):
2wzno = qm = cotrst, (22)
whence
The second boundary condition is
Thus we have to solve the equation
4m.. 
wz = 2n  const.
0
nz ~ nz~ (Tn~) when y ~ oo .
D2 d? 22 ~ w2 dn2 +dn2 ` O
dy dy di
with boundary conditions (20) and (24). We linearize (25), using (9). We get
den u;Z do B
dy2 ~ Dz ? d y } Dc n = 0.
r d 3 lli~ \ .y ~ lli~ J
i d,~2 I ~i;r ~nl  n~ n2n1J I }n2nz~ _ ~'r L `~nloo T nz (nlaonZoo)
ll L
Expression (26) corresponds to the characteristic equation
1 12 u; 1 B
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1_ w2 w2 2 B ~ 1 w2 w2 2 B
l1  ~ 2Dz+ ~(2Dz) Dz ~ ~' lz.  ~ 2Dz C2Dz) . Dz .
The general solution of (26) is of the form
When y  ~, ny > nZ,~ and n ? 0, so that Cl = 0 and n = CZ ey/lz, or, returning to~our previous notation,
nznaw = CZeY/lx. When y = 0, (nz)y = o nt ~ = CZ and
nznz??= ~(nz)y=o nzro] ev/12.
Differentiating (29),
But, according to (20),
dn2 _ 1 ~
dy I(nz)y=o  nz??] lz ey/ a
it
dy y=o=[(nz)y=onz~] l
2
dr.L 1 w2 (nz)yp
C dg / r=o  ~ Dz ?
n~~
y=~ = f ~ wzl~
Dz
(lz < ~)
From the constantpressure condition (17) it follows that
n1~ (Tn~)  (ni)p=o =_ (nz)~=o  nz~ (7'?~).
Onph = n1~ (T,,~)  (no)r=o,
~n~, _ (ni)y=o  n1~ (Tx); ~IPh _ (%',~),~=o  Tt;,
~n = Ondc I Onp~ n1~ (T,~~)  n1.,, (T?),
4T = ~Tdc ~ 4Tph.
The subscript do denotes quantities associated with the diffusionchemical resistance. The relative concentration
difference arising from the phase transition can be found from (14" ):
4m Lnm q?z '/ 2tcnz
On ~ _ ~ 2 ~ kTx ,~ f 2 V kTn~ ' (32)
Knowing nl,~ as a function ofTao (see the table) we easily go from the concentration differences to the con?e
sponding temperature differences.
For the case of condensation and evaporation of sodium with condensation (evaporation) rate qm = 1.5 ? l O20
atoms/cmz ? sec (thermal flux q = 233 kw/m2) we calculated the concentration differences ~trdc, anph, and On,
and the corresponding temperature differences OTdc, GTph, and DT. The table gives the initial data and the course
and results of this calculation.
The diffusionchemical resistance depends markedly on the kinetics of the dimerization reaction. Unfortun
ately, we have no data on the kinetics of this reaction or on the possible variation of a2 with the degree of deviation
from equilibrium, qm/qm maxi the changes of liquid structure with temperature, and other factors unknown to us,
and so were unable to analyse this process in more detail.
Nevertheless, we can assert that at pressures near to atmospheric the coefficient of heat transfer is very large
(more than 150 kw/mz ? deg), even allowing for diffusionchemical resistance (of course, in the absence of impurities,
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noncondensing gases and other extraneous factors hindering heat transfer). From the table it will be seen that for
the chosen scheme of evaporation (a2 = 0) the diffusionchemical resistance must increase with decreasing saturated
vapor pressure. This is explained by the sharp retardation of the chemical reaction which occurs when the pressure
is reduced. However, measurements [9] of the temperature field in the vapor near the condensate surfaces of con
densing potassium and sodium have shown that at low pressures (1100 mm Hg) there is no diffusionchemical
resistance, despite the fact that there are quite a lot of diatomic molecules (112%) at these pressures.
In this pressure range, much sinallei' amounts of noncondensing gas (argon) give a diffusion resistance which
exceeds the phasetransition resistance by a factor of ten, and leads to the appearance of a temperature gradient in .
the layer of vapor near the liquid surface. Such gradients weie measured by the present authors in experiments on
the condensation of mercury and the alkali metals. The absence of diffusionchemical resistance for pure vapor at
low pressures shows that at these pressures the coefficient of condensation of the diatomic molecules is close tbunity:
At low pressures evaporation proceeds via libera'tiori from the liquid surface of monatomic as well as diatomic
molecules. If the accepted scheme of evaporation, which entails dimerization in the vapor, is correct for high
pressures, there must .be a transitional region in which qq changes from zero to unity.
1. Symposium: "Liquid Metal HeatTransfer Agents," translated under the editorship of A. E. Sheindlin,
Moscow, Izd. inostr..lit. (1958).
2. E. L`. Shpil'rain and E. I. Asinovskii, Inzh.fiz. zh., V, No. 4 (1962).
3. F. Metzger and E. Miescher, Helv. phys. acta, 16, 205, 323 (1943).
4. O. Knacke and I. Stranski, Progr. Metal. Phys., 6, 181 (1956).
5. Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and HighTemperature Hydrodynamic Pheno
mena, Moscow, Fizmatgiz (1963), p. 285.
6. R. Ya. Kucherov, and L. E. Rikenglaz, ZhETF, 37, No. 1 (1959).
7. R. Ya. Kucherov and L. E. Rikenglaz, Dokl. AN SSSR, 133, No. 5 (1960).
8. V. I. Subbotin et a1.,Teplofizika vysokikh temperatur> 2, No. 4 (1964).
All abbreviations of periodicals in the at,ove bibliography are letterbyletter translitera
tions of the abbreviations as given in the original Russian journal. Some or all of this peri
odical literature may well be available in English translation. A complete list of the coverto
cover English translations appears at the back of the first issue of this year.
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
THERMAL DEFORMATION OF FUEL ELEMENTS
E. Ya. Safronov, B. A. Briskman, UDC 621.039.548
V. D. Bondarev, and V. S. Shishov
The authors calculate the temperature drops in the walls of cassette.type fuel elements under neutron
fluxes with radial gradients. The thermal deformations of the walls are measured in the working range
of temperature drops.
In the fuel elements of nuclear reactors, together with their reflectors and control or compensating rods, there
arises a radial neutronflux gradient due to splashing in the reflector or neutron absorption in the rods. Simultane
ously there is created a radial gradient of heat emission in the fuel element; for constant heat removal at the cir
cumference of the fuel element, this leads to the appearance of a radial temperature drop which causes thermal
deformation of the casing (1]. For complex fuelelement geometry, it is very difficult to calculate the deformation,
and therefore practically the only method of determining the deformation in such cases is the use of experiment. ?
To widen the scope of our ideas on the operation of fuel elements
of a model cassettetype ftiel element of hexagonal cross section.
Analytical Determination of Temperature Drops
we have studied the thermal deformation
The calculation is performed for an external hexagonal casing in the form of a thin plate. Let us write down
the equation of thermal conductivity for a thin plate (onedimensional problem) with an internal heat source:
a2T 4v __
axe I ~ 0.
(1)
aT _
C ax x=0 ~' (5)
Fig. 1. Diagram of working section. 1)Water;
2) current busbars; 3) rubber sheath; ~ 4) indicators;
5) ebonite manifold.
Qvl = gvmin [ 1 ~ L (n  1) J
(we are taking a linear heatemission gradient); and
where n is the degree of nonuniformity of heat emission, L is
the semiperimeter of the model fuelelement casing, ~ is the
coefficient of thermal conductivity, a is the .coefficient of
heat transfer from the wall to the water, gvmin is the minimum
rate of heat emission, to is the mean temperature of the cooling
water, S/V is the surfacetovolume ratio, and T is the temper
ature of the casing.
"Some experimental results on deformation of model fuel ele
ments, obtained at the affiliated branch of the A. I. Ioffe
Physicotechnical Institute, Leningrad, were available to the
authors of the present article.
Translated from Atomnaya ~nergiya, Vol. 21, No. 1, pp. 2226, July, 1966. Original article submitted
November 17, 1965.
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S, mmi
0, 7
4
/ ~ 4
3
~
2
1
x
/
n
?~
Fig. 2. Deflection versus temperature drop between faces 4 and 3 halfway
up the fuel element. (1)(6): Numbers of faces. )Outer casing
of fuel element; = ~ inner casing of fuel element, face 4. Experi
mental results: O, )Face 4 for outer and inner casing, respectively; 0)face 1;
x)face 3; ).face 2.
4
3
1
/
4~
i S`
~~~
~j ?' \
\\
70 20 30 40 50
Height? of fuel element, cm
Fig. 3. Distribution of deformation over height of fuel
B2 = 2 ~8 .
element. (1)(4) Numbers of faces. ) 4t=  For the range of heat emissions studied, ~To
24.2 ?C;  ) ~t = 14 ?C. Notation of experi varies from 12.5 to 20.2 ?C when n = 1.5, and from
mental points: same as for Fig. 2. 25 to 40.4 ?C when n = 2.
From what has been said, it follows that the thermal deformation of the model fuel element must be studied
for temperature drops up to 40? C. With constant coefficient of heat transfer a across the gap, the maximum tempera
ture drop must occur in the outer casing. However, since the inrier casing has lower rigidity, the point of maximum
drop does not necessarily coincide with that of maximum deformation. Thus'the deformation must be measured
both for the external jacket and for a possibly greater number of internal jackets. Since the model is an exact copy,
we can quite correctly transfer our results to the prototype fuel element.
Figure 1 is a diagram of the experimental equipment. The model was heated by direct current from an AND
5000/2500 set (nominal power 30 kw). The model was cooled by means of circulating water. To create the required
temperature drop, the model was divided into two halves in cross section, one cooled and one not cooled.
The head and foot of the model were of ebonite. The water pipes were so arranged as to cool the current
leads as well as the model. The current busbars were made of packets of 0.5 mm thick copper foil, sufficiently
flexible to eliminate any influence on the rigidity of the model.
uT
C ~x )xL 
then (1) has the solution ,
~`4(n1)b_4(n1)S, eBL1
2a LaB eBL+1 '
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a
b?
c
S
2 6
4
2
4
2
S 1 5
'S5?
3
1
t=85?C
3 1
t=
16,5 C
173 C
7?C
27?C
21 ?C
Fig. 5. Distribution of deformation round perimeter of fuel element.
Points
at which
deflection
was measured
(a) Lower
cross section; (b) central cross section; (c) upper cross section. Positive deforma
tions refer to the inner casing, negative deformations to the outer casing. De
formation of inner casing refers to Ot for outer casing.
m a
b~
~~
0
8
,
~
~,
~
i
~/
f 
Q6
i
i
d:
~~~
\~
~,i
i
04
~
~
_
e_~~
_
~ ~i
_~


0,2
~~s
,
O
f 6
5
4
1
e 3
Number of
0,2
face
b
0
4
,
a
9
s
~
,
Fig. 4. Distributions of temperature and deflection in
central cross section of fuel element, round the peri
meter. )Deflection of fuel element;  
~_.) temperature distribution. Curves with the same letter
were measured in the same experiment. Designation of
experimental points: same as Fig. 2.
measurements were made so as to record the generator
temperature drop and current strength:)
The casings were welded together alternately
in the upper and lower parts of the assembly, so that by
connecting them in series the total electric resistance
should be as large as possible. The resistance of the
model was 3.7 ? 104 ohm at t = 0 ?C.
The fastening of the lower end of the model was
exactly the same as the attachment of the fuel ele
ment in the support grid of the separator. The upper
part was fixed down with special bolts allowing for
free movement in a vertical direction. In a slot in the
base was a slidebar to which were attached the gauges
(type ICh, scale division 0.01 mm) for the deformation
measurements.
The depth of camber was measured for each face
of the model. The wall temperature was measured by
means of 15 chromelcopel thermocouples of dia
meter 0.4 mm arranged in three cross sections at differ
ent heights.
Experimental Method
When conditions (as read on a recording device)
were steady, we measured the temperatures, defom~a
tions and voltage drops ~U in the model. (The ~U
currents in order to calculate the relation between the
Owing to the comparatively high temperature coefficient of the resistance, the current in the model's peri
phery changed quite appreciably (with the temperature drop). In these conditions, the current strength J through
the model was given by
L
J 0U dz
2LRo ~ 1{ ~t (x)
0
Ro the resistance of the casing at 0 ?C, and t(x) the
In the actual conditions we took as an approximate valve of the integral the expression
where S is the' temperature coefficient of the resistance in ?C
measured temperature distribution on the periphery.
0,
6
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8
,r ev 1
'j'".12Ro ~ i+~ti
t=~
We made a spot check on the use of (9) to evaluate the integral in (8), by
planimetry of the curve 1/[1 + R t(x)]: the error made by using (9) was less than 2?Jo,
f The apparatus was constructed so as to allow measurement of the deformation
of the first internal casing on the uncooled side. For this purpose, after a series of
Fig. 6. Cross section of fuel tests on thedeformation.of the external casing on the uncooled side, sets of three
element. 16; numbers of holes were drilled on the axes of the faces at the three heights at which the measure
faces. ments had been made. Repeat measurements in the same conditions, made in order
to test for changes of rigidity of the outer casing due to the drilling, showed that
there were no appreciable changes in the deformations. We made simultaneous measurements of the deformation
of the outer casing (on the cooled side) and the inner casing (on the uncooled side) under various conditions. As no
temperature measurements were made on the inner casing, the temperature drops were determined by calculation
in this case (see Appendix). The appropriate curves were constructed from the calculated relation between the
temperature drop and the current strength. The results of the calculations were found to be in good agreement with
the experimental data for the external casing (et =12?C for J = 3500 A, Dt = 21?C for J = 4500 A ). The cal
culated results could thus be regarded as trustworthy and could be used for determining the temperature drop in the
inner casing. In practice, the curves of Ot versus J were almost the same for both casings; this is explained by the
fact that the greater heat emission for the internal case was compensated for by the smaller distance between.
.opposite faces of the casing, i. e., the corresponding reduction in thermal resistance to heat flux from the uncooled
to the cooled section.
Discussion of Results
The results of the deformation measurements are plotted in Figs. 25. Figure 2 plots the deflection of the
wall, S, in mm, versus Ot, in ?C, for the cross section halfway up the model. Figure 3 shows the variation of the
deflection with height for the various faces of the model. Figure 4 shows the deflection around the perimeter of the
casing halfway up the model, for various values of Ot. It also gives the corresponding temperature curves. Figure
5 gives the results of the simultaneous measurements on the internal and external casings for various cross sections
around the perimeter for various values of Ot.
The straight lines in Fig. 2 were obtained by processing the experimental results by the method of least
squares [2]. This figure also gives the relation between Sand Ot for the internal casing at the middle cross section,
face 4. As seen from this graph, in the range of Ot under examination, the deformation of the inner casing was
about 20% greater than that of the corresponding face of the outer casing, i. e., the inner casing was less rigid than.
the outer one.
It should be noted that in the prototype the specific heat emission in the inner casings is practically equal
to that in the outer ones, while the temperature drop is less. In the experimental apparatus the current strength was
the same in both casings (which were connected in series), and therefore the specific heat emission in the inner
casing was the higher, although the temperature drops obtained were practically the same.
It must be pointed out that the two opposing factorsreduction in rigidity and decrease in temperature drop
for the internal casingcompensated each other to some extent, and therefore the deformations of the external and
internal casings should be approximately equal. In actual fact, the values of OT calculated from (7) confirm the
present authors' assumptions.
As will be seen from Fig. 2, in the region plotted there is no tendency for the curve of S versus Ot to deviate
from linearity, i. e., it is possible to extrapolate to the neighboring regions.
From Fig. 3 it is seen that there is a certain asymmetry in the distribution of deformation with height of the
model. This is due to the different possible ways of fastening the model (two degrees of freedom at the upperattach
ment and one at the lower),. which are also characteristic of the fastening of a fuel element in the reactor.
The deformation and temperature distributions round the central perimeter of the outer casing, shown in Fig. 4,
show that the corresponding temperature and deformation profiles are symmetrical; as ~tdecreasesthecorresponding
profiles become smoothed out. The rigidity nodes (points of zero deformation) approximately coincide with the
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boundaries of the cooled and uncooled halves. The scatter for varying Ot of the points corresponding to the rigidity
nodes is due to inaccurate setting of the gauges on the central axes of the faces. This error is characteristic of the
temperature curves. In this case a specially large error can occur for faces 6, 1, 5, and 2, because the derivative
dt/dx is a maximum on the joints between the cooled and uncooled parts.
In conclusion, we must note that all the deformations were elastic.
1. W e have devised a method of simultaneous measurement of the thermal deformation of the different
casings of a model cassettetype fuel element.
2. W e have obtained calculated data on the temperature drops in fuel elements as functions of the magnitude
and degree of nonuniformity of the heat emission.
3. We found that with temperature drops of ~ 25? C the maximum deflection in the central cross section is
0.60.7 mm.
4. W e derived theoretical formulae for the temperature drop in terms of the current strength for an electrically
heated assembly (allowing for the temperature dependence of the ohmic resistance).
5. Since the gaps between the casings are small, the deformations obtained are very substantial, and show
that the deformation behavior of a fuel element in a reactor must be studied (in theoretical and experimental re
search on heat transfer in the distorted cell). It is quite probable that temperature deformation of the fuel elements
will be the factor limiting the power of a reactor.
Appendix (calculation of relation between temperature drop and current strength)
A solid hexagonal section of thickness S, height H, and perimeter 4L (where L is 3/z of the length of a side)
is electrically heated by a current of strength J.
The section is divided by an impermeable diaphragm (Fig. 6). Section I is cooled by air with heattransfer
coefficient cxl; section II is cooled by water with heattransfer coefficient az. We are to determine the stationary
temperature profile round the perimeter, given that H is infinitely large; the air temperature (mean) is t', the water
temperature (mean) is t".
We write down. the equation of thermal conduction for regions I and II:
S
8 t 4vai y (tt')
2
I. axe } ~ = 0,
8 t 4ua2 V (tt?)
II. axe } ~ = 0.
S 2
H ere V S
Let us write down the boundary conditions.
3 (cf. Fig. 6). Then (d t/a x)x = n = 0.
At points e and f we must have
We take the origins of coordinates for the two regions on
ti = trrr x = ~ L;
We introduce the notations
A=(0.86 Ro/~)JZ, Ro = resistance of jacket at t = 0? C;
2 S1A~ A~2a1 8 z 2 S A~ A~Laz b
z
al _ ~ az = ~ ; b1= ~ z = ~
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2 8 A~
If ~ _ ~ ~ 0: ,the solution of (10) and (11) is
/ai_b2
~t = tp  tg = I ai bi
a
28AS
while if ai =  , ~.
1 b~ sh b1I,
+ a1 ~ sh a1L
b1 sh biL '
ch b1L ~ Qt ' sh a1L oh a1L.
b1 sh b~L _ 1
a2 bZ ai ~ sh a1L ._ 1
Ot=tptg = 2 
C al bl b, sh b1L ctg aiL  ch b1L
a1
The relations between ~t and J found from (12) and (13) have been confirmed by experiment.
1. A. Rapier and T. Jones,. J? Nucl: Energy, 19, A/B, 145 (1965).
2. R. S. Guter and B. V. Ovchinskii, Elements of Numerical Analysis and Mathematical Processing of Experi
mental Data, Moscow, Fizmatgiz (1962).
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STUDY OF THE. SPECTRA AND DOSES CREATED IN THE IRON WATER
SHIELDING OF A MONOENERGETIC NEUTRON SOURCE
O. A. Barsukov, V. S. Avzyanov, UDC 621.039.58:539.125.5
Manygroup calculations were made for the penetration of neutrons, emitted from monoenergetic
sources, through water, iron, andwateriron systems of finite dimensions; the results of these cal
culations are presented. The neutron spectra resulting from the passage of such neutrons through
water and iron shielding layers were calculated on the twentygroup diffusiontransport approxi
mation. Detailed attention was paid to the highenergy part of the spectrum; certain peculiarities
in neutron migration and moderation processes in shielding of the type in question were elucidated.
Dose curves D(r) were plotted for neutrons of various energies.
By using the superposition principle, the results enable the neutron spectrum to be determined
for sources having any arbitrary spectrum.
Presentation of the Problem. and Method of Calculation
In developing optimum neutron shielding it is important to know the structure of the inteinal neutron field.
In order to solve this kind of problem, the real source, with its complex spectrum, may be replaced by a set of
monoenergetic sources. This approach makes it possible to observe. some important effects which are difficult to
observe when ?studying integral fluxes created by sources with complex spectra. Moreover the results obtained by
studying the neutron distributions of monoenergetic sources are easy to interpret physically.
The problem reduces to the consideration of a monoenergetic neutron source screened by a layer of finite
thickness. The spaceenergydistribution of neutrons inside the shielding is found. The following shielding com
positions are considered: 1)water shielding 62 cm thick; b)iron shielding 62 cm thick; c~ironwatershielding, the
iron forming an inner layer 10 cm thick. and the water forming an outer 52cm layer.
The basis of the calculations is a multigroup diffusiontransport approximation to the kinetic Boltzmann
equation
(1)
where cp i is the integral neutron flux of the ith group, Di is the diffusion coefficient, Ei is the neutron transfer
cross section (i. e.> that characterizing capture and transition to lower groups), f i is a neutron source including
(in general) both source neutrons and neutrons brought into the range of the group as aresult ofslowingdowri processes.
Energy Groups
Group
~ M VgY range,
I Group
I Energy range,
I
10,8
9,8
XI
1,5
1,1 MeV
II
9,8
9,4
XII
1,1
55 keV
III
9,4
7,75
XIII
55
28 keV
IV
7,75
7
XIV
28
15 keV
V
7
6
XV
15
6 kev
VI
6
5,45
XVI
6
1,5 kev
VII
5,45
4,8
XVII
1,5
450 eV
VIII
4,8
4
XVIII
450
220 eV
IX
4
3,1
XIX
220
6 eV
X
3,1
1,5
XX
6
0,025 eV
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 2735,July, 1966. Original article submitted
September 16, 1965; revised March 2, 1966.
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N,.rel. units
20 r, cm
c:
x
X
x
x
X
Iron
Water
Fig. 1. Radial distribution of neutrons of various energies: A)In water; B)inironwater shielding, a)First neutrons;
b) neutrons with energies between 5 and 220 eV; c) neutrons with energies between 0.025 .and 5 eV; x , O) expeti
10' 10r
r=1C' T
20
30
x
x
x
x~
x\
%
60. .
x
x
x
~
x x
x
x
x
x
x
10P
r=10
x
2G
x
x
~I
x
x
1
R
x
x
x
x
x
x
x
x
Fig. 2. Neutron spectrum in water for a point source (a) and in iron for a plane source (b).
(r is measured in cm.)
The system of Eq. (1) was solved numerically by the method of differential factorization [1]. In order to
allow for the transformation of the neutron spectrum arising from migration in nonmultiplying media, we used the
method of successive approximations (iteration over the spectrum). The latter reduces to a refinement (with respect
to a variable spectrum) of the group cross sections and group diffusion coefficients defining the constants of the
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103
1,2 1,0 0,8 0,6 D,4 Q2 0
Lethargy
~
~
r=
2
8
14
0
0
yG'
0 2 4 6 E
Lethargy
b
6 8 10 12 14 16
Lethargy
104
103
8 10 12 14 16 18
Lethargy
c
Neutron spectrum in water. Source: a)In group I; b)in groupIX; c)in group XIV.
(r is measured in cm.)
difference equations [2]. The Fermi spectrum was taken as the original. The variation of the microscopic cross
sections with energy and other neutron parameters were taken from [3 6]. Data from these papers were used in
setting up the matrix of elastic transitions in hydrogen and inelastic transitions in iron.
The distribution of monoenergetic electrons from the source was determined by analytic solution of Eq. (1).
This was due to the fact that there was a deviation from the exact solution of the diffusion equation when the method
of differential factorization was used at large distances from a concentrated source.
The analytic solution for a plane source in a homogeneous finite medium has the form
~_ ~r~  QzLt .
2Di
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~
~
,~
3
2
r.
g
14
N
0
0
w
?
30
o
~ G
1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0
Lethargy
. 10 f
103
a~~
lOs
lOs
1e4
103
103
102 102
2 0 2 4 6 8 TO 12 14 16 18 0 2
Lethargy
b
r=2
8
~\
1
i
I
~
~
I\
ti
4 6 8 10 12 14 16 18
Lethargy
c
Fig. 4. Neutron spectrum in iron. 'Source: a) In group I; b) in group IX; c) in group XIV.
(r is measured m cm.),
where Qi is the strength of the course in neutrons /cm~ ? sec, Li is the fictitious diffusion length of monoenergetic
neutrons in cm, ai is the thickness of the shield, 'including the extrapolation length, and r is the distance from the
source in cm.
If, however, the source neutrons diffuse in'two adjacent layers of iron and water of finite thickness, the solution
may be put in the form
_ r r
~, 1r~  QiFeLiFe Bi B LiFe + 1 gLiFe ~
iFe 2DiFe ~Bi1 Bq 1
ro t?
Bi a 1'iFe + 1 e LiFe _ r _ i _
(2a r)
~r~ = QiFeLiFe . Bi 1 Bq 1 (e 1'iHZO e L'iHgO t ~ .
tHzO 2DiFe  r0  1 (2a, rnl 1
e LiH2O  e LiH2O
r=2
8
~t
~
ti~ .
~~
~.
7 2
4 6 8 10 l
2 J
f 16 1
8
Lethargy
r=1
8
14
20
30
40
I
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~~
dui
102 102
~Fe
2'
m
~~
c
rs
~~ Z`R'
`
\
`
p`"~

,
\
,~
~
f
'~
20cm
?~D
~'~
,30~
m
1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 D 0 2
Lethargy
104
 
~~
~`
r=~
cminFe


1
2 cm
10 cm
G,cm
~Qcrn
5
10
lOf
10'1
102 102
1,2 1,0 Q8 0,6 0,4 0,2 0 0 2
Lethargy ,
6' 8 IG 12 14 1C
Lethargy
8 10 12 14 16 18
Lethargy
1~
,
s
O
IOS
/'=2;c
1
m
4
10
10
3
20/cm
10
Z
0, c
m
lO
5 8 10 1T 14 16
Lethargy
Fig. 5. Neutron spectrum in the ironwater system. Source: a}ln group I; b)in group VII; c)in group IX.
Here we have introduced the following notation
2(airo)
tai (DiFe + DzH2O ~ (DiFe DiHaO e LiH2O
L `LiFe I'iH2O ~  \ LfFe LiH2p
Bi == 2 zFe .,,_ _ . .
DiFe _ ~iHgO DiFe DiHzO 1 LiH2O
e
LiFe LiH2O /  \LiFe + LiH O
a
ro is the thickness of the first layer (Fe}; LiFe and cpiHZp are the fluxes of monoenergetic neutrons in the layers of
iron and water respectively.
~/'=20

cm in
'~
H2O
Z,~m
~_
~
10~m
_
20, cm
~
30 cm
~
i 4a,
\
..,
~
\
u
`
'
_
r
_
2cm
r 2 ~m
"'Fe
10 ~fi
0 cm
O ~
m
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8 16 24 32 40 48 56r, cm
a
lo''
0
16
24 31 40 4B 56 r, cm
b
D, mrad/h
10
2
10
10~3
le''
10_B
I
I
0
or
G p
~G ~
~
s
~
t,
cQ',~
~''
. LP
~
~
I
~
G
o J
c
~p
~
O
0
~io
.r
G
~
~G
L
12 16 20 24 28r, cm
c
Fig. 6. Doses of neutrons of various energies in water. Source: a)In group I; b)in group LX; c)in group XIV.
The calculation was made in plane geometry for twenty monoenergetic sources with strengths of 2 ? 106
neutrons/cm2 ? sec, embracing the energy range between 11 MeV and thermal energies (seeTable).
The results of these calculations enable us to find the neutron distribution in other shield geometries also.
The transformation from plane to spherical geometry (assuming apointsource center) may be effected by means
of the formula
~sph (r) 2:tL ? r tPpl ~~1)
The transformation from plane to cylindrical geometry with a filamerit source at r = 0 is effected by means of the
approximate relation
~Pcyl ~r~ ~ 1/2nL ~/r ~.pl ~r~'
where L is the diffusion length of the neutrons, and rp (r) is the neutron flux in the corresponding geometry. For
deriving the latter relationship, an asymptotic expansion of the function ko is used [7].
We compared the calculated results with our own experimental data and the data of other authors.
Figure 1 shows the radial distribution of neutrons with various energies emitted by a point PoBe source in a
sphere of water and in anironwater:system. The theoretical curve agrees closely with the experimental data.
Figure 2 a shows neutron spectra in water a't distances of 10, 20, 30, and 60 cm from the fission source. The
continuous curves correspond to the neutron distributions obtained by the method of moments [8]. The crosses
indicate the values calculated from the superposition principle on the basis of the results in the present paper. The
spectra agree closely in the range E> 6 MeV. The discrepancies at low energies are due to leakage of the moder
ated neutrons, since in the second case the medium is finite.
Figure 2b gives an analogous comparison between calculation and experimental data for iron [9]. The cal
culated spectrum is normalized to the experimental results for E = 4.8 to 5.45 MeV at a distance of 20 cm from the
source. There is good agreement for r values of 10 and 20 cm. For r = 40 cm the calculated curve lies below the
experimental. In all cases the calculated values exceed the experimental in the range En < 2 to 3 MeV; this is
apparently due to the different geometries used in experiment and theory. The experimental and theoretical curves
have the same general character.
The comparison shows that the diffusiontransport approximation gives calculated values of practically accept
able accuracy, at least in a range up to 50 or 60 cm.
o
'r
~~
w o?
.iA~ o
7P N
7
'~~
~
~. ~r ..
s ~i
o ~
_
'c
'`
~
~
~
~O ~P ~%
O c.~
O J `rs~ I
+o
~
l ~
~
?Gi
'~ ~G
J
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
X/I!_ r r
Xl~///g,ySS
s
e
2
,ke f ~O
:p?
X/,Y,Y
{,l
,
er ~22p p
~p
S
" ~'~
~~
~~
r `'
j
~
~~ ~ Q
I
~ ~
~ ~
~
~
J
~~ s
J
J
2r
~~ PJ
`0G
J
i
~~' To ~
,
~/I~f~6'r taj7o
is se
O11k
o
I
tJ
a/.
~i
~
~^~~
~~r/11O
O~~.J
,Sk
" D
PG
J
0 8 16 24 32. 40 48 56 r,.cm
c
Fig. 7. Doses of neutrons of various energies in iron. Source: a)in group I; b)in group IX; c)in group XIV.
D, mrad/h
,Total dose
I I
T
tal d
i
o
ose
n
wale
XI/ g=
\
(110,055
Me V j
\
XIII XY//!gr(550,
2Z.ke
V)
XIX X X g = (220 D, 025 e v )
105
24 32 40
b
Fig. 8. Doses of neutrons of various energies in the ironwater system.
group IX.
D, mrad/h
\`



;To
tal d
ose
\ T
otal dose in wale
\\X
XIS=(3,1;11 Me V
I I
/X (~ 31I M V
(2200,025ev)
\
\
111 XV/If a=
\
(550,221keV)
~ ~
Xlbgr(1,10,0551Mev)
\
1
10 0
Source: a)in group I; b)in group VII; c)in
Energy Spectra of Neutrons Emitted by Monoenergetic Sources
The results of the calculations enable us to trace the transformation of the neutron spectra during migration
in the compositions considered.
Figures 3 to 5 show the energy spectra of neutrons for several monoenergetic sources situated in water, iron,
and an ironwater system.
Analysis of the histograms shows that the neutron spectrum has certain characteristic features in water (see
Fig. 3, a, b, c; initial neutron energy 10 MeV, 4 MeV, and 20 keV respectively). In the highenergy range, even
"In the histograms the middles of the energy ranges are connected together for clarity. In calculating lethargy, the
standard energy is taken as E = 2 MeV.
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
near the source, the spectrum passes from the monoenergetic to the continuous (and hence softer )type. The. inver
sion of the spectrum is maintained on further increasing r. For an initial energy below 1 MeV, the monoenergetic
.source neutrons are absent even in the neighborhood of the source, which is explained by the effective slowing down
of the neutrons at hydrogen nuclei.
Analysis of histograms 4, a,b, c, shows that iniron there is a considerable softening of the spectrum with in
creasing distance .from the source. The characteristic feature in the highenergy region (see Fig.4,a) is the dip in
the curves over the range 6 to 7 MeV, later transforming into a high maximum at E < 1 MeV. This is due to the
fact that, during the inelastic slowingdown processes, the neutrons pass into the intermediateeriergy range, missing
out the values E > 1 MeV. However, further slowing down of the neutrons at the iron nuclei takes place extremely
slowly, in general as a result of elastic scattering. As a result of this, there is an accumulation of neutrons with
energy E < 1 MeV.
The neutron spectrum in the ironwater system is a peculiar superposition of those corresponding to homo
geneous iron and water shields and contains the characteristic features of both (see Fig. 5, a, b, c).
For example, for a source in the first group (see Fig. 5,a) and r = 2 cm (i. e., at a point within the iron layer),
there is a dip in the spectral curve at 6 to 7 MeV. In this case, however, the minimum is less severe than in the
case of homogeneous iron.
This circumstance implies the development of a counterflow of neutrons with energies between 6 and 7 MeV
in the twolayer system, moving from the water to the iron. Hence the effect of the water on the spectrum is even
felt at this great depth in the iron. The leveling effect of the water rises`^still more with increasing r. Thus the
curve for r = 10 cm (boundary point) is characterized by quite a small minimum in the range in question, while
a long way from the iron, in the water (r = 20 cm ), the character of the histogram resembles the analogous distri
bution in water.
In the case of a source in groups VII and IX (see Fig. 5, b, c) the histograms have smooth curves in the high
energy range, while in the lowenergy part of the spectrum the curves are much the same as in the preceding
case (see Fig. 5a).
Effectiveness of Various Shielding Compositions
The effectiveness of the shielding was estimated from the distribution curves of the doses created by neutrons
of various energies.
Figure 6 shows some D(r) curves for water. In the case of a source lying in the first group (see Fig. 6a ), at a
distance of 40 cm from the source, the total dose bf the ItoXI energy groups (fastneutron dose) is more than 30
times that of the XIItoXVIII energy groups, which correspond to neutrons of medium energy. If, however, the
source lies in group IX, the contribution of fast neutrons exceeds that of the intermediate neutrons by an .order of
magnitude (see Fig. 6, b). In all cases considered, the contribution of the slow neutrons is small.
If the source lies in the lowenergy part of the spectrum (E < 1 McV)thenthe dose falls'to zeroeven in the
source zone (see Fig. 6, c).Hence for such sources a single layer of water shielding is so effective that additional
layers of iron are superfluous.
The spectral composition of the dose in iron differs considerably from that described above (Fig.7, a, b, c).
Thus the dose distribution for a source in the first group (see Fig. 7, a)shows that the total dose is mainly affected by
neutrons of intermediate energies' (groups XII to XVIII, corresponding to energies between 1 MeV and 0.22 keV).
At r = 40 to 50 cm, the contribution of these to the total dose is almost two orders greater than that of the fast
neutrons. As regards the latter (groups I to XI, E > 1 MeV), the dose curves of these groups rapidly fall to zero with
increasing r.
The energy distribution of the doses has a similar character for all the remaining groups of sources (see F ig. 7; b,
c). It should be noted that, as the initial energy of the neutrons falls, the curves for the total dose approach the
component curves. Hence the spectral composition of neutron radiation must be taken into account for sources with
a spectrum situated above 1 MeV.
A point worth noting is the slow fall in the totaldose curve, which indicates the undesirability of using a
homogeneous iron shield.
The dose distributions for the ironwater system are shown in Fig. 8, a,b, c. We see from the D(r) curves that
a characteristic trait of these is the existence of a break at the boundary between the media, due to the redistribution
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
of the neutron fluxes. By way of example, let us consider the dose distribution for a source of the first group (see
Fig. 8, a). The curves have a considerably greater slope in the iron layer than in the water. This is because the
water slows the neutrons of this group (9.8 to 10.8 MeV) down very poorly.
The dose curve of groups II to VII (4.8 to 9.8 MeV) falls out of the general picture, being very shallow. The
point is that there is a peculiar vacuum for neutrons of these energies in iron: This creates conditions for the migra
tion of neutrons from the water into the iron, and it is this which causes the peculiar form of the curve.
The neutrons from energy groups XII to XVIII, which in the case of an iron shield constitutes one of the main
components, contribute less than 10% of the total dose in the ironwater system.
It is interesting to make a quantitative comparison of the doses in water and in the ironwater system (see
broken curves in Fig. 8, a, b, c). Thus, for fast neutrons with energies between 9.8 and 10.8 MeV, the totaldose
curves in the ironwater system lie half an order lower than in the case of pure water. This difference gradually
diminishes and vanishes entirely at about E = 1 MeV. Hence the ironwater shielding is effective for an initial
sourceneutron energy of over 1 MeV.
The detailed study of fastneutron migration in iron, water, and ironwater shielding enables us to make a .
quantitative estimate of the effectiveness of these forms of shielding for neutrons of various energies. The dose
curves presented may be used for calculating the neutron shielding associated with a source of any energy spectrum.
1. G. I. Marchuk, Numerical Methods of Calculating Nuclear Reactors [in'i Russian], Moscow, Atomizdat (1958).
2. O. A. Barsukov and V. S. Avzyanov, Atomnaya Energiya, 10, 478 (1961).
3. D. Hughes, Neutron Cross Sections, BNL (1958); Supplement, No. 1 (1960).
4. I. V. Gordeev et al., Handbook on NuclearPhysical Constants for Reactor Calculations [in;Russian], Moscow,
Gosatomizdat (1960).
5. I. V. Gordeev et a1.,NuclearPhysical Constants [in, Russian], Moscow, Gosatomizdat (1963).
6. L. P. Abagyan et al., Group Constants for Calculations of Nuclear Reactors [in RussianJ, Moscow, Atomizdat
(1964).
7. I. N. Bronshtein and K. A. Semendyaev, Handbook on Mathematics [in Russian], Moscow, "Nauka'` (1964).
8. Shielding of Transport Equipment with Nuclear Motors [Russian translation], Moscow, IL (1;361), p. 40.
9. A. P. Veselkin et al., Atomnaya Energiya, 17, 32 (1964).
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M. M. Dorosh, Ya. E. Kostyu,
V. A. ShkodaU1'yanov,_A. M. Parlag,
and A. K. Berzin
A method of differentiating between oil and waterbearing rock strata based on the difference between
the nuclear compositions of oil and water (as regards 013 content) is described. A property of N17nuclei
based on the emission of delayed neutrons is used. , ,
The separation of the oil and waterbearing components of a stratum in uncased wells is in the majority of
cases quite easily effected by electrometric methods. In cased wells, this problem can only be solved by non
electrical (e. g., radiometrical) methods.
Oxygen and carbon, by the percentage content of which water and oil are distinguished, have small cross
sections with respect to the processes usually used for the solution of such problems, and main attention in nuclear
geophysics is concentrated on the properties of other elements present in water (Na, C1, etc.). The establishment
of indirect methods by no means fully solves the problem, as is very apparent when working with weaklymineralized
waters, or waters freshened by the injection of fresh water usedfor extracting oil during the intensive exploitation of
oil fields.
One possibility. not so far studied is the use of the (y ,n)reaction of the C63 nucleus which occurs on bom
barding this with monochromatic y quanta; another possibility is the use of the nuclear properties of the O83 isotope.
This is less abundant than other isotopes (around 0.2 %), but on bombarding this nucleus with y of fairly high energy
the specific reaction Ola (y, p) Nt7 R 017  016 + n takes place*. The unstable N17 nucleus is a wellknown
source of delayed neutrons with ahalflife of 4,15 sec. Since determination of the boundaries of watercontaining
media by existing methods presents no difficulty, we have here a new principle for separating water and oil bearing
strata in these media by recording the delayed neutrons formed in the Ots(y , p) Nt7 reaction.
*Preliminary experiments show that the "next zone" does not eliminate the effect, but only necessitates an increase
in the intensity of the y quanta, since the delayedneutron yield falls by 20 to 30?lobecauseofthe"nextzone" effect.
DelayedNeutron Yields from Water and OilBearing Strata
Q,x 10'3 de
layed neutrons
Q,x l0~de
layed neutrons
Q,x 103 de
layed neutrons
ao
~
o0
o""~
o~
o
17
0,10
0,05
12,90
7,43
3,87
2,23
18
1.,57
0,86
19,83
11,81
5,95.
3,56
19
5,19
2,93
21,01
12,50
6,33
3,75
20
11,03
6,f7
23,74
14,36
7,12
4,32
21
18,88
10,72

19,69

5;92
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 3538, July, 1966. Original article submitted
January 20, 1966.
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78 >9 E,MeV
Fig. 1. Calculated curves for the delayedneutron yield
from: 1}'water; 2)waterbearing stratum (70% SiOZ +
30% HEO); 3)sand; 4)oilbearing stratum (70% SiO2 +
30% petroleum).
,1
I
2
,3
1'~
~
~
~
5
~
Fig. 2. Measured delayedneutron yields per act of y
quantum irradiationlfor:l~water, 2)waterbearing stratum,
3)sand, 4)oilbearing stratum, 5)petroleum..
petroleum, stratal water, and mixtures of sand with water
bearing strata, respectively.
The point is that petroleum contains anegligibly
small quantity of oxygen, so that on passing from the
oilbearing to the water.bearing stratum there will be
a sharp change in the neutron yield. As regards the
deleterious effects of the "next zone" in actual strata,
these will be small in the method proposed owing to
its great depth.
In the present investigation, we calculated the
delayedneutron yields for a target of almost infinite
thickness by means of the Belen'kiiTatum avalanche
theory, using the excitation function of the Ot$(y, p)
Nt~ reaction, experimentally measured in [1]. Figure
1 shows the results of these calculations for water,
sand, and also for oil and waterbearing strata when
these are bombarded by 17to20MeV electrons.
The small variation in the delayedneutron
yields for water, sand, and awaterbearing stratum is
due to the fact that there is a special kind of com
pensation between the oxygen in the SiOz and the
water. This gives rise to the sharp jump on passing
to an oilbearing stratum. The greater the petroleum
content, the lower will the curve giving the delayed
neutron yield from the oilbearing stratum lie in rela
tion to curve 2 (Fig. 1), which serves as a boundary
criterion.
For the petroleum concentration in question
(order of 30% petroleum in the stratum), the jump in
the delayedneutron yield on passing from the oil to
the waterbearing stratum, corresponding to irradiation
in the 17to20MeV energy range, is characterized
by a factor of 2.
TheTable shows the delayedneutron yields for
the case of primary bombardment by y radiation. As
might be expected, the yields are considerable.
In order to elucidate the practical possibilities
of the proposed method of warding off waterpetroleum
contact, we made some experiments on the 25MeV
betatron of Uzhgorod State University. At maximum
energy, the intensity of the radiation is 30 R/min ? m
for a y quantum pulse length of 10 to 12 ? sec and
a repetition frequency of 50 cps. The mean beam
electroncurrent falling on the target is of the order of
10$ A.
The thick target constituted a metal tank 72 cm
long and 13 cm in diameter, filled successively with
or petroleum, these imitating waterbearing and oil
The apparatus for recording the delayed neutrons consisted of a paraffin cube 50 x 60 x 70 cm in size with a
central channe113 cm in diameter for accommodating the samples and two counters of the SNM8 type. The
neutronrecording efficiency of this system, using a PoBe source, was 0.33%.
Relative monitoring of the beam was effected by means of astraightthrough integral chamber with an RC
circuit having a time constant of 6 sec, equal to 1/~ for the N17 isotope; this enabled errors in the experimental data
due to changes in the intensity of the y radiation to be avoided.
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After 15 to 20 sec of irradiation, the activity of the Nt~ nuclei practically reached saturation. Assuming that
the interval between two successive pulses of y quanta in the betatron equals 20 msec and the maximum operating
time of the relay is of the same order, we may consider that the recording of neutrons took place within not more
than 40 msec after removing the ybeam. The corresponding loss in neutron count is of the order of 0,7% for N17
with ahalfllfe of 4,15 sec.
The leading edge of the sample was placed at a distance of 44 cm from the tungsten target of the betatron,
the beam intensity of which did not exceed 10 to 15 R/min (at a distance of 1 m from the target) and a maximum
energy of 25 MeV during the experiments:. In the basic measurements, the intensity of the y beam was measured
by an absolute aluminum ionization chamber.
The experimental results for the delayedneutron yields are shown in Fig. 2: The x axis represents the maxi
mum energy of y quanta and the y axis represents the number of pulses per act of irradiation (each point corresponds
to the results of five to seven measurements).
W e see from the results presented that even for relatively small y beam intensities (current of the order, of
10y A in the absolute ionization chamber at the position of the sample)atan energy of 21 MeV and higher there is
quite a marked jump in the delayedneutron yield on passing from the oilbearing to the water bearing stratum and
vice versa, i. e., we obtain information on the position of the contact zone. The method proposed may also possibly
provide quantitative information on the petroleum content of the strata, although there are certain difficulties in
this owing to specific characteristics of each particular well. We note that it is not absolutely necessary that the
recording of the delayed neutrons should only be carried out after the accelerator has been switched off.
In the present experiments, delayed neutrons were also recorded in the intervals between y quantum pulses
within 7 msec of the electron .throw on to the inner target of the betatron. The neutroncount rate for waterbearing
strata (recorded with a neutron apparatus of about 1~/o efficiency) was 100 to 130 pulses/min.
Thus the theoretical and experimental results presented show that there is a real possibility of warding off
wateroil contact if an accelerator giving y quanta with an energy higher than the 16.4MeV threshold of the
Ol$ (y, p) N17 reaction (say 17 to 20 MeV) is available.
Experiment showed that adelayedneutron intensity adequate for recording is obtained if there is a y quantum
flux at the stratum sufficient to give a current of the order'of 109 A in the absolute ionization chamber described
in [2]. This order of intensity can be obtained even with lowpowered equipment.
The creation of a smallscale cyclic accelerator giving y quanta of 17 to 20 MeV at an adequate intensity
is a complex and as yet unsolved problem; considerable work has however already been done in this direction and a
certain amount of success has been achieved.. The following possibilities, in the opinion of the authors, deserve
attention in this respect. ,
It is well known that, on bombarding lithium or tritium targeu with protons, the following reactions take place:
3Li' }1Hi ~ 4Be$ } ~ with E =17.6 MeV,
iH3 i1Ht ~ ZHe4 } ~ with E = 20 MeV<
In the first reaction y quanta with an energy of around 17.6 MeV are formed; this is sufficient for excitation of the
Ol$(y, p) N17 reaction.
Approximate calculations showed that, in order to ward off wateroil contact, the protonaccelerator current
should be not less than 100 ? A.
Work being done on the design of smallscale (oilwell) betatrons in the Tomsk Polytechnic Institute under
the direction of A. A. Vorob'ev [3], heavycurrent smallscale ironfree betatrons with equilibriumorbit radii of 3
to 20 cm (A. I. Pavlovskii et al. [4]), plasma accelerators, and ironfree synchrotrons (under the direction of G. I.
Budker) [5], all suggest that the method described here [6] will prove promising as regards further technical development.
1. W. Stephens, J. Halpern, and R. Sher, Phys. Rev., 82, 511 (1951),
2. B. Flowers, J. Lawson, and.F. Fossey, Proc. Phys. Soc., 65B, 286 (1952).
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
3. Summaries of Papers Presented to the Fifth InterUniversity Scientific Conference on Electron Accelerators
(Tomsk, March 17 to 21, 1964) [in Russian], Tomsk, izd. Tomsk. gosudarstvennogo univ.: V. A. Gorbunov,
G. A. Kunitsyn, and Yu. A. Otrubyannikov, Starting an IronFree Pulse Betatron; L. M. Anan'ev and V. L.
Chakhlov, Economic System for Throwing Electrons in HeavyCurrent and SmallScale Betatrons; V. L.
Chakhlov and M. M. Shtein, SmallScale Source of Gamma Radiation with an Energy of 17.4 MeV; L. M.
Anan'ev and Ya. S. Pekker, SinglePulse IronFree Betatron; L. M. Anan'ev ed al., Portable SmallScale
Betatron for the Defectoscopy of LargeScale Features in Field and Assembly Conditions; V. A. Vorob'ev,
G. V. Titov, and V. L. Chakhlov. Use of SmallScale Betatrons for the Radioscopic Control of Materials under
ErectionPlatform Conditions.
4. A. I. Pavlovskii et al., DAN SSR, 160, 68 (1965).
5. G. I. Budker et a1.,IronFree SingleTurn Synchrotron (BSV) [in Russian] Preprint, Novosibirsk (1965).
6. A. K. Berzin et a1.,Authors' Certificate No. 174, 284, December 12, 1963, . .
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G. V. Byurganovs.kaya, E. G. Gvozdev, UDC 621.387.46:621.386.82
and A. 'I. Khovanovich
Information on the composition and sensitivity of glass dosimeters, the operation of which is based on
the change in optical density caused by irradiation, is reviewed. The principal dosimetric character
istics of the Soviet y dosimeter SGD8 and the y neutron dosimeter L15 (based on sodium and
lithium silicate glasses with nickel additives) are described; these enable doses from a few tens of
roentgens to a million roentgens to be determined.
In view of the growing use of nuclear radiations in various departments of science and technology, it has be
come necessary to devise a simple, versatile dosimeter capable of repeated use. Glass dosimeters have proved
promising in this respect. By suitable choice of compositions it is possible to produce glasses by means of which the
y component in mixed y and neutron radiation can be determined.
The first glass dosimeter which found practical application was made of ahomeproduced optical glass (with
a large content of alkalimetal oxides); this darkened substantially under the influence of y  and x radiation. The
dose was measured from the increment in the optical density of the irradiated glasses. However, since this glass is
sensitive to slow neutrons and also undergoes severe spontaneous decolorization (regression), it is very limited in
application.
Outside the Soviet Union, a phosphate glass composed of 50 wt. % Al(PO8)s, 25 wt. % Ba(PO8)Z, and 25 wt. %
KPOs has been proposed for dosimetric purposes [1]: The transparency of this glass falls linearly with increasing dose
up to 105 R (for larger doses saturation effects set in).
Of special interest are silicate glasses containing traces of cobalt oxide, which raises the sensitivity of the
glasses to radiation in the shortwave part of the spectrum [24]. Glasses containing 60 to 70 wt. %SiO2, 10 to 20
wt. %Na20, 1 to 20 wt. %BZOy CaO, Mg0, A1ZO8, with the addition of 0.1 to 16 wt. % Co8O4 have been studied.
With increasing cobaltoxide content, the sensitivity of the glasses to radiation increases and the regression diminishes.
The glasses may be used for doses from several hundred to 107 R. The presence of boric anhydride makes the glasses
sensitive to neutrons and hence suitable for the dosimetry of mixed radiations. The marked spontaneous decoloriza
tion of the boronsilicate glasses, however, limits their field of use.
Dosimeters for doses of 104 to 107 R may be made from silicate glasses containing manganese and cerium
oxides [5, 6]. For stabiliza~on of the induced absorption of manganese glasses, compounds of iron and tin are intro
duced into them. The addition of vanadium or chromium to manganese glasses raises their sensitivity to smalldoses.
Examination of the possibilities of determining large doses of radiation (106 to 109 R) showed [7] that the most pro
mising in this respect were glasses with a high content of SbEOB (60 to 70 wt. %), and also glasses [8] containing 50
wt. % BizOs; in these glasses there was no saturation even at a dose of 109 R; the optical density after irradiation
with 108 R was of the order of 10 in 1 cm. Great sensitivity to radiation is shown by iodidemetaphosphate glass [9],
which changes its tint on irradiation by a dose of 70 R. Sodiumborate glass tinted to a blue color with elementary
sulfur may be used as an indicator. Under the influence of y and x radiation this becomes colorless [10].
The authors of the present paper made a special study of glasses not containing BZOs, Ba0, and Pb0. As
additives, cobalt and nickel oxides were introduced.
The sensitivity of the glasses to radiation was expressed in terms of the increment in the optical density (for
~ = 350 m?) per unit thickness (in the present case 1 cm) after irradiation with a dose of 104 R, i. e.,
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 3841, Juiy, 1966. Original article submitted May
21, 1965; revised December 22, 1965.
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0S = s  S0
Z
where S is the optical density of the irradiated sample
(S = log T, T =transmission coefficient), Sa =optical
density of the nonirradiated sample, and l =sample
thickness.
Study of silicate and phosphate glasses containing
nl
various quantities of Coo (0.1 to 1 wt. %) showed that the
sensitivity systematically increased with increasing cobalt
0 0,1 0,3 0,5 0,7 CoO, wt.% oxide content (Fig. 1), being considerably smaller for the
phosphate glasses. Increasing the cobaltoxide content to
10 wt. % reduces the sensitivity of the glasses to radiation.
Fig. 1. Sensitivity of silicate and phosphate glasses
Glasses containing cobalt and nickel are two or three
irradiated with y radiation (up to a dose of 104 R) as
times more sensitive to radiation than those containing
a function of the cobaltoxide content (~ = 350 m?.):
other additives (Ce02, Nd203, Fe203, Sn02 and etc.).
1) Silicate glasses; 2) phosphate glasses
The most suitable types for dosimetric purposes
SS were silicate glasses of complex composition containing
~ NiO. These had a rather larger sensitivity to radiation
~ 1 1 ~ 3i
than cobalt glasses, a smaller regression factor, and a
I 1 11 \~~
~'2 rapid fall in induced radioactivity after irradiation with
11 ~ 111
a mixed radiation flux. The regression factors K =
~ ~ 11
0, log (St/SZ)/log(tz/tl)(where St and SZ are the optical
8 i ~2 ~ 2/~
densities at times tr and tZ respectively) of cobalt glasses
~ 2 _i ~1
ford values of 350 and 740 m? are .0.02 and 0.05
0'4 respectively, while for nickel glasses they are 0.005 and
~~ / 2
0.02. The spectral curves for the optical density of the
1 ~..,~ r
0 glasses (SGD8) before and after irradiation are shown in
300 400 500 600 700 A, m? Fig. 2. The sensitivity of the glass with the nickel addi
tive equals 0.45. The relationship between the sensitivity
Fig. 2. Spectral curves of optical density: } (for ~ = 350 m?) and the radiation dose is linear over the
silicate glass; ) bariumsilicate glass; 1)before ran a studied Fi 3 B measurin "the o tical densit
irradiation; 2)104 R; 3) 2 ? 106 R. g ( g' )' y g p y
(for ~ = 350m?) of :lmples 100 and 5 mm thick, we can
determined doses in two ranges: 50 to 4000 and 2000 to
750 DX1C;~R 80;000 R respectively.
dS
In order to determine doses of 2 ~ 104 to 106 R, the
longwave part of the spectrum (~ = 740 m?) is used
with sample thicknesses of 5 mm. A study of the sensi
tivity of glasses 100 mm thick to radiation in the energy
range 50 to 1500 keV showed that, on using lead filters
ZO S of appropriate thickness (0.3 to 0.5 mm), the readings of
the dosimeters would be practically independent of the
energy of radiation above 60 keV. When using the
dosimeters in the temperature range100 to + 100? C,
the error in determining the optical density due to
~~
decolorization does not exceed t 10%. By heating the
irradiated glasses to 400 or 450? C for 6 h, the original
D 1000 2000 3000 D, R 0 optical density can be completely restored; since the
sensitivity of the glass dosimeters does not depend on the
number of restorations, they can be used repeatedly.
Fig. 3. Sensitivity of silicate glass containing nickel
as a function of y radiation dose: 1) ~ = 350 m? ; Z
_ .100 mm; 2) ~ = 740 m? ;l = 5 mm. +On the SF4 spectrophotometer or the photoelectric
colorimeter FEK60.
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For measuring doses of y radiation with a narrow
spectral energy range, for example, from a Co60 source,
we may use glasses of any composition having negligible
Fig. 4. Sensitivity of silicate glass to slow neutrons
as a function of Bz03 and Li~O content (~  350 m? ): In order to examine the possibility of setting up a
O) BZOs; e} LiZO, yneutron dosimeter the sensitivity of certain experi
mental glasses with various proportions of boric anhydride
and lithium oxide to slow neutrons was determined. The presence of BZ03 or Li20 produces an additional increase
in sensitivity as a result of the B10(n, a)Li7 and Lip (n, a) T reactions. The sensitivity of the glasses to neutrons is
characterized by the quantity
il7l
Rn = D e
n
where IIn is the neutron flux in 1 cm2, Dn = Dn+y  Dy is the dose of neutrons. in rem.cmZ/neutron(D n+y ~
the total dose of y and neutron radiation,.determined by measuring the optical density of the irradiated glasses with
a correction for regression, Dy is the dose of y radiation). As the content of BZ03 or Lilo in the glasses increases,
the neutron flux producing the same darkening as y radiation (dose of 1 R) systematically falls, tending to a certain
definite value in the case of boronsilicate glasses (Fig. 4). Hence there is no point in raising the boricanhydride
content of the glasses above 20 wt. ?10. The Li20 content is limited by the chemical stability of the glasses.: For
dosimetry of a mixed flux of radiation, we can recommend lithiumsilicate glass containing a nickel additive (L15j.
In sensitivity toy radiation, type of absorption spectrum, relationship between optical density and the dose and
energy of the radiation, and kinetics of spontaneous.and thermal decolorization, L15 glass hardly differs from SGD8 .
and is suitable for repeated use.
1.
J. Schulman, C. Keick, and H. Rabin, Nucleonics, No. 2, 30 (1955).
2.
N. Kreidl and J. Hensler, J. Amer. Ceram. Soc., 38, 423 (1955),
3.
N. Kreidl and H. Blair, Nucleonics, No. 1, 56 (1956).
4.
N. Kreidl and H. Blair, Nucleonics, No. 3, 82 (1956).
5.
J. Paymal, M. Bonnaud, and P. Clerk . J. Amer. Ceram. Soc., 43, 430
(1960).
6.
J. Kugler, Atomkernenergie, 4, 67 (1959).
7.
W. Hedden, J. Kireher, and B. King, J? Amer. Ceram. Soc., 43, 413 (1960).
8.
A. Bishey, Phys. Chem. Glasses, 2, 33 (1961).
9.
A. Hiesenrod and B. Gehauf, Chem. Phys, 24, 914 (1956).
10.
K. Otley and W. Weyl, J. Appl. Phys, 23, 499 (1952).
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NOTES ON ARTICLES RECEIVED
REFLECTION OF 2501200 keV ELECTRONS
L. M. Boyarshinov UDC 539.124:539.121.72
For primary radiation with energies of 2501200 keV, the electron reflection coefficient (back scattering) was
measured for targets of bismuth, tin, molybdenum, copper, and iron. The reflected electrons were collected in an
aluminum Faraday cup and recorded with a microammeter.
The values of the reflection coefficients for primary monoenergetic electrons with energies of 1200 and 250
keV are shown in Figs. 1 and 2, respectively. In addition, a determination was made of the secondary electron
emission coefficient, which was 1015% of the value of the reflection coefficient for primary electrons.
As is clear from Figs. l and 2, the values for the reflection coefficient at 1200 keV are approximately 15%
less than the reflection coefficients for the same targets at 250 keV. Such a reduction in reflection coefficient with
increasing primary electron energy was first established in this work for the 250600 keV energy range and was
verified for the 6001200 keV region.
Also shown in Fig. 1 is a comparison of the results of this work with published data [13] obtained from meas
urements using a similar technique. As can be seen from Fig. 1, the results of the present work are in good agree
ment with published data. The curve in Fig. 1 was constructed from data for 22 independent measurements of re
flection coefficients for 18 elements in the periodic table with atomic numbers 492, and can be used to determine
the nature of the dependence of reflection coefficient tl on atomic number Z. From this most representative curve,
and also from similar curves for other primary electron energies, one of which is shown in Fig. 2 for 250 keV (where
the reflection coefficient for aluminum was taken from [4]), it is possible to establish that this dependence is deter
mined by the expression
tl = AZn,
In determining the thickness of coatings [5], and in doing chemical analysis by reflected s radiation, it has
been shown that sensitivity is greater for larger exponents n. For monoenergetic electrons, it was established that
the exporient n increases with increasing energy, and therefore it is most advisable to use harder radiation sources for
the abovementioned practical purposes.
n, i
50
40
30
0 f0 20 30 40 50 60 70 80 90 Z
010 20 30
Fig. 1. Reflection coefficient as a function of atomic Fig. 2. Reflection coefficient as a function of
number for 1200 keV electrons: O) This work; A) atomic number for 250 keV electrons: O) This
work; e.) [4].
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 4243, July, 1966. Original article submitted
February 18, 1966; abstract submitted March 17, 1966. ,
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Note that the reflection coefficients for copper are higher than those. for nickel with 6001200 keV primary
beam energies, which is not in agreement with the data of Danguy [6] obtained by using S sources. According to
[6], nickel has an anomalous reflection coefficient which is 0.5% higher than the reflection coefficient for its
neighboring element in the periodic table with higher atomic number, copper.
1. P. Ya. Glazunov and V. G Guglya, Dokl. AN SSSR, 159, 632.(1964).
2. V. G. Guglya, Candidate's Dissertation, Moscow (1964).
3. K, Wright and I. Trump, J. Appl. Phys.; 33, 687 (1962).
4. I: Trump and R. Van de Graaf , J. Appl. Phys., 19, 599 (1948).
5. N. N. Shumilovskii and L. V. Mel'ttser, Fundamentals of the' Theory of Automatic Control Equipment [in
Russian],Moscow, Izdvo AN SSSR (1959).
6. L. Danguy, Inst. Interuniv. Sci: Nucl. Monographic, No. 10, 3 (1962).
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S. B. Goryachev and I. N. Meshkov UDC 621.384.61]..3
To increase the intensity of ahighcurrent betatron with spiral storage [1 ], an external 500 keV injector with
a current of several amperes was developed. The operating length of the current pulses is ~ 20 ?sec. An overall
view of the apparatus is shown in the figure. The injector is ahighvoltage do accelerator which uses as a voltage
source a controlled pulsed voltage generator (PVG) with shortcircuiting sparkgap cascade permitting smooth
regulation of the length of the voltage pulse in the range 11000 ?sec. The accelerating unit consists of an electron
gun at 200 keV and a 300 keV accelerating tube with an intensity of 10 kV/cm. The insulators are porcelain and
are in sections. To increase electrical stability, the external surface of the tube is located, in a tank filled with
transformer oil. Supply for the cathode heater of the gun is obtained from a GSR3000M generator, which is at
Accelerating
unit
Heater supply
system Shortcircuiting
spark  ga p
cascade
Fig. 1. Diagram of the injector: 1)IMY100/0.1 condenser; 2) 200 kS2 resistance;
3)spark gap; 4)tank of transformer oil; 5)accelerator tube; 6)cathode assembly; 7)
insulator; 8) cathode heater supply generator; 9) monitoring lamp: 10)1.5 kSd resist
ance; 11) photomultiplier; 12) motor; 13) Rogovskii coil; 14) lens; 15) aligning mechan
ism; 16)solenoid; 17)bending magnet.
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 4344, July, 1966. Original article received
February 18, 1966.
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cathode potential and is driven by an insulated shaft. Heater current is controlled by a photomultiplier through the
brightness of an incandescent lamp included in the heater circuit.
An electronoptical channel, consisting of magnetic lens, shielding solenoid, and bending magnet, serves to
carry the beam through the betatron magnet yoke and to inject it into the chamber:
One can calculate the behavior of the beam in the channel by matching the solution for the variation in the
dimensions of an intense beam y(z) in free space [2]:
dy
y (z)=y in "~" dz )in
,4222
z ,
yin
3/2
A2 _ e7 ~ me \
mc3 P
in the thin lens and solenoid. The behavior of the beam in the solenoid is described by the equation
2y 2
dz2 +w2y_ 2y 0' ~= 2pc '
whose solution is a periodic function. For w2yent ~ 2A2/yent and small (dy/dz)ent we have y(z) ~yent (1 +
1/2A (dy/dz)ent sin ,~wz); in other cases, a solution can be obtained numerically. The parameters for the channel
elements were selected on the basis of calculations of this type.
A current of ~ 2 A was obtained at the injector output. Beam dimension is 8 x 8 mm with ~ 2.5? angle of
divergence.
1. G. I. Budker et al., Proceedings of the International Accelerator Conference, Dubna (1963) [in Russian],
Moscow, Atomizdat (1964), p. 1065.
2. I. N. Meshkov and B. V. Chirikov, ZhTF, 35, 2202 (1965),
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COMPOSITION AND SPATIAL DISTRIBUTION OF RADIATION
AROUND A 10 GeV PROTON SYNCHROTRON BUILDING
A study of the relationships governing the propagation of mixed radiation from highenergy accelerators at
large distances is of decisive importance in connection with the need for reliable prediction of radiation levels in
planning new installations. In the case under consideration, the space profile of the. radiation field around a proton
synchrotron was determined along eight radial directions located at 45? to one another. In these directions, existing
equipment made it possible to differentiate the following components: thermal neutrons; slow and intermediate
neutrons (0.4 eV0.1 MeV); fast neutrons (0.120 MeV); very fast nucleons (> 20 MeV) and pions (> 50 MeV);
charged particles (electrons, muons) and y rays of various energies.
The paper shows that fast neutrons (< 20 MeV) were distributed symmetrically at large distances from.the
target with respect to the center of the building. The effective energy of the fast neutrons was in the range 0.74
MeV.. In the case of shield geometry, neutrons of such energies are the greatest hazard. The dose distribution for
the radiation components mentioned are shown in the figure. The direction with maximum flux density of high
energy nucleons was taken as the basis for the determination of the dose from such particles. In this situation, the
doses from fast neutrons and from highenergy nucleons were approximately equal.
?
?
~
6
\~
~
~ ~~
~ ~ 5
~.~
~
3
7
\~'
2 ~~\
v
0 20D 40D 600 800
Distance, m
Dose as a function of distance from the geometric center
of .the accelerator buildirg; 1) thermal neutrons; 2) slow
and intermediate neutrons; 3) muons, electrons, and y
rays (tentative); 4) fast neutrons; 5) nucleons and pions;
6)total dose.
(where Eo = 10 GeV); kgeom is a geometry factor:
An empirical formula is presented in the paper
for calculating the fast neutron flux at any distance
from the accelerator. The results of measurements
made at the proton synchrotron are compared with data
obtained by other authors.
'The experimentally determined function for the
spatial dose distribution of 0.4 eV20 MeV neutrons
has the form
_ r
~ (r) _!~1 kik geom k d a. eff
4~tr2 e
? rem /1 Otl protons.
Here, I is the intensity (proton/sec) of the internal
proton beam at an energy Ep, GeV; A is a factor taking
into account target thickness and material, shielding
thickness and configuration, and also the effective
solid angle for the yield of radiation in the upper hemi
sphere; the factor A can be interpreted as the effective
neutron yield in the upper hemisphere per unit flux of
protons with energy Ep = 10 GeV (A = 7.84 ? 102
n/p); kt is a factor taking into account the value of
the final energy of the protons:
k1_C$p\0.7
Eo /J11
_ r100
kgeom ti ~[1 rt 2 ~ 104 (r 100)2 a 5s j F (e)
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 4445, July, .1966. Original article submitted
February 18, 1966; abstract submitted April 9, 1966.
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(where F(8) = 0.51, depending on the chosen radial direction);r is the distance from the axis of the vacuum cham
ber of the proton synchrotron to the point under consideration; Jeff is the effective mean free path of the neutrons
in air (~eff = 391 m); kd is a dose conversion factor (for neutrons of the given spectrum,kd=1.15.10E?rem/n/cm2).
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FAST NEUTRON RADIATIVE CAPTURE IN Cuss
V. A. Tolstikov, V. P. Koroleva, UDC 539.17.012:539.172.4
V. E. Kolesov, and A. G . Dbvbenko
This paper gives the results of measurements and of calculations of the fast neutron radiative capture cross
section in C uss.
The relative activation method of measurement, which has been described in detail [1], was used. The U2ss
fission cross section for fast [2] and thermal [3] neutrons and the thermal neutron radiative capture cross section in
Cum [4] were used as reference cross sections. The measured results are compared with data of other authors in the
figure. Cross section calculations were made on the basis of the statistical theory'of nuclear reactions rising the
optical model~of the nucleus. The method of calculation has been described [5]. The potential in the calculation
of nuclear surface penetrability contained aspinorbit term. The parameters for the levels in the target nucleus,
the values of D, I'y ,and of the parameter a were taken from [12, 4, 13], respectively. The sharp bend in the
radiative capture cross section curve for neutrons with an energy of ~ 1 MeV is explained by competition from
inelastic scattering.
,~1=2
~1=3
IR. II
Results of neutron radiative capture cross section measurements for Cu63: Data from: ?) this work;
?)[3]; O) [6]; p) ['1]; ~) [8]; ~ [9]; C) [10]; D) [11]. Arrows indicate the position of excited
levels; )total capture cross section; ) capture cross section for neutrons with different
angular momenta.
100
90
80
70
60
50
40
30
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 4546, July, 1966: Original article submitted
February 18, 1966; abstract submitted April 9, 1966.
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1. Yu. Ya. Stavisskii and V. A. Tolstikov, Nuclear Reactions at Low and Medium Energies [in Russian],Moscow,
Izdvo AN SSSR (1962), p. 562.
2. K. Parker, AWREO82/63 (December, 1963), ;
3. Neutron Cross Sections, BNL325, Second Edition, Supplement No. 2, Vol. III, Z68 to 98 (February, 1965),
4. I. V. Gordeev, D. A. Kardashev, and A. V. Malyshev, Nuclear Physics Constants [in Russian], Moscow,
Gosatomizdat (1963).
5. V. A. Tolstikov et al., Atomnaya Energiya, 17, 505 (1964).
6. R. Booth, W. Ball, and M. MacGregor, Phys. Rev., 112, 226 (1958).
7. R. Macklin, N. Lazar, and W. Lyon, Phys. Rev., 107, 504 (1957).
8. D. Hughes, R. Garth, and ]. Levin, Phys. Rev., 91, 1423 (1953).
9., J. Perkin, L. O'Connor, and R. Coleman, Proc. Phys. Soc., 72, Pt. 4, 505 (1958).
10. V. Dementi and D. Timoshuk, Compt. rend.,Acad. Sci,URSS, 27, 929 (1940); M. Mescheryakov, Compt.
rend., Acad. Sci.URSS, 48, 555 (1945).
11. W. Lyon and R. Macklin, Phys. Rev., 114, 1619 (1959).
12. R. Ricci, R. Girgis, and R. Lieshout, Nuovo Cimento, XI, 156 (1959).
13. A. V. Malyshev, ZhETF, 45, 311 (1963).
All abbreviations of periodicals in the above, bibliography are letterbyletter translitera
tions of the abbreviations as given in the original Russian journal. Some or all of this peri
odical literature may well be available in English translation. A complete list of the coverto
cover English translations appears at the back of the first issue of this year.
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THE HOMOGENIZATION OF A HETEROGENEOUS PERIODIC SYSTEM
Homogenization of a heterogeneous periodic system consists in the replacement of this system by an equivalent
homogeneous medium such that the neutron flux and current in that medium coincides with the corresponding
quantities for the heterogeneous medium on the average in each elementary cell. Neutron diffusionin the equivalent
homogeneous medium is described by the diffusion coefficient tensor Dik, which obviously has a diagonal form in a
coordinate system coinciding with the symmetry axes of the elementary cell. There are two known methods for
calculating the tensor Dik for a heterogeneous periodic system.
The method of meansquare ranges was first used by Behrens [1) for calculating neutron diffusion in a medium
with hollow channels. The basic theorem of this method is the equality
Le.n (h)2, (1)
where Li is the diffusion length along the axis i; n is the average number of neutron mean free paths; (li~ is the
average value of the square of the neutron mean free path projected on the axis i; i is a unit vector.
The second method is based on the use of an integral neutron transport equation. This method was developed
by Laletin [2] for weaklyabsorbing media. The essence of the method is that the exact neutron flux is broken down
into two terms: one of them fi(r)takes into account the overall drop in flux over .the entire system; the second,
which is proportional to the gradient of ~, takes into account the variation of neutron flux within an elementary cell
of the medium. The second term, the socalled microflux, is zero for longitudinal diffusion in. a medium with
cylindrical channels.
However, the microflux is different from zero and makes a corresponding contribution to the magnitude of the
diffusion tensor for the case of transverse diffusion. In [2], on the basis of a comparison of the results of that paper.
with Behrens' formula [1], it was asserted that the meansquare range method was not applicable to the calculation
of neutron diffusion in a direction perpendicular to a channel axis.
The present paper shows that with correct consideration of the angular correlations between individual neutron
mean free paths, both methods mentioned are completely equivalent to one another: To do this, Eq. (1) should be
replaced by the more general expression
Li? 2 (Ri)2,
where R is the vector for total displacement of the neutron from an arbitrary point in the elementary cell. Writing
R in the form of a sum of all separate neutron mean free paths, one can represent expression (2) in the foml
L2 2 ~ Ps (I1) pS (12) ... PS (In1) PQ (ln) [ ~ (lki)2~ ~ (lkl) (lk'1) ),,
n=1 k1 k#k'=1
where Ps(1~), Pa (t)are the probabilities that the rangex is ended by neutron scattering and absorption, respectively.
The first term in expression (3) reduces to equality (1) after appropriate transformations. The second. term takes into
account the contribution to the diffusion tensor from angular correlations between individual neutron mean free paths.
It is shown in the paper that angular correlations exist in a homogeneous medium even for spherically symmetric
scattering ir1 all components of the medium. In a medium with cylindrical channels, these correlations of neutron
mean free paths, which are specific for heterogeneous media, make a contribution to Li only for transverse diffusion,
the sign of the quantity depending on the ratio between the scattering cross sections of the various components. An
analysis of the equation which determines the microflux makes it possible to assert that the microflux in a hetero
geneous medium is uniquely determined by the angular correlations of the neutron mean free paths.
Translated from Atomnaya E,nergiya, Vol. 21, No. 1, pp. 46, July, 1966. Original article submitted January
21, 1966; abstract submitted April 18, 1966.
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LITERATURE CITED
1. D. Behrens, Proc. Phys. Soc., A62, 607 (1949).
2. N. I. Laletin, Proceedings of the Second International Conference on the Peaceful Use of Atomic Energy
(Geneva, 1958) [in Russian],Dokl: sovetskikh uchenykh, Voi.'2, Moscow,Atomizdat (1959), p. 634.
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LETTERS TO THE EDITOR
EQUILIBRIUM OF PLASMA IN A STELLARATOR WITH A CIRCULAR MAGNETIC AXIS
V. D. Shafranov UDC 533.9
When plasma is introduced into a toroidal magnetic trap (for example, the stellarator [1]), a magnetic field
perpendicular to the plane of the torus is developed, leading to a displacement of the plasma pinch from the center
of curvature and distortion of the shape of the magnetic surfaces. In this paper we calculate the displacement of
the plasma pinch for the case in which the cross sections of the magnetic surfaces are nearly circular. The solution
is obtained by the perturbation method in the linear approximation with respect to the dimensionless parameter
S?yR/b, where S is the ratio of the plasma pressure to the pressure of the magnetic field, ? is the torsional angle of
the magnetic lines of force divided by 2tr , R is the radius of the torus, and b is the transverse size of the system.
Our main approximation to the problem (which, in contrast to analogous papers [2, 3], enables us to obtain a
solution in simple analytic form) is that the vacuum magnetic fields and surfaces are presented as expansions in
powers of the distance from the magnetic axis.
Zero Approximation. Neglecting the curvature of the system, the magnetic field Bo = ~ ~ of an mturn
stellarator is described by the scalar potential
_ u'
~ Bo (sIE meo _2 p"` sin mu~ , 1
( )
and the magnetic surfaces z/i(r) = const by the function
~o=e2+E ~~z Q,n cos mu, (2)
meo
satisfying the equation BoO:Gu = 0. Here Bo is the longitudinal magnetic field, s the longitudinal coordinate, pthe
distance from the axis (polar radius), e and po parameters characterizing the amplitude of the helical field and
the form of the magnetic surfaces:
~ls n
mR ml{
where wis the azimuthal angle, and n is the number of periods of the field in the length of the torus. The amplitude
of the azimuthal component of the helical field equals BoEU'p u (p /po)mt For m = 2 the parameter p o falls out and
the configuration is characterized by a single dimensionless parameter e < 1. Form >_ 3 the parameter ~ may be
taken as unity. In this case p u constitutes the distance from the axis to the edge of the separatrix [4]. Subsequently
we shall consider that the second term in the expression for ~u is small in comparison with the first, so that the
sections s = const of the magnetic surfaces are nearly circular. Hence,in the calculations we may formally take
e ?1.
i
The derivative of the transverse magnetic flux with respect to the longitudinal, ?, related to the torsional angle
i of the lines of force by the relation i = 2tr?, is easily calculated by the method described in [5]; near the axis
it equals
~ / 2 m
Er (e)= mm21) n s2 ( ~z ~ 2.
\ eo
The formulas given are valid for p ~ R/n.
Currents in the Plasma. The curvature of the system produces a certain distortion in the shape of the magnetic
surfaces in vacuum. Let us neglect this effect and consider only the curvature of the magnetic surfaces associated
with the presence of plasma. The density of the current arising on introducing plasma into the trap may be written
in the form [6]
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 4749, July, 1966. Original article submitted
February 8, 1966.
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[BOp] $p mt
J=~ B2 IhB=~p~ (~"n`1) {[ B ]~"htB
where p is the plasma pressure, constituting a surface quantity [6], i. e., a function of ~. From the solubility con
dition for the equationdiv j = 0, which corresponds to the requirement that the solution be finite at p = 0, it
follows that the pressure must be an analytic function of ? ~ = const ~mt. Hence the function ~m1 is taken as
argument of p. W e note that, for finite plasma conductivity, the solubility condition for the electricfield scalar
potential equation E _ ~cp
BAS= hB2/o II
(6)
(a II .being the longitudinal electrical conductivity of the plasma) requires that p should be an analytic function
?Z ~, = const ~zms . The si. aplest distribution of plasma pressure in the zero approximation (neglecting curvature)
which satisfies this condition'tas the form
The current continuity equation div j = 0 leads to an equation for hl of the form
[BO~m_lJ ~B2
Bvh,= B4 r
The main contribution toC~BZ is associated with the toroidal longitudinal magnetic field Bs = Bo/[1 p/R
(cos w)]. In the remaining terms of Eq. (8), Band ~ may be taken in the zero approximation described by Eqs. (1)
and (2). In the lowest order of expansion with respect top the equation for hl takes the form
~7h1 u'p'n1 ahg ~h1 m_s 4 (m1)
ds fe ?1z Csinmu ap }cos mu e8c,~ ~ ~ =qC sin w, where 4= R
It is easy to see that the solution of this equation takes the form
m02~m3 e
+ _e_
cos w m C Co
cos (muco)~ q.
~m1) s2u' Co
Thus fora ?1 the density of the longitudinal current js = cp'(~i m1)htBois determined from the simple expression
4cm2 2
2)
2cm2 (CU
2(m2) dp
(m
~ mt
I s =  Boe2n 0o p ('~ ) 0 COS co
= Boe2n (m1) \ p /
dp cos w.
For comparison we write the transverse component of current density
2 (m1) gyp' (lam1) ~2m3
~1~ Bo (12)
2
We note that the ratio of the mean squares of the longitudinal and transverse current density, ~ =~]s )/ Q 8e i edw
Taking account of the relationship js ~ cos c~, solution of these equations may be expressed in terms of a single
function Br (p)
Bp=B1 sin ~, B~,=d dQ 1) cos w.
For Bl we obtain a differential equation of the second order which can be integrated once. Thus we obtain
2 2(m~) P .
dB1 _ 8~tm E 0 1 Os2m dp
d0 s2n (m1) e3 ~ de
0
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Let us assume that the radius of the plasma pinch, a, is smaller than the radius of the chamber. Then outside the
plasma pinch
E Nt / 2? \ 2 (m2) ll2 `l o
where C is a constant of integration and S denotes the integral
a
41tm ~ 162m dp
For atwoturn stellarator (m = 2) we obtain ~ = 8tr p /Bo ,where p is the plasma pressure averaged over the cross
section; for athreeturn stellarator (i = 6trp(0)/Bo . The factor in front of the integral is chosen so that the pressure
distribution of formula (7) corresponds to S = 8tr p /Bp for any value of m.
Distorted Magnetic Surfaces. The new magnetic surfaces in the presence of plasma, ,~ _ ~ o + ~ t ,may be
found from the linearized equation BD~V = 0:
d'Fo
BoDYri=B10'Yo,6
0
4
U
~'
U
~
,
'ti
.~
~
'?
~
~
1,2
0,2
0
~
0,8
0
4
,
0
4 B 12 >6 20
Deuteron energy, MeV
Fig. 1. Yield of Mn54 versus proton energy, for thick
targets of manganese and chromium. (1) Mn + p;
(2) Cr + p.
X~'
Alphaparticle energy, MeV
Fig. 3, Mn54 yield versus alpha particle energy,
Fig. 2. Mn54 yield versus deuteron energy, for thick tar
gets of iron and chromium. (1) Fe + d; (2) Cr + d.
The integral irradiation currents were measured by means
of the induced activity of Zn~ with the aid of copper monitor
foils. Calibration data on the Zn65 activity induced in the foils
were previously found experimentally, using a precision current
integrator.
The Mn54 activity was measured with a 100channel
scintillation gamma spectrometer with NaI(Tl) crystal of size
40 X 40 mm, with gammaline photopeak area 840 keV. .The
photoefficiency of the gamma spectrometer was determined
by means of the activity of aliquot parts of Mn54 solution meas
ured in an ionization chamber. The chamber was calibrated
with standard Co60 sources.
The present authors measured the Mn54 yield versus particle
energy for thick targets: the results are given in Figs. 1, 2, and 3.
The errors in the Mn54 yields are due to errors in the measure
ments of Mn54 activity, integral beam current and particle energy,
and amount tot 15%.
for thick targets of chromium and vanadium. The greatest Mn54 yield was observed on irradiation of
(1) Cr + a ;(2) V + a . manganese by protons, but the product is obtained in a carrier.
In addition, it is difficult to prepare heatresistant manganese
targets. The remaining five methods give Mn54 without a carrier: the highest yield from these is from irradiation
of chromium with alphaparticles. Since a method has been perfected for preparing heatresistant targets by gal
vanic coating of a copper substrate with chromium, this latter method must be preferred.
The authors would like to thank Z. P. Dmitrieva and G. A. Molin for help with the work, and Yu. G. Sevast' 
yanov for the radiochemical separation of the Mn54.
1. W. Garrison and J. Hamilton. Chem. Rev., 49, 237 (1951).
2. A. Ateti. Phillips Techn. Rev., 16, No. 1 (1954).
3. J. Gruverman and P. Kruger. Internat. J. Appl. Rad. and Isotopes, 5, 21 (1959).
4. K. Chackett et al. Nucl. Instrum. and Methods, 14, 215 (1961).
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5. H. Moeken. Productions of Radioisotopes with Charged Particles, Amsterdam (1957).
6. J. Martin et al. Nucleonics, 13, No. 3, 28 (1955).
7. P. Kafalas and J. Irvine. Phys. Rev., 104, 703 (1956).
8. K. Wagner. Kernenergie, 5, 853 (1962).
9. M. Z. Maksimov. Proceedirigs of Conference on Preparation and Use of Isotopes (Moscow, 1957), Moscow,
Izd. AN SSSR (1957), p. 31. .
10. P. P. Dmitriev et al. Ibid, p. 28.
11. N: N. Krasnov et al. Pribory i tekhnika ~ksperimenta, 4, 22 (1965).
12. M. Z. Maksimov.. ZhETF, 38, 127 (1959).
All abbreviations of periodicals in the above bibliography are letterbyletter translitera
tions of the abbreviations as given in the original Russian journal. Some or all of this peri
odical literature may well 6e available in English translation. A complete list of the coverto
cover English translations appears at the back of the first issue of this year.
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CALCULATION OF THE DOPPLER TEMPERATURE COEFFICIENT
OF REACTIVITY FOR ISOLATED RESONANCES IN A HOMOGENEOUS MEDIUM
P. E. Bulavin and G. I. Toshinskii UDC 621.039.512.26
The calculation of the Doppler temperature coefficient of the reactivity in a nuclear reactor is linked with
calculation of the temperature derivative of the selfscreening factor at the resonances. Reference [1] gives cal
culated results for the temperature derivative of the selfscreening factor for isolated resonances in a nonhomo 
geneous plane medium (curves of G. Roe). These results can clearly also be used for a homogeneous medium if we
go to the limit of zero thickness of the absorber and moderator plates. However, [1] does trot give the method of
calculation, and therefore we cannot assess the accuracy of the results. We have therefore calculated the tempera
ture derivative of the selfscreening factor for isolated resonances in a homogeneous medium. Below we give the
method of calculation and the results.
The expression for the selfscreening factor at an isolated resonance in a homogeneous medium can be written
in the following form (see, e. g., [2, 3]):
2
e
x  d~
_~
is the approximate form of the resonance, allowing for the Doppler effect for the gas model of an absorber; ~ = r/D
is the BreitWigner ratio and the Doppler resonance width; ~ = 2 E is the Doppler width; ? h = pa o /Es (in the
case of the narrowresonance approximation)t; pis the nucleat concentration of the resonance absorber; ao is the
total cross section at the resonance maximum; and Es is the total cross section of potential scattering.
Expression (1) is valid on the assumption that we can neglect the effect of interference between resonance and
potential scattering. This assumption is satisfied for purely absorptive resonance (I'n ? t) or for a dilute medium
(papa ? Es where a Pa is the cross section of potential scattering of the resonance. absorber).
When h ? 1 the integrand in (1) can be expanded in a series in h and is limited by terms of order h. Then,
using the relation ~ ~I''2 (x, ~) dx = 2 n'Y' (0, ~ v2) [4], we get
Differentiating (3) with respect to T, we get, for h ? 1,
T 8/ = 4 [(1+52)'1`~0,~~)521?
?For a crystalline substance T is the temperature of the substance, provided that 6D ~ T (AD = Debye temperature).
If 8 D >`T , we must replace T by the effective temperature Teff [5]?
tIn the case of the wideresonance approximation [6],h = p?oa /~sm~ whereaoa is the capture cross section at the
resonance maximum, and Esm is the cross section for potential scattering by all the nuclei except the resonance
absorber.
Translated from Atomnaya E`netgiya, Vol. 21, No. 1, pp. 5456, July, 1966. Original 8rticle submitted
January 21, 1966.
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Curves for calculating
Dopler temperature
coefficient
Tal/aT
0,01 0,1 1,0 >0
Using (1) and (2) we obtain an expression for T (a f / aT) for any h,
r
of __ 4 ~ _L 2 (x21) 1 ] `Y (x, ~) I 2  x~2~ (x> i;)
0
z
00  4 (xb)2
v _~
The functions V~(x, ~) and ~(x> ~) bear the following relations to the real and imaginary parts, u(x, y) and y(x, y)
of the complex probability integral:
~ (x, ~) = 2 v~ o C 2 ~~ 2)
Tables of the functions u(x, y) and v(x, y) are given in [7].
The function T (8 f/c3 T), for which an expression is given by(5), has maxima in ~ and h. For convenience, let
us introduce a new function [1],
a/
which has no maximum in ~, and, when ~  0 or ~> ??, has nonzero limits which differ from one another very
little. From (5) we get an expression for the function W(~, h'):
?
?
r 22 (x2 1)  1 ]
2
 z~2~ (x, S)
'Y (x, ~) I
11
1
2
(9)
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W (~, h)= 1 ~ (1)n(2ni3)!I n_!1 hn+1;
n=0
`~~
W (0, It')= 2 LJ (q)n n+1 h'n+t.
where h'= Pao ~(0, ~) is the ratio of the macroscopic cross section at the resonance maximum (allowing for the
s
Doppler effect) to the total cross section of potential scattering. .
For resonance close to the BreitWigner type (with ~ ? 1), using an asymptotic expansion of ~ and ~[7]
and integrating (l0), we get
T~4. (oo, h) = 4 } 31z + 4 .  2
2h ~/(1 { h)3 h2 ~j/1 ~ h h
For resonance close to the Doppler type, using the expansion of ~ and ~[7], we get, for g ? 1,
TT' (0, It')= 1 ' (2v2f)E v2dv. 12
When h' < 1, the integrands in (10) and (12) can be expanded in series in h'. We then get the following formulae:
~n (~) _  f n'Y 0 1 ` { [ ~2 (x' 1) 1 ] tY (x> s) I ~2  x~2~ (x, ~). r ~ (x, ~S)1 "+` dx;
[ (, ~)1 ~ n 2 2 ~ L ~Y (0, s) _l
From (10)(15) we can calculate the function W(~, h') in the ranges 0.01 s h' ~ 100 and 0 s g ,0 1,2
0,2 0,4 0,6 0,8 >,0 1,2 Shielding thickness, m
Shielding thickness, m
Fig. 2. Distribution of neutron fluxes in shielding
Fig. 1. Distribution of neutron fluxes in ironwater shielding. of ironheavy concrete. p, ~) Distribution of fluxes
^) Distribution of highenergy Neutrons (E > 20 MeV); ?) fast of resonance neutrons, according to data from two
neutrons (1.5 < E < 20 MeV): ~) resonance neutrons (E ~ 1.44 MeV ). experiments.
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 5657, July, 1966. Original article submitted
February 22, 1966.
~
~
?
~

~
I'~
I
Iron
Wate
r
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~~
E ~
? ^
^ ~
s ~
~
I
~
I
?
.
,
~~
~~
1~
I
~ r
.,
#
T
T
~ 1 7
i
II
T
Z
~ ~
,
~~
~
~
Water
Iron
I W a e
0,4 0,6 0,8 1,0
Shielding thickness, m
Fig. 3. Distribution of neutron fluxes in waterironwater shielding.
^) Distribution of highenergy neutrons; ?)fast neutrons; m)resonance
neutrons. ?) Distribution of gammaray dose rate, 10s ?r/sec.
On analysing the experimental results shown in Figs. 13, we conclude that, within the experimental error,
the presence of a preceding layer has no effect on the attenuation of fluxes of highenergy neutrons in the following
layer. .
Statistical data for many shielding materials [4] indicate that there is a linear relation between the inelastic
interaction cross section Ein of highenergy neutrons (E > 100 MeV) and the density p (in g/cros), to within about
5%:
Etna=0.59(f.5~~) ,rr.,
The extraction cross section Erem of highenergy neutrons is proportional to Ein [2, 3, 5]:
din
Ererit ~ Ct >
where the parameter a varies from 0.9 to 1.4, according to the neutron spectrum, and varies little with the material
of the shielding. In homogeneous shielding of sufficient thickness [2, 5] the following relation holds good:
~f _  Ein
tPtr ~ n ; f '
'rem
where ~ f and ~h are the fluxes of fast and highenergy neutrons, respectively, n is the mean number of evaporative
neutrons emerging from the excited nuclei, and Ejem is the extraction cross section for fast neutrons.
The value of n Ein/Erem increases with the atomic weight of the shielding material. It was estimated to
vary from ~ 0.1 for water to 1 for iron. The varying values of this quantity for each layer satisfactorily explain the
behavior of a flux of fast neutrons.
Surges in the fluxes of resonance neutrons at the boundary between two materials are due to the difference
in these materials's moderating properties and also to deformation of the intermediateneutron spectrum with
,increasing distance from the boundary.
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Attenuation of the resonanceneutron flux in the material behind the iron can be regarded as exponential,
after short transitional sections. The transitional sections are approximately equal to the relaxation lengths, and
are ~1 ~ 3 cm in water and ~Z ~ 9 cm in heavy concrete. For these materials, the ages of the intermediate
neutrons up to 1.44 eV (Eo = 1.5 MeV) are approximately T t ~ 30 cmZ and T2 ~ 120 cm2 [5]. From these values
of T and 1, we can infer that, to a certain approximation, ~ characterizes the attenuation of a flux of inter
mediate neutrons in the second layer. The increased indications of the xray film in the layer of water following a
layer of iron (cf. Fig. 3) are due to the hard component of the scattered capture gamma radiation.
Owing to the appreciable accumulation of intermediate neutrons in the heavy materials, especially in steel,
it is desirable to make a subsequent layer of shielding of watercontaining material.
The authors would like to thank Z. Tsisek and A. P. Cherevatenko for help in the experimental work.
1. L. N. Zaitsev et al. Atomnaya Energiya, 12, 525 (1962).
2. B. S. Sychev et al. Atomnaya Energiya, 2Q 323 (1966).
3. B. S. Sychev et al. Atomnaya Energiya, 20, 355 (1966).
4. L. N. Zaitsev et al. Atomnaya Energiya; 19, 303 (1965).
5. D: L. Broder et al. Concrete in Shields for Nuclear Plant. Moscow, Atomizdat (1966).
686
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HEAT EMISSION FROM POTASSIUM BOILING IN' A TUBE IN THE REGION
V. M. Borishanskii, A: A. Andreevskii;
K. A. Zhokhov, G. .S. Bykov,
and L. S. Svetlova
Fig. 1. Working section of apparatus.
UDC 621.039.517.5
Until recently, heat exchange during the. boiling of alkali metals
has ,been studied mainly for the case of free convection of the ligtiid
in a large vessel [14]. In [1] it was shown that, for sodium or
potassium boiling with bubble formation in a large 'vessel, the heat .
transfer coefficient is proportional to the 0.7th power of the specific
thermal load, i. e., the relation between a and q is the same as for
the boiling of nonmetallic liquids. A similar relation was found by
the authors of [2 ,8]. This problem was analyzed theoretically in
[5, 6]. However, less work has been done on the boiling of alkali
metals in tubes.
In this letter we give some results on heat transfer during the
boiling of potassium in circular tubes of diameter 10 mm and length
600 and 800 mm..
The apparatus used for this work consists of a closed circulation
loop made of steel 1Kh18N9T. The main unit is the working section
(calorimeter), which is directly heated by an electric current, and
consists of two tubes (Fig. 1). To reduce the electrical resistance, the
gap between the tubes was filled with copper. It was calculated that,
for the given thickness of the copper layer (S = 4 mm), the heat
emission in the liquid metal (in absence of vapor formation) was less
than 10% of the total heat emission in the working section. During
boiling practically all the heat was emitted in the walls. The wall
temperature was measured at ten positions along the working section,
in each of which was installed a chromelalumel thermocouple. The
temperature of the potassium was measured at the inlet to the working
section, and also inside it at 30, 90 and 210 mm from the inlet and
30 mm from the outlet.
The experiments took place at saturation pressures in the range
ps ~ 0.423.38 atm (ts ~ 678910?C) with thermal loads of up to
t,'C  ; ~ i
900 ~ o ~ e ~
890
880  
8700 100 200. 300 400 500. 600 700 [, m m
Fig. 2. Temperature distribution along working section. Operating
conditions: q= 263, 000 kcal/mE ' h; G = 131:5 kg/h; p = 3.2 atm;
xout = 10.8%.
Translated from Atomnaya Energiya Vol. 21, No. 1, pp. 5859, July, 1966. Original article submitted
February 18, 1966.
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~
/0
t,?C  530,000 kcal/m ? h. The vapor content at the inlet was ~15
by weight. The apparatus was constructed so that potassium
870
\ could be fed to the working section both after heating to the
850 ~?. saturation temperature and with a content of the vapor phase:
\ ? ? ? ?
Figure 2 gives the temperature distribution curve along
830
the working section with the vapor content at the inlet slightly
o~~ 
790 hence also the coefficient of heat transfer, are approximately
~ I i constant along the tube.
1JUIlilg C[LC eXpCIlIIlGlll ulc w~aauuul Wa? uwcwcu w uc
come superheated above the saturation temperature. This
Fig. 3. Temperature distribution along working phenomenon took place when the working section was fed with
section. Operating conditions: q = 460,000 liquid metal not heated to the saturation temperature, so that
kcal/mZ ? h; G = 84 kg/h; p = 1.78 atm; xout = further heating took place in the working section. However, .
25.6%, after the potassium reached saturation temperature, it became
' further heated during the course of its motion. The extent of
the superheating was 3050? C above the saturation temperature. After this the temperature of the potassium
rapidly fell to near the saturation value. This process was accompanied by strong temperature pulsations of the wall
and vaporliquid mixture throughout the length of the working section. The maximum amplitude of these tempera
ture pulsations was observed to occur in the superheating zone and amounted tot 20? C.
Figure 3 plots the temperature distribution along the working section when the latter was fed with potassium
not heated to saturation temperature.
Our experimental results on heat transfer are plotted in Fig. 4; this diagram also gives results from [1] on
potassium boiling in a large vessel, and from [7] on potassium boiling in tubes of diameters 8.3 and 22 mm. Satis
factory agreement is observed between the data for the large vessel and the tubes, in the region of moderate vapor
content. The experimental points are grouped near the line which represents the equation given in [1] for boiling
with free circulation in a large vessel: '
^
^
a
^ o ~
.
o
~~
o?~
?.
?
?
?
s
~
o?
t
d
00
0
o
~
.
0
~ oo?
0
0
o
~oo
oo
~
00
I
j
~o
i
Fig. 4. Heat emission for potassium boiling in a large vessel and in tubes of
various diameters. O)Large vessel (data of'presenf work); ?)d= 10 mm (data
of present work); ^)d = 8.3 mm [7]; ^)~d = 22 mm [7].
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where a is the coefficient of heat transfer in kcal/mE ? h ? ?C, q is the thermal load in kcal/m2 ? h, and p is the
pressure in 'atm. Thus, Eq. (1) can be used to calculate the heat transfer from potassium boiling in a tube, in
the absence of effects due to the vapor content.
LITERATURE' CITED
1 . V. M. Borishanskii et al. Atomnaya Energiya, 19, 191 (1965).
2. R. Lyon, A. Faust, and A. Katz. Chem. Engng Progr. Sympos. Series, 51, No. 7 (1955).
3. R. Noyes. Trans. ASME (Series G), 5, No. 2 (1963). ,
4. N. Madsen and C. Bonilla, Chem. Engng Progr. Sympos. Series> 56, No. 30 (1960,).
5. V. M. Borishanskii and K. A. Zhokhov. Atomnaya 1`nergiya, 18, '294 (1965). .
6. V. I. Deev and A. N. Solov'ev. Inzh.fiz. zh., No. 6, 8 (1964).
7. A. Fraaz. Atomnaya Tekhnika za Rubezhom, No. 6; 12 (1964).
All abbreviations of periodicals in the above bibliography are letterbyletter translitera
tions of the abbreviations as given in the original Russian journal. Some or all of this peri
odical literature may well be available in English translation. A complete list of the coverto?
cover English translations aPPears at the back of the first issue of this year.
689
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CHANGES IN THE MECHANICAL PROPERTIES OF AN AGING ALUMINUM
ALLOY AFTER USE IN A NUCLEAR REACTOR
A. P. Kuznetsova and B. V. Sharov
This investigation deals with the alloy"Avial' Mark SAV1", which consists of aluminum plus 0.61.2%
silicon and 0.450.9% magnesium.
The phase diagram of the system AlMgSi contains a .quasibinary eutectic betweeri an aluminumbased solid
solution and the intermetallic compound Mg2Si. The solubility of Mg2Si in aluminum decreases from 1.85% at the
eutectic temperature to ~ 0.1% at room temperature [1]. Thus, after quenching of the alloy, age hardening takes
place, owing to the appearance in the aluminum matrix of zones enriched with the alloy components and the forma
tion of particles of Mg2Si during the later stages of aging.
~
~
y
~cC~
L.
(~''!!
G
(
~'!!
G
4.
0
~
0 ~
~
~
~
aoi
o
~
~
`V
.x
x
,~
~, ~
0
~ th
q
~
0
.o

O
1
1(l~.
._ lOta
30,5~0,(i
22,8_T1,6
i1,5?0,8
i(1
'~


3(l,'1t0,7
23,5~1,4
11,6~0,9
8
3
2.1(1'r`'
fi?90t?~
i0,1.~0,4
23,2.~0,6
10,4}0,5
5
4
2.10r~4
(i?'10~~~
30,3~0,6
24,8?0,9
10,31,1
11
Before

27,50,6
21;1?0,9
12,50,2
ic;
irradia
~
tion
SAV1 is used as a structural material for reactor
cores, because it contains no substances with a large
absorption cross section for thermal neutrons.' It is
also resistant to corrosion in water, carbon dioxide
and other media.
We have studied the properties of the material
of an. "Avial'" tube which has been acting as a pro
cess channel in the reactor of the Institute of Theoretical
and Experimental Physics (Fig. 1). The "Avial' "
"References [2, 3] give some data on the effect of
irradiation on the properties of annealed SAV1 and
the similar American alloy 6061(61S).
TABLE 2. Results of Tests on Control Specimens and on Specimens Irradiated by 6.1020 neutrons /cm2
Conditions of creep
Residual
Results of rapid testing to destruction after
test
deformation
creep tests
~
S
i
after * reep,
I
No. of tests
T, ~c
a, kg/
i,. h
men
pec
i
%
6B, kg/
6o,z, kg/.
6, ?/,
performed
mm2
,
2
mm
mm2
Control
2,31
19,2?1,6
16,(i~2,1
101,7
3
9544
7
I
L30
j Irradiated
~
1,81
1~9,1~1,8
~
16,11,5
101,7
3
Control
I
~ 2,5~f
18,01,2
16,00,6
7,9.0,1
3
154f4
5
i 350
Irradiated
I
j
j 1,41
I
14,71,1
,,
1,31,3
10,9}0,7
4
Control
i
I. D. 65 cm.
The cable must be irradiated in an inert atmosphere, say argon, in order to forestall oxidation. Before
commencing the irradiation, the processor together with the cable loaded into it is to be "washed" with argon by
successively evacuating and refilling the space three times. After this operation the radiLtLUirchemical processor
is filled with argon to an overpressure of 0.3 arm, and the cable is then irradiated in the argon environment. A
large amount of hydrogen (as much as 160 liters daily) is given off during the irradiation process, and for that reason
the argonhydrogen mixture is pumped out every 12 hours the plant is in operation, after which the plant is refilled
with argon to an overpressure of 0.3 atm.
The KP200 radiationchemical plant [6] using a Co60 gammaray source with a total activity of 180,000
gramequivalents of radium proved well suited to the purpose. The irradiator in this unit consists of 20 individual
channels placed, in this application, on two concentric circles. The inner irradiator consists of six operating
channels, with a diameter of 55 em, while the outer irradiator consists of 14 channels and is 113 cm in diameter.
=The activity distribution between the inner and outer irradiators was decided upon in such a way as to provide the
required uniformity of dose field in the horizontal cross section. There were seven Co60 preparations in each channel,
forming line sources 74 cm in height. The radiation sources were transferred from the storage pond to the irradiator
channels under compressed air at 0.4 atm.
Calculations of the doserate field distribution in the horizontal cross section of the radiationchemical pro
cessor were checked experimentally with the aid of ferrocuprosulfate dosimeters placed in a processor filled with
water or cable material. The choice of water as simulator is dictated by the close agreement between the values
of the bulls density of the cable material and the specific weight of water (respectively 0.95 and 1 g/cm3).
Discrepancies between calculations based on data reported in [7] and the experiment kept to within 2%. The
processor was rotated on its axis at a speed of 2 rpm in order to obtain the required uniformity of doserate field
over the cylindrical surfaces concentric about the surface of the irradiators. The height of the irradiator had to be
increased to 150 cm in order to obtain a uniform field of dose rates up the entire height of the cablefilled radiation
chemical processor. Pneumatic conveying of the radiation sources made it possible to cope with this problem
with ease (i. e., doubling the irradiator height) by positioning the sources in two tiers.
Experimental checking revealed a need to smooth out the doserate field along the height of the radiation
chemical processor. The existence of a clearance of 3 cm between the top and bottom tiers of sources in the
irradiator, plus partial shielding of the middle of the irradiators by lead filters 20 cm high and 2 mm thick, brought
about the required field uniformity of absorbed dose throughout the volume of the cablefilled processor. The
experimental doserate field values throughout the volume of the processor loaded with cable, with lead. filters in
place, are shown in Fig. 3.
The dose required for different types of cables was chosen on the basis of product specifications and service
conditions. When an insulated core in the geophysical cable was irradiated, a dose of 140 Mradt 10% was arrived
at on the basis of preliminary experiments. The productivity of the facility was 0.7 kg of cable per hour at a dose
rate of 63 r/sec and exposure time of 610 h. This means agammaradiation efficiency of ~ 13% for the plant.
Crosslinking of polyethylene insulation for the insulated core of geophysical cable 9 km in length was brought
about on a KP200 isotope facility. The practical realization of this process demonstrated how feasible it is to use
isotope facilities for radiationchemical processes in the treatment of largesize stock.
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~.
The authors are indebted to G. N. Lisov for his part in the design of the facility, and to M. E. Eroshov, M. D.
Larionov, L. K. Topil'skii, Yu. D. Kozlov, and the late N. A. Kuznetsov for their kind assistance in the experimental
phase of the work.
1. E. E. Finkel' et al. In the book: Proceedings of the Cable Industry Research Institute [NIIKP] [in Russian],
No. VI, Moscow, GosBnergoizdat (1962), p. 151.
2. N. P. Gashinova et al. Ibid., No. VII, Moscow, Gos~nergoizdat (1963), p. 109.
3. E. E. Finkel'. Coll: Applications for Plastics in the Cable Industry [in Russian], Moscow, AllUnion Research
Institute for Electromechanics (1964), p. 25.
4. V. L. Karpov et al. Proceedings of the II AllUnion Conference on Radiation Chemistry, Moscow, Izd, AN
SSSR (1962), p. 547.
5. G. I. Gladkov et al. In the book: Proceedings of the Cable Industry Research Institute,[in Russian], No. LX,
Moscow, Gos~arergoizdat (1963), p. 131.
6. N. G. Gusev et al. Shielding Against Emission by Extended Sources [in Russian], Moscow, (Gosatomizdat)
(1961).
7. V. I. Volgin et al. Atomnaya ~nergiya,'18, 546 (1965).
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An exhibition hall devoted to the peaceful use of atomic energy in the USSR has found great popularity
among visitors to the Polytechnical Museum. A central position in the exhibition hall is assigned to a section
showing the role of nuclear power in the USSR. Numerous models, posters, and exhibits illustrate recent advances
in nuclear power in the USSR. Among the most interesting ofthem is a working model of an atomic power station
which will soon be put into operation at Shevchenko with the BN350, the first commercial, fastbreeder power
reactor in the USSR. Energy generated in the reactor will be used both for the production of electrical power and
for a desalinization plant with a capacity of 100,000 ms/day.
A prominent place in the exhibition is occupied by low level nuclear power, which is represented by models
~of a 1500 kW portable atomic power station with aboilingwater, watercooled reactor and of a 750 kW organic
cooled reactor (ARBUS2).
At the center of the hall, there are working models of the largest Soviet atomic power stations complete with
buildings and equipmentthe Kurchatov station at Beloyarsk and the one at NovoVoronezh.
At the Beloyarsk atomic power station, uraniumgraphite reactors have been installed which have nuclear
superheating of steam to ~ 500? C making it possible to use series turbines. The efficiency of the station is 3538%.
The reactor of one section of the NovoVoronezh atomic power station has six circulating coolant loops, each pair
of loops producing steam for one 70,000 kW turbogenerator. A single reactor forms a unit with three turbogenerators.
This reactor is enclosed in a vessel in the form of a steel cylinder 3.8 m in diameter and 12 m high. The reactor
core contains 312 operating fuel assemblies each of which contains 91 uranium dioxide fuel elements enriched to
1.5%. The efficiency of the station is 26.6%.
Attracting the attention of visitors is a model of the First Atomic Power Station reactor and operating engi
neering loops which demonstrate clearly, and in detail, the operating principles of an atomic power station and of
a reactor core.
Of great interest is an exhibit of a model of the Romashka device, an outstanding direct converter of thermal
energy to electricity. The device was shown at the Third International Conference on the Peaceful Use of Atomic
Energy. The energy source in the device is a fast reactor with fuel in the form of 49 kg of 90% enriched uranium
carbide. Energy is converted by means of semiconductor thermal converters. Temperature at the reflector surface
is 1000? C, and power of the device is 0.50.8 kW.
Tables presented in the exhibits reveal the prospects for the development of nuclear power in the USSR and
the economic efficiency of an atomic power station in comparison with an ordinary coalfired station. They indicate
how the competitiveness of an atomic power station with respect to a coalfired station increases in proportion to
increase in the power of the atomic power station.
In addition to nuclear power, the exhibition hall includes other fields in the peaceful use of atomic energy.
Models of thermonuclear devices, toroidal chambers, and of the Ogrenok device give an idea of thework on
mastering thermonuclear power. Of them, the most interesting is a model of the Ogrenok magnetic trap for thermo
nuclear research which is a cylindrical vacuum chamber with longitudinal magnetic field and magnetic mirrors. To
produce ahightemperature plasma, deuterium ions, previously accelerated by a powerful accelerator, are injected
into the chamber. Charged particles in the plasma are captured by the magnetic field.
Also shown in the hall are instruments and equipment which demonstrate modern capabilities for the detection
and measurement of radioactive radiations. Of particular interest is a model and diagram of a scintillation counter
intended for measuring intense radiation fluxes and also for counting individual particles. The radiation detection
efficiency is extremely high (it is about 100% for aand /i radiation, and as much as 50% for y radiation). A
model and diagram is also shown for agasdischarge counter intended for detecting individual radioactive particles
(the detection efficiency fora and t3 particles is close to 100%).
Several instruments illustrate the use of radiation counters in various pieces of apparatus. For example, type
SCh3 equipment for counting neutrons is intended for the measurement of neutron fluxes by recording the electrical
Translated from Atomnaya Energiya, Vol. 21, No. 1, pp. 7476, July, 1966.
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impulses produced by neutrons in a SKM5A boron counter, the latter acting as a sensor. The equipment is used for
monitoring reactor operation and for research. The resolving time of the equipment is less than 50 ?sec. Also on
exhibit is a type B2 counting equipment which consists of a VSP (1) scaler with electromechanical pulse counter
and scintillation attachment for measuring the intensity of radiation with a scintillation counter, the apparatus
being intended for detection and pulse counting in the measurement of cx, p, and y radiation. The count rate of
the apparatus goes to 6400 cts/sec separated by more than 50 ?sec. In a number of exhibits, there are PS100 scalers
with special decatron tubes in which counting rates of 20,000 cts/sec are achieved. The use of counters in biology
is demonstrated by IMA1 tracer atom ratemeters which are intended for qualitative and quantitative differential
determination of soft and hard a and y radiation in working with tracer atoms. The instrument makes it possible to
follow the path and the point of accumulation of tracer atoms in plants and animals. Indications of radiation inten
sity are given by measuring instruments, sound, and light signals. The pulse sensor is an SBT 7endwindow halogen
counter in a hermetically sealed case.
A special section is devoted to the use of radioactive isotopes and to equipment, and the operation of equip
ment, using radioactive isotopes for flaw detection and measurement. Among the interesting exhibits in this section
is a CUPCo0,51 flawdetector for industrial xray work and a portable GUPTi0.53 which makes it possible to
manage without expensive xray equipment. Also exhibited is working demonstration equipmenta Sliva radio
active soilmeter which makes it possible to measure the percent content (from 0 to 40%) of soil in the silt passing
through the silt pipes of a dredge; this enables one to regulate? the optimal mode of dredge operation. Operation of
the instrument is based on the measurement, with an ionization chamber and tube circuit, of the radioactive radiation
passing through the soil pipe from a radioactive source. Any change in the consistency of the silt produces some
kind of attenuation in radiation intensity and a corresponding change in the reading of the instrument.
Of interest is a UR4 radioactive level gauge which is intended for continuous, contactfree measurement of
the height of the interface between two media by illuminating the object with y rays from a Co60 source. The
instrument consists of two columns and an electronic unit. The columns contain movable carriages, one of which
carries a container with the radioactive source, and the other, two STS8 counters.
Dosimetric equipment is also exhibited in the hall. Included is the Tiss type universal radiometer which is
.intended for measurement and warning when a given level of radioactive contamination by a and aactive
materials is exceeded on the surface of equipment, or on the clothing and hands of operating personnel. Instru
r~ents on exhibit enable one to measure radiation dosethe Kaktus microroentgenometer (a fixed linefed instru
ment for measuring yray dose rate) and the KND1 individual dosimeter (for measuring total doses of 0.022
R from y rays with energies from 115 keV to 2 MeV).
Numerous posters and illustrations acquaint one with a brief chronicle of the most important events in the
field of the peaceful use of atomic energy and also show the structure of the atom and the nucleus simply and
clearly; they tell about radioactivity, nuclear reactions, the principle of chain reaction, and the operation of fast
and thermal nuclear reactors.
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In Dubna, the jubilee session of the Scientific Council of the Joint Institute for Nuclear Research has completed
its work. It was decided to confer the name of Academician Igor Vasil'evich Kurchatov on the new, one hundfed
fourth element in the periodic table ~in memory of his outstanding service in the development of Soviet and world
wide physics.
Research carried out at Dubna on the synthesis of elements one hundred two, one hundred three, and one
hundred four indicated that the most promising method of synthesis was connected with the irradiation of heavy
elements by accelerated, complex nuclei. This is particularly apparent in the work on element one hundred four.
The first data on the properties of the new element were obtained in 1964 in the JINR Nuclear Reactions Laboratory
by G. N. Flerov, Yu. Ts. Oganesyan, Yu. V: Lobanov, V. I. Kuznetsov> V. A. Druin, V. P. Perelygin, K. A. Gavrilov,
S. P. Tret'yakov and V. M. Plotko. One hundred and fifty spontaneous fission events in the new element were
recorded as the result of extremely complex and lengthy experiments. Its lifetime turned out to be about thirty.
seconds. After completion of the physical experiments, a group of Soviet and Czechoslovak staff membersI. Zvara
Yu. T. Chuburkov, R. Tsaletka, T. S. Zvarova, M. R. Shalaevskii, B. V. Shilovbeganastudy of the chemical pro
perties of element 104. ~ This .problem was proposed by G. N. Flerov, and the development of techniques had
already started in 1960. The investigations used original, rapid methods for continuous separation of the products
of nuclear interactions.
The method developed by the chemists made it possible to study the chemical properties of an element in
fractions of a second while having only individual atoms at their disposal. The idea of chemical identification was
based on an assumed sharp difference in the properties of the higher chlorides of element 104. In the chemical
experiments, atoms of element 104 were separated from all actinides. It was shown that the new element was an
analog of hafnium. Thus the cycle of research on the identification of element 104 was completed.
Now a new element, bearing the name of an outstanding Soviet scientist, must take its place in the periodic
'The paper of I. Zvara et al., Chemical properties of element 104, will be published in the August issue of
Atomnaya Energiya.
Translated from Atomnaya Energiya, Vol. 21, No. 1, p. 76, July, 1966.
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BIBLIOGRAPHY
M . A . H e a 1 d and C . B . Wharton , Plasma Diagnostics with Microwaves. New YorkLondon
Sydney, John Wiley and Sons (1965), 452 pages.
Microwave diagnostics of plasma is a widely used technique, not only in thermonuclear fusion experiments,
but also in space research, ionosphere studies, the development of spacecraft engines, MHD energy converters,
microwave instruments, and other applications. The great advances in microwave diagnostic techniques have
rendered it a standard technique in plasma investigation in many laboratories throughout the world. In this connec
tion the book by M. A. Heald and C. B. Wharton, pioneers in this field, is of .enormous interest. These authors set
themselves the goal of writing a book whichwould serve as reference text and handbook for the experimental
physicist first approaching the study of plasmas by microwave techniques. The book contains an exhaustive pre
sentation of the theoretical fundamentals, plus a very detailed and what appears to be a unique, to date, description
of the experimental technique. One special merit of this book, writteri by experimental physicists for experimental
physicists, is the large number of photographic plates, oscillograms, graphs, and diagrams, which will be valuable
tools to anyone working in the field.
The presentation of the material begins at the elementary level and gradually rises to the frontier of research
in this field. In the first chapter, the authors acquaint the reader with the now familiar theory of wave propagation
through a cold plasma. In the second chapter, discussion centers on the role of collisions, especially electronion
coulomb collisions. The third chapter applies kinetic theory to wave propagation in a hot plasma, when the random
thermal velocities of the electrons are commensurate with the phase velocity of the wave. This chapter concludes
with a brief discussion of Landau damping. The fourth and fifth chapters deal with the theory of wave propagation
in a confined plasma. They take up microwave probing of plasma and the theory of plasmafilled waveguides and
resonators. The sixth chapter presents a detailed discussion of all possible practical schemes of active microwave
diagnostics of plasma (measurement of transmission, attenuation, and reflection of waves, microwave interferometers,
measurements of Faraday rotation, wave scattering experiments, and so forth). The next two chapters take up the
theory of microwave emission by the plasma itself as a result of both thermal and nonthermal processes, and discusses
techniques of passive radiometric diagnostics. The ninth chapter cites a very detailed description of microwave
equipment and microwave plumbing for use in plasma diagnostics. The tenth and concluding chapter of the book
gives a brief description of other plasma diagnostics techniques. Here we find laser measurements, Langmuir and
magnetic probes, optical spectroscopy, and similar topics, plus a discussion of how to use the various techniques to
check the other diagnostic techniques. The book ends with a generous bibliography (mentioning over 500 titles)
and an alphabetically ordered subject index.
J . H . Sanders . The Fundamental Atomic Constants. Oxford Univ. Press, Oxford (1965), 98 pages.
This is the second edition of a monograph devoted to the fundamental atomic constants. It includes: the
charge on an electron (e), the mass of the electron (m ), the mass of the proton (M), the speed of propagation of
electromagnetic radiation in vacuum (c), Planck's constant (h), Avogadro's number (N), Boltzmann's constant (K ),
and the gravitational constant (G).
Modem atomic physics requires a knowledge of the exact values of these constants. The experimental (direct
and indirect) and theoretical determination of these values is the subject of a large number of papers which serve as
the basis for this book (the list of pertinent literature extends over 213 titles). The content of the monograph can be
divided into four basic sections: earlier measurements of the constants, modern exact measurements and measure
ments of the speed of light, and deviations in values of the constants.
The appendices give the commonly used designations for the constants, standardization of measurements,
and a table of values of the constants with precision indicated.
The monograph will be of interest to both theoretical and experimental physicists as a reference containing
the most exact values available for the atomic quantities in question.
Translated from Atomnaya Energiya Vol. 21, No. 1, pp. 7780, July> 1966.
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Seventh Report on the Activities of the [European Nuclear Energy] Agency. Paris, ENEA (1965), 125 pages.
The European Nuclear Energy Agency, in which 18 European nations enjoy membership, issued its seventh
report on its activities in 1965. The report starts off with a description of the work carried on in joint efforts at
the Halden and Dragon reactors and at the Eurochemic spentfuel reprocessing plant. The reactors are presently in
operation, and the reprocessing plant will be on stream before the end of 1966.
A description of the collaborative efforts of the ENEA in the field of nuclear constants, reactor physics, reactor
safety programs, computer programming, neutron constants, irradiation of foodstuffs, power. production with radio..
active isotopes, and similar topics, takes up a lot of space in the report.
Close attention is given to international rules and regulations on reactor safety, radiation shielding, disposal
of radioactive wastes, transportation of radioactive materials, etc. The outlook for the development of nuclear
power in member nations of the ENEA and is dealt with in brief, and the fuelpower balance of those countries is
also described.
The book has several appendices: the organizational structure of the agency, the work of the committee on
reactor safety terminology, irradiation programs, a list of power reactors, research reactors, and critical assemblies
in the ENEA membernations.
The report is mainly of an informative and descriptive character and may prove useful to those readers who
are primarily .interested in the activities, organization, and administration of international atomic agencies.
Use of Plutonium for Power Production. Vienna, IAEA (1965),162 pages.
This publication comprises a collection of papers submitted to an IAEAsponsored conference on the use of
plutonium in power production. The increase in production of plutonium in power reactors of different countries
places added emphasis on plutonium recycle operations and on more efficient utilization of plutonium supplies.
For example, ~?3000kgofplutonium will be produced annually in Great Britain's reactors during the Seventies; the
annual production of plutonium in the USA is expected to reach 15,00020,000 kg by 1980.
The collection of papers is divided into two parts. The first section presents papers from different countries
(twelve papers in all); the second section presents brief reviews summarizing the discussion at the conference
(7 reviews).
The research program on the use of plutonium in Belgium's reactors is discussed in a paper by E. Bemben.
The brunt of this paper is the description of trends in research and the organization of research work. There are
some brief remarks on irradiation experiments in the BR3 reactor using plutonium fuel elements.
A costs analysis of a plutonium recycle fuel cycle in thermal reactors appears in a report by O. Reynolds
(Canada). The author concludes that the use of plutonium produced in CANDU type reactors in watercooled
watermoderated reactors will bring down the fuel component of power costs to 0.05 cent per kWh. The physics
of plutonium utilization as nuclear fuel is discussed in a paper by J? Vandres et al. (France). Costs are discussed in
general outline. Similar topics are discussed by S. Paranipe (India), but here attention is centered on fuel cycles
utilizing thorium fuel in systems with thermal and fast reactors.
L. Sani (Italy) centered his attention on the isotope compositions of fuel discharged from the reactor at
different bumup levels. The next two papers are from Japan. The first (S. Omachi) deals with the status of re
search work on plutonium utilization in Japan, and the second (M. Takahashi) deals with the outlook for plutonium
utilization in electric power generation.
Great Britain submitted a fundamental paper on plutonium utilization (H..Kronberger). Physics in thermal
reactors and fast reactors, fuel element fabrication, costs, burnup in thermal reactor, and fast reactors are discussed.
F. Albauch (USA) cited a large amount of experimental data on plutonium fuel technology for thermal reactors.
This report was complemented with one by S. Lawrowski (USA) on the USA fast reactor plutonium utilization pro
gram. The technology and fabrication techniques of plutonium fuel elements, plutonium fuel material, and their
utilization were stressed in this report.
The last two reports were presented by Euratom. These were a paper by W. Rajewski on plutonium utilization
research and one by H. Mikhaelis on plutonium utilization costs. The reports gave most of their space to the out
look for plutonium production and plutonium utilization (extrapolated to 1980).
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International Symposium on Working Methods in High Activity Hot Laboratory, Volumes I, II. Paris,
European Nuclear Energy Agency (1965), 1030 pages.
A symposium, whose proceedings appear in a separate publication, was organized by the Commission of
Economic Cooperation and Development of ENEA in collaboration with Euratom, and held at Grenoble in June 1965
at the atomic research center of the Commissariat de 1'Energie Atomique of France.
Representatives of sixteen nations and five international bodies participated in the symposium. The two
volume publication includes 53 papers and material on 12 discussions following presentation of the papers. All the
papers are grouped by according to the six sessions, each of which was devoted to a particular topic.
Xradiographic and similar radiographic inspection of irradiated fuel elements were discussed at the first two
sessions, as well as several nondestructive techniques for inspecting fuel elements and experimental capsules (gamma
ray spectroscopy, ultrasonic inspection, eddy current techniques, fluoroscopy, metrologic determinations of dimen
sional changes and warpage, remote photography and remote inspection techniques). The reports cite diagrams of
remote control facilities designed for these studies.
A. Fudge, R. Coser (Great Britain), H: Engelman (France), et al. discussed topics pertaining to the study of
fission product distribution and migration in the interior of fuel elements by gammaray scanning techniques.
Results were cited.
Reports by F. Browne (USA) and G. Vinebliss (Great Britain) et al. discussed various methods for nondestructive
inspection of fuel elements, and cited some diagrams of remote control accessories and facilities for sampling
gaseous fission products to determine their composition and quantity.
The third session was devoted to various techniques and equipment for disassembly and mechanical treatment
of spent fuel elements and experimental capsules in hot caves for the fabrication of inspection samples.
The fourth session discussed several techniques and methods for the transportation of spent fuel elements and
experimental capsules following inpile irradiation. Close attention is given to shielding techniques designed to
eliminate contamination of rooms, equipment, and the surrounding atmosphere at fuel reloading sites (paper sub
mitted by F. Larsen, Denmark). The problem is handled by correct organization of the ventilation system (inflow
discharge), by bringing about a properrarefaction in rooms occupied by personel, in hot caves in a, p, andy
shielded glove boxes. Reports by P. Pesenti (Euratom), M. Heeren (West Germany)>et al. cited diagrams and
sequencing of reloading operations, with all manner of polyethylene and polyvinyl chloride films 0.3 to 0,4 mm
thick in jacket and sleeve configurations employed for protecting the environmental atmosphere from a, S, and
y contamination.
P. Graf (Switzerland), G. Schult (USA), A. Ritchie (Great Britain), P. Gotlob (West Germany),and others dis
cussed various types and designs of transporting and reloading devices employed in hot laboratories in their re
spective countries.
Reports submitted at the fifth session discussed deactivation of rooms,. hot caves, a, S, and yshielded boxes,.
manipulators, and various approaches and techniques in the conveyance of contaminated materials from radiation
hazard zones to deactivation and maintenance rooms. Reports by C. Watson (USA), H. Wells (Great Britain)>et al.
cited a number of physical deactivation techniques (ultrasonic cleaning, pneumatic chisel treatment of con
taminated surfaces, treatment of contaminated surfaces with metal brushes, abrasive grinding wheels, vacuum
suction dust collectors and moisture collectors, etc.) and chemical deactivation techniques (acids, alkalis, organic
solvents, water), and the equipment and materials utilized in this work. Recommendations are given for the deactiva
tion of floors, walls, ceilings, and the structural materials employed in building hot caves and glove boxes. Reports
by H. Brinkmann (West Germany), C. Cesarino (Italy), L. Hayette (France),, and others cited examples of organiza
tion and planning of rooms for deactivation of contaminated equipment (manipulators, aand 13shielded glove boxes
for work in hot cells, instruments, facilities, devices ).All the authors are of the view that deactivation operations
should always be carried out in a specially isolated room which is properly planned and equipped (air locks) and
designed to prevent the propagation of radioactive contaminants through clean rooms in a hot laboratory. Examples
of correct organization and outfitting of rooms for deactivation are cited.
The last session heard reports on planning of hot laboratories (USA, Great Britain, etc.) and shops for repro
cessing and inspecting spent fuel elements; organization of ventilation systems, transportation of irradiated materials,
equipment for inspection of fuel elements in hot caves with heavy shielding against gamma rays, gloveboxesshielded
for a and aemissions, and organization of inspection, measures .to prevent radioactive contamination of
laboratory rooms, shops, and surrounding premises or of the equipment used in those facilities.
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Sections appended to those symposium papers list hot laboratories in the participant nations represented at
'the symposium, their locations, brief data on them,and some indication of the work pursued there. A list of con
tributing authors is also given.
The symposium materials are accompanied by a large number of illustrations and diagrams, with references
to the literature.
The appearance in print of this collection of symposium papers will enable many specialists working with
highly radioactive materials to familiarize themselves with techniques in use, and to broaden their horizon on topics
pertaining to the proper organization of conveying radioactive materials in hot laboratories and deactivation of
different types of contaminated equipment. .These materials will also be of great value to designers of hot caves,
glove boxes, and hot laboratories.
Exchange Reactions. Vienna, International Atomic Energy Agency (1965),417 pages.
"Exchange reactions" is the title of the proceedings of a symposium on exchange reactions organized by IAEA
and held in MayJune 1965 at Brookhaven. National Laboratory (USA). The collection contains 29 jpapers,
with abstracts in English, French, Russian, and Italian. Each paper is followed by a brief account of the ensuing
discussion.
Some of the papers deal with the theory of reactions involving electron transfer and their significance in
structural effect, with the effect of the stability of complex compounds on electron exchange reactions, with
electron transfer and proton transfer by the Grothus mechanism in aqueous'solutionsand inbiological systems, and with
techniques used in the study of exchange reactions (mass spectroscopy of exchange regions of isotopes and investiga
tion of exchange reactions of alkyl groups in aluminoalkyl compounds by proton magnetic resonance). The bulk
of the reports submitted concern research on concrete systems. The mechanism and kinetics of electron transfer
reactions in systems of elements of differing valency (tetravalent and hexavalent uranium, divalent and trivalent
iron, trivalent and pentavalent antimony) occurring in aqueous and organic media. One of the papers reported the
effect of the nature of the solvent, of salts present, and of temperature on exchange reactions in systems containing
neptunium and uranium. Many of the papers dealt with exchange reactions in complex compounds (hexachlorides
and pentachlorides of trivalent radium; complexes involving divalent platinum; halide complexes of elements of
the platinum group with coordination number six) and in organic systems (electron exchange reactions of aromatic
molecules, electron transfer in vinyl aromatic polymers, etc.). Finally, some of the papers reported results on
exchange reactions occurring on the surface of ionic crystals.
Nondestructive Testing in Nuclear Technology. Vienna, IAEA (1965), 393 pages (Volume I) +446 pages
(Volume II).
This is a collection of 46 papers presented by leading specialists from 20 countries and two international
organizations at a Budapest May 1965 international symposium, as well as accounts of the discussion at the sympos
ium sessions. The collection reflects the advances registered in recent years in the use of nondestructive testing
methods for quality control of structural materials and finished products employed in nuclear technology. Included
are methods for detecting cracks and latent defects, gaging of dimensions of tubes and fuel elements, and mapping
uranium and plutonium distributions in fabricated fuel elements. Much attention is given to both already established
and recently proposed techniques of nondestructive testing to secure detailed data on physical properties and the
state of materials,and on the effect of processing technology on those properties.
The papers presented are buttressed by a generously detailed bibliography (over 380 titles), and will be
greeted with interest by specialists and production experts in nuclear power industry.
Atomic Handbook. Vol. IEurope. Edited by Y. W. Shortall. London, Morgan Brothers Ltd. (1965),
868 pages.
This first volume of a reference handbook set encompasses Europe, with socialist countries included, and con
sists of 6 sections. The first section presents a brief review of the current status of atomic industry and of the
development of scientific research in 29 countries in Europe. According to incomplete data, capital investments in
all sectors of atomic industry are estimated at four billion dollars, and Europe's 1965 "atomic budget" is placed at
around one billion dollars, the minimum estimate of the number of personnel employed in atomic industry and
scientific institutions is 230,000, the total power output of electric power. generating stations now on the line is
326 million kW, with nuclearfueled power stations accounting for 3.3 million kW out of that total. The number
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of nuclear power generating stations is: 26 now in operation, 23 under construction, 17 in the planning stage.
Reactors and critical assemblies number 160, and there are 92 atomic research centers.
The second section contains information on international organizations (IAEA, Euratom, CERN, COMECON,
and others) based on European countries. The third, and principal, section contains reference material on European
countries: atomic research and development programs, membership in international organizations, agreements with
individual countries, jurisprudence in atomic power, utilization of radioactive isotopes, atomic budget, number of
persons employed in atomic industry, development of electric power on the whole, and development of nuclear
power in particular, reactors, research centers, governmental organizations, private films, universities, and mis
cellaneous organizations concerned with atomic energy.
The fourth section lists periodicals and newspapers (with specialists and pertinent journalists indicated) which
regularly publish material on atomic energy, the fifth section lists leading personnel in the principal firms and
atomic agencies, and the sixth section lists yearbooks and reference handbooks on atomic energy published in
European countries.
Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
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Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
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r Declassified and Approved For Release 2013/03/12 :CIARDP100219680007000400013
Declassified and Approved For Release 2013/03/12 :CIARDP1O0219680007000400013
Crystallization Processes.
Institute of Solid State Physics and Semiconductors
Academy of Sciences of the Belorussian SSR, Minsk.
Translated from Russian by Geoffrey D. Archard
Corrected by,the editors for the American editioh.
Edited by N. N. Silrota, F. K. Gorskii
and V. M. Varikash
Devoted to a consideration of the mechanism and kinetics ~
 of crystallization and the production of singlecrystal semi
conductor materials, their purification and the controlled
distribution of impurities. Several articles in this important
new volume cover theoretical and experimental aspects of
the relief and the state of the surface of growing crystals
and the surface energy at crystalmelt.boundaries. Attention
is given to the competing mechanism in crystallization prroc
esses,"compared with experimental data on the temperature
, dependence of crystallization parameters, the linear velocity.
of crystallization, and the rate of crystal growth. A number
of papers consider the structural and kinetic laws of crystal
dissolution and the role of the structure of liquids in crystal
lization processes. ,
Most of the'articles in this collection were presented at the
AllUnion Conference on the Theory of Crystallization,
thermodynamics; and. the Kinetics of Phase Transform~
tions. Translated from afour=part Russian volume, Mecha
nism and Kinetics of Crystallization, the present work com
prises two of the sections. The remaining two parts are being
published simultaneously in a translation entitled Solid State
Transformations. The Russian text from which the transla
tion was prepared was thoroughly corrected by the .editors.
CONTENTS: Experimental end Theoretical Study of Processes of Crystal
lization: Interphase surface energy of sodium chloride at the crystalmelt
boundary, F. K. Gorskil, A. S. Mikulich ? Relief on the surface of crystals
growing from solution, G. R. Bartlnl, E. D. Dukove, 1. P. Korshunov, A. A. .
Chernov Molecular roughness of the crystalmelt boundary; D. E.
Temkin ? `Mechanism of the growth of safol crystals from the malt, D. E.
Ovsienko, G. A. Alfintsev ? Character of the linear crystallization rate?
temperature curve of,hexoacetate, M. M. Mezhul', L. K. Sharik ? Study of
the temperature dependence of the linear crystallization rate of ealol,
169 pages '
betol, salipyrine, antipyririe, and codeine; L. O. Maleshko Method of
determining the temperature dependence of the number of crystallization
centere, L. O. Maleshko Effect ,of crucible materiel end the purity of
the original metal on the supercooling of iron, V. P. Kosryuchenko, D. E.
Ovsienko ? Broadening of the region of primary,solid solutions in alloys
of eutectic end peritectic types, 1. S. Mlroshntchenko ? Formation of the
structure of eutectictype alloys at high cooling rates, f. S. Miroshnl
chenko ? Kinetic equations of alloy crystallization, V. 7. 8ortsov ~ Experi ,
mantel determination of kinetic coefficients for binary syeteme, V. T.
Borisov, ;4. 1. Dukhln, Yu. E. Matveev, E. P. Rakhmanove ? Effect of mor'
phology of the etch figures on the form of diseciving metal crystals, 1. M.
Novosal'Skif ? .Dissolution structures of individual faces of aluminum
single crystals in a solution for chemical polishing, V. A. Dmltriev, E. V.
Rzhevskaya, V. A. Khristoforov ? Etch spirals on single crystals of steel,
L. 1. Lysak, B. i. Nikolin ? Effect of the pH of the solution an the form of
emmonbrn dihydrophosphate crystals, 1. M. Byteva ? Growing alkalihaLlde
single crystele from the melt by directional heat extraction, A: E. Mallkov
Two types of skeletal crystals, S. A. Stroltelev Structural features of
zonemailing iron, F. N. Tavadze, 1. A. Balrarrtashvlli, L. G. Sekvarelldze,
V. Sh. Metrevll, N. A. Zoidze, G. V. Tsagarslshvili ? Phase transformations'
in the processes of reducing uranium oxides, V.' M. Zhukovsk/!, E. V.
Tkachenko, V. G. Vlasov, V. N. Strekelovskll ? Theimodynamica of phase
transformation of the interstitial solution In frozen soils and mountain
rocks, N. S.,Ivenov ?`Effecb of External Aetions on the Processes of
Crystallization: New experimental results on the etching of single crystals
In an ultrasonic field, A. P.~Kepustin Dispersion herdenin0 of leadbase
alloys M an ultrasonic field, F. K. Gorskii, V. 1. Efremov ? Role of insoluble
impuritles~in the crystallization of metals In an ultrasonic field, O. V.
Abramov, 1. 1. Teumin ? Kinetics of the decomposition of supersaturated
solutions of aluminum fluoride in ultrasonic fields, Yu. N. Tyurin, S. 1.
Rempel' Decomposition of aluminete solutiona~under the influence of
ultrasound and with mechanical agitation, V. A. Derevyankln, V. N. 71kho
. nov, S. /. Kuznetsov ? Effect of an electric field on the crystallographic
parameters of a substance, L. T. Prishchepa ? Effect of a magnetic field on
the, formation.. of crystalline nuclei in supercooled betol, F. K. Gorskll, .
A. ~V. Akhromova. ~ ~ ~,
Crystallization.Processes: $22.50
Solid State Transformat'ions': $22.50
Set Price: $40.00
6 CONSULTANTS BUREAU 227"West 17th Street, New York, New York 1001.1
Declassified and Approved For Release 2013/03/12 :CIARDP1O0219680007000400013