ORIG. RUSSIAN: CHOICE OF SOME OPTIMUM CHARRACTERISTICS FOR THE REACTOR CONTROL SYSTEM

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100110002-7
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 19
• Document Creation Date: December 22, 2016
• Document Release Date: August 26, 2009
• Sequence Number: 2
• Publication Date: May 1, 1964
• Content Type: STUDY

 Third United Nations
International Conference
on the Peaceful Uses
of Atocnic Energy
Confidential until official release during Conference
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
A/CONE'. 28/P/354
USSR
May 1964
Originals RUSSIAN
CHOICE OF SOME OPTIMUM CHARACTERISTICS FOR
THE REACTOR CONTROL SYSTEM.
V.V.Orlov, V.S.Andreyanov, E.I.Grish.anin, L.I.Isakova,
A.G.Kalashnikov, J.G.Pashkin, G.I.Toshinsky, V.V.Chekunov.
The control system compensating the excess reactivity
can essentially influence upon the physical and operating
reactor characteristics. This influence increases when com-
pensating big reactivity excess. That is why the problems
of choosing reactor control system optimum characteristics
along with the problems of principal reactor characteristics
optimization are of a great interest. In the first part of
this report some questions of optimum burnable poison cha-
racteristics choice are considered. The second part describes
the choice of an optimum resonance absorber mixture for cont-
rol rods .
PART I.
BURNABLE POISONS.
In power reactors along with mechanical control devi-
ces for compensating reactivity excess burnable poisons are
widely used now (for instance see L1 I. Some problems of
the calculation theory and of the use of burnable poisons
have been considered in C 2 , 3 , 4 , 5 1. These problems of
thermal reactors are discussed in C 21[ 3 some particular
problems for intermediate reactors being studied in ~ 4 ~
The method of burnable poison calculation is discussed as
a more general case in [ 5 ].
The main purpose of the burnable poison application
is to decrease the excess reactivity compensating
by the mechanical control devicese That is to say the OhOic;e
of optimum burnable poison is the first of all the choice
of absorption materials and a means of distribution them
to provide the best agreement between the reactivity loss
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
caused by fuel depletion and poison burn-up. Thereforethe
residual poisoning caused by non burnt-out absorbers and
other isotopes which were present in the original material
and were also formed after burning out must be minimized.
To minimize the residual reactor poisoning due to
the non--burnt up absorber at the end of the core lifetime
the poison burn-up rate must be much more than that of fuel
depletion.
If such a poison can be chosen properly for the reactor
under consideration the homogeneous poison distribution
over the reactor results in the rapid poison burn-up and the
premature reactivity release. In this case the heterogeneous
poison distribution turns out to be more effective because
of decreasing neutron flux (self-shielding effect) in the
absorber which results in decreasing the absorber burn-up
rate that in itsturn permits to reduce the reactivity mis-
match caused by different burn-up laws of poison and fuel.
If such poison can't be chosen properly for reactor
under consideration the heterogeneous distribution results
in greater reactivity loss caused by the big residual non
burnt-up poison to the end of the core life-time and there-
fore homogeneous distribution may by more expedient
A. Homogeneous poison distribution.
The homogeneous poison distribution is considered in
detail in [5]. The plotts given there permit to `efine the
maaimim reactivity mismatch and residual poisoning due to
non burnt-up poison to the end of the core life-time if
poison and fuel life-time are known.
B. Heterogeneous --poison distribution
a). Plate-type absorber. Heterogeneous poison distri --
bution in plane geometry is considered in C 5, and some cri-
teria are found which permit to determine the poison cha-
354
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
r :cteristics providing the maximum reduction of the number
of mechanical control devices (or their efficiency),.
According to the method given in L5 1 some calculations
were carried out to determine the region where the plate-
type absorbers are the most effective ones. The pertubati-
on theorAis used for calculating the reactivity change due
to poison burn-up, fuel depletion and poison4ng. The approxi-
mate formula derived in C5 3 to calculate reactivity change as
a function of these processes is
(0) = (Y)+P.1 / ~ 1 46 poRI C~-
(1.1)
and
IUA
Xr
Definition of symbols:
?rtC-)-- reactivity introduced by an absorber into the reactor
at tirae.
'y - dimensionless time expressed in endurance fractions
- reactor life-time scaled to rated power.
T - endurance.
- optical width of absorber plate at the beginning of
the reactor life-time PO - J`~n (o)cc a
n Co}- absorber nucleus concentration in the plate at the be-
ginning of the reactor life-time.
~c. -- microscopic absorption cross section averaged over
the neutron spec-44i
run,
I~ - thickness of absorber plate .
- parameter giving the best approximation of the plate
self-shielding factor dependence (fS) as a function
of its optical widths ~- ((b) 1/(I -'qp o
)Cr - dimensionless fuel life-time Xr = i/T S Ecr(u) cu)du
(5cr- fuel microscopic absorption cross section.
Cu). ~.neutron flux in the reactor at the beginning of the rc
actor life-time, also normalized to the rated power.
354
-- 3 -
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
0 ' I - ? r, (14 1 ~.,( 0 ) rn - WA _ n(i) nto 1 r.~un ~I?-y (1.4)
4r.
Pn l1 /'pr.wn m I n(- )/ n(o) C 5)
where ifl n(o) the ration of reactivity
/ un
released by burnable poison at the and of the core life-
time to initial reactivity excess comeneating the fuel dep-
letion and poisoning.
pp(y}- reactivity :2ismatoh at time t .
?n(,.}- residual poisoning at the end :,)f the col: life-time.
In t 5 1 the maximum reduction of u3c'aenioa1 coxC,-.ro1 de-
vices is shoTfn to take place at such velaes of the plate op-
tical ~idtn ~ ~xha:~ maximwn miamateb j)n ('3) / r wr'
']f,~xi8 a
Tract ion of i i tlal ceactirity axcesr for ftae1 depletica and
pois?nikg - ? which are compe-a ated by the AnEohaaic J. con-
trol cagier, iii. this case the res ctiv*ty inthnatch hieiz to
vani-sh a.;:e during the aora. life-t i.c e,
' Itt' ^ 1.13111atx0 'n.3 Ner- 4e PK~, = ?, ;'fl ?43 ?j ~},a
is I/xr:), 3 rA Xn 0 n,
This 'ri ' rose~-'3 '.he cost i. 3 i.a3 P.-a ..L x..r. C ?a80a when
the c0aorber msy h :i.ccapted, 'Pr,,-. a'i.tial optical
x1.3. ah jSo of the absorber plate providtG the l iximur. reduc
;Scan --.31 mechanical control device 1.,i plotted as a fu notion
of absorber life-t Lme Xn In i v r 'i.g.2 shows the a.ximum
r?eaot'ifit ?i"'a tCa and non b,_i ahie resiw al olsct.
cat culated as a function of absorber life-time for
determined above.
:the ar n,ge :'he7e :h8 :1?.f he. k..1-F,." :;r.b r3n ber" he
cotes more e`! fec ir a U;3 ,j 1wI `IAL -In y'T f ._ ~r ~J {~'~ `?'e' 1.t ~.t .1'! t~..i o. .~..a.
O.,2T he re a, idu~a1. )o ?L =, on!_r. wheit X~t, t?~25 -
-iln6 ve- , qu,ich
0,30 an d t:u. vsX i. Z?rrti reuc ~l. t .. , ..:~. ;..., wz. _. )L
up to 1/(1 `l - ) at
The use of voc large crow absorbers
AIi e'~+
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100
distributed as plates the big reactivity mismatch is observ-
ed. The mismatch can be decreased by using the combination
?30'->l that allows simultaneously to get small residual poi-
section absorbers as cylindrical rods' with optical width
The simplest solution is to distribute the large cross
of different optical width plates.
b). Rod-type absorbers.
rast to the absorbers with temperate self-shielding may be
Dross sections. The absorbers with surface burn-up in oont-
burn-up taking place practically completely at very large
reactivity mismatch and the residual poisoning vanishes with
depletion and poisoning and the contradiction between the
which is similar to that one required for compensating fuel
hence the releasing reactivity will vary according to the law
row surface layers. The diameter of rod "blackness" and
In this case the rod will be burnt up only within a nar-
soning and small reactivity mismatch,
tion differs from zero, r - rod "blackness" radius. On the
ron flux within energy range where the absorption cross see-
is equal to tt) 2 T rdt D where'P (t) is integrated neut-
derations . The number of neutrons absorbed during time Jt
time oa, be established on the basis of the following consi-
The law of rod "blackness" radius change as a function of
Thus the neutrons will be absorbed in infinite thin layers.
ted as (S c_ = oo at U >- u o and Gcn = 0 at u c u o
ber with the very large absorption cross section 6' repre:ien-
n
bers it is usefull to consider the limiting case of absor-
To find out physical features of tfe burnt-around absor-
figuratively called burnt around absorbers.
The cylinder cross section may have a convex poligonal
form where circle can be inscribed.
Here and below the assumptions made above are used.
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
other hand the corresponding change of the rod volume due
t o burn-up at the rod surface i s equal t o 21r cl r . Thus the
following relation can be written
t)2JLrd.t = 2Ti.rJfn,?cr (1.6)
~)(
ZF_
After integrating the relation (1.6) in the correspond-".:s."
limits we obtain
St~Ct~at` Rah C'- R)
0
The rod "blackness" radius as well as its absorption capacity
is seen to decrease approximately as a linear function of
time giving a small reactivity mismatch. Let us evaluate
the reactivity mismatch arising due to uncomplete correspon-
dence b ween fuel and poison burn-up laws, With (-L)
cj (A:) 4 C~o(u)cu (where'(t)= i/(i- X )) and the requirement of
the comps ete absorber burn up to time -~Q~ of the core life-
time the expression of rod radius change can be written as
En (i -- xr1 /fin Ci y? (I- e7)
1 X r)
the initial rod optical width being 2 :n e `~_ 7C,)
it is here convenient to take the absorber cross-: c::;tion as
finite one,
Using the expression (1.7) we obtain the rc Lati on for
reactivity release during burning around of a -rod.
I _ 1d) ~.-~y~s~~~~~ _ ~.-Ci - (/e (JI-LJO ]/(t-L)ci p8)
Pn lol X 7e
and
From the relations (i.8) and (7.2) we find hb--
lion for reactivity mismatch under condition c hunt'`:
around absorber compensating (at the
tim.e) the fraction rn of tota for 'burn.
up and poisoning.
r
7 PO (0)
at I G Lj
and 0
lull,
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
optimum value rn is got
Setting equal to zero the ~ derivative from the expres-
sion (1.9) we obtain the relation for the maximum reactivity
mismatch within the range
Xr-I+m XP-1+M ( l_~ l
M yrnox/rw~=(X"_~+m~ 4 P m "'
P ~ xr- +rn r 1.1Oa
TMXK
When ~o the reactivity mismatch is
0m X)/(I (1.10b)
and at theend of core life-time (uu =1)
FP ? - -
1 P - (I- M) (1.100)
The maximum reactivity mismatch can be easily shown from
(1.1Oa) as being always negative. This means that at the be-
ginning of the core life-time the burnable poison can compen-
sate not the total reactivity excess for burn up and poisoning
but only its fraction Tn . The residual part of the reacti-
vity excess (1-11x1) must be evidently compensated by mechani-
cal control devices and (1-m) has not to be smaller than
maximum reactivity mismatch. With the aim of reducing the
use of mechanical control devices it should be make 1-ma
pr?441% and the following equation connecting
~o and m results xr,-I+rn
- enC
e rn x)n) (1.11)
The reactivity mismatch at c4j o may be positive, negati-
ve or equal to zero depending on the value of parameter ~?
(1.10b). Optimum case can be shown as a oa.!re when the mis-
match at ~1. is equal to zero. From there we obtain the se-
cond equation connecting the values o and m
IT, -XrL
xr ~ (1.12)
From (1.11) and (1.12) the equation to determine the
where
ac 6
a_i - i 4 & car 4 c1) -4 efl eri
ac-i
lac Xr-I+rn
1,1 = t- rn
m m
(1.13)
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
The results of calculations plotted it Fig-3 show the
maximum reactivity mismatch (1.--m) to be considerably smaller
in case when the burnable poison with the large absorption
cross section is distributed in form of rods than when it is
distributed in form of plates. So the use of burnable poisons
with the infinite absorption cross section results in mini-
mum number of necessary mechanical control devices without
reactivity loss due to non burnt up poison residue. The tran-
sition from ideal model to practical absorbers sets some
additional problems. We shall discuss the following ones,
1). To clear up the burn up kinetics of absorbes with
finite cross section 6e we shall consider the problems of
determining the absorber distribution over the semi-infinite
medium; the neutron flux incident at it2 surface is j neutron
o m
If the initial absorber distribution was uniform so by time
it will be 36 6 -L
.l`~ l (X JV n e. ) eX (G t. - G go o
With the use of this formula the absorption capacity can be
shown to decrease slowly during time t L = i /,I G . At
time {^'L the X(x )distribution front of the width A X
has formed and it is moving with the constant rate at
inside the absorber~~ee. 'Pcg? 4)
Since the value 6 being finite it could be expected the
deviation from linear dependence t (t) during time t -36
at the first operation period (the incident flux being iso-
tropic the front width decreases two times as compared to
the normal incident flux. Thereby=). This deviation from
formula (1.7) will also take place at the final stage of
burn ups the optical rod width having decreased up to the
value P b- , and consequently, the burn up rate will increase.
The sum time turns out to be equal to -t = _ -G- and
so that it would not exceed for example 10% of the core life-
time it is necessary that 'C~0.1 T, or 6 - 0. k
ye" . This
estimation shows that the isotopes of (a > LAGS oan be used
354
- 9
N Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100
As burnt-around poisons.
The cross sections greatly exceeding cross sections of
fissionable isotopes exist only in the thermal region when
the energy of one of the resonances is near to zero. That
is why the burnt-around poisons in practice can be used only
for thermal reactors, of stable isotopes only Cd113, Sm149,
Gd1 55 and Gd157 satisfying the above condition.
2). The volume absorber burn up due to neutron absorp-
tion in energy region where the cross sections are not large
leads also to the change of the burn up low. In the thermal
region very large absorption cross sections caused by low -
lying resonances decrease with the energy increase according
to the Brieght-Wigner formula (Gc - -i
law). If the spectrum
E -41Z
of neutron incident onto the rod is cp (E) the number of
neutrons absorbed by this rod at the energy E>E2p (their
free path being 7t (E) >)L 2R) is _
AV = P(E) VN,t 66 (E)d 4 = V1 /,,' 6c (E'=p~ .~(e)1dE4w(E,,)E)
and /V?? 6~ (E?p) = - so that finally
A = ,,-o E? p 9(-'?p) ,o VT ~
The spectrum is assumed here to be Fermi spect . The number
of neutrons absorbed as the surface is ~s = y 1P~(E)dE
therefore the volume absorption fraction is O nv z /As
that usually constitutes in the thermal reactors the value
L 0.1.
The value A must be supplemented with the absorption of
resonance region which is small for the isotopes mentioned
above. The volume absorption effect leads to some increase of
reactivity release rate with burning up.
3). Neutron flux depression near the rod (external shi-
elding) leads to decreasing of burn-up rate at the beginning
of core life-time. This effect becomes negligible with using
of small diameter rods.
The absorber distribution over a core.
The above mentioned consideration permit to choose oont-
- 10 -
Approved For Release 2009/08/26: CIA-RDP88-00904R0001
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
tol rods (their number, diameter and absorber density) pro-
viding a small change of the neutron multiplication factor
in some reactor volume if the fuel burn-up reached in this
volume to the end of the core life-time is known. As power
distribution over the reactor depends in its turn on the
rod distribution the nonlinear problem arise and they can
be solved by the iterative method.
In ideal case we can reduce this problems to following
nonlinear equation. Suppose that a) the absorber provides
constant multiplication factor Kam, as a function of time in
every point over the reactor; b) the absorption probability
at point? of a neutron born in point 1 is P(V` ~') and does
not vary during the core life-time (for instance it takes
place in thermal water-moderated reactors where L2
Then the neutron source density Q(rjor power density proporti-
onal to it) is described by the following equation
QCr) _ kcoC~Z)f Q(-^) PCr, - ~) cVYX' (1.15)
The value K? dnay be expressed in term of fuel burn-up
reached at oint' ~ at the end of the core
P *r(F') Q(')
life-time. So we obtain the nonlinear equation for Q(-^)
QCr) = kC-?(Ct (")'r) J QC-) PCr,r dr' (1.16)
Expanding Q(r) at point r -'v' and taking into account only
three terms of this expansion we have at PP('-')
\72Q - k c CG(, r ) - i 2 a = 0 (1.17)
u.~ CQ,r) M
where M2 PCr) HcA r JP(r) r2J r
Boundary conditions for Q can be written with the help
of reflector albedo. With known power distribution Q and
with burn-up distribution proportional to it the law of
absorber distribution over the core which provides constant
"K" at every point r may be easily found. This distribution
provides not only constant reactivity during the whole reac-
tor life-time but also uniform power distribution over the
354
- 11
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
reactor' with its simultaneous flattening (compared to
uniform control rod distribution),
I (, Resonanceabsorbers for control rods.
The absorption cross section energy dependence of the
materials is especialy important for control rods. The use
of resonance absorbers permits within some limits to get
the most profitable absorption cross section energy depen-
dence for the reactor under consideration with regard as
to increasing of the effeciency so to decreasing of neutron
flux depression near the rod. The latter is the most impor-
tant for thermal reactors.
To increase the rod efficiency or to decrease neutron
flux depression near the rod it is of great interest to use
a mixture of different resonance absorbers. In this case the
total resonance absorption can be more than the absorption
of a component with the greatest resonance integral due to
the reduction of every component resonance self-shielding.
For instance if there are "n" absorbers of narrow and strong
resonances every one of which differs from one another
only by resonance energy the maximum value of mixture reso-
nance integral will be fl -1-1 times more than resonance integ-
ral of a single absorber. The practical absorbers differ from
one another by nucleus density, resonance energy v resonance
parameters and so on. Furthermore the absorption by weak re-
sonances and by "smooth" part of the absorption cross sec-
tion constitutes the considerable part of the total absorp-
tion. That is why the optimum mixture composition depends
not only on the properties of chosen absorbers but also
on the form of neutron spectrum, temperature and so on.
The problems of control system providing the flat
time-independent distribution over the reactor was set
and solved by Sharapov V.N.
354
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
As Determination of _Utimum resonance absorber
composition to obtain the maximum rod efficienw,
According to the perturbation theory L GI the rod ef-
ficiency is
d, d u W(u) Xi,Goc Cu) 1, [d S )GC Cu) , (2,1)
where W (u) product of neutron flux with energy "u" and
the importance of these neutrons, ~~ - self-shielding factor
of its element absorption cross section which depends on
all the values of GCk and i'C ; OT)- importance of f iss ion
neutrons; d - rod diameter; rl - a number of mixture compo-
nents.
To obtain the maximum effioiency of the rod of given
size which is made of the resonance absorber mixture it is
necessary to determine the maximum of , expression (2.1) with
=1 (V - a volume part of i-th component). This problem
is the conventional extremism one and is solved by means of
vmderfined Lagraagian multipliers method. According to this
method the absolute extremism of function F = 9+,-k L , where L={ii-1
onck.is an indefined multiplier must be found. Necessary condi-
tions of the function F extremism
I'D F:
'Z F L -o (2.2)
give us the system of (n+1) differential equations with un-
known quantities J'41 and I . On this system we obtain a volume
part of every component. In general case the system (2.2) is
solved by the iterative method. When calculating the self-
shielding faotor it is necessary to tab into account the
mutual resonance shielding of different nuclei, the resonance
self-shielding by "smooth" part of cross section and Doppler
effect for resolved and unresolved levels.
Fig.5 shows the sample efficiency (diameter 10cm) in the
reactor n(P-4 as a function of content for Re - duZmixture .
The results of calculations point at the maximum efficiency
value to exist which exceeds the effioiency of samples made
354
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
Of a single component. To obtain the subsequent encrease at
control rod efficiency the optimum mixture of three or more
components has to be used.
B.4At1mum corn sition of resonauee_ -absorber
mixture to obtain the minimum depression of
energy release field in thermal reactor.
The absorption cross section energy dependence is very
important not only for the rod efficiency but also for a
neutron flux depression near the rod. Neutron flux depression
can be reduced not only by means every rod absorption decrease
due to increase of the rod number but also by using the
resonance absorbers as an absorption material which permit
to vary the correlation between the absorption in thermal and
epithermal regions. In fact the more neutron will be obsorv-
ed by a rod in the epithermal region the less absorption
will take place in the thermal region at the fixed rod effi-
ciency and therefore the neutron flux depression will be
smaller in the thermal region, where the greatest part of
fission take place. The least energy release shield depres-
sion will be in the limiting case when the total absorption
takes place only in the thermal region.
As an example we consider the absorption in the plate-
type rods. Using the expression 1 - G + 6/ as a resonance
integral (a and b constant' X -. nucleus density, C1 - plate
width) and assuming the constant "a" generally to depend on
the absorption due to 1/v cross section the total resonance
absorption in the plate can be written
where E -plate surface f or a quit volume of a core 9
plate optical width for the nj utron of energy E=0,0253 ev,
Err the energy on the boundary between Na=ellien speet-
rr: and moderated neutron spectrum,. It is clear from (2.3)
that the absorption contribution Gassed by s tr?ong resonances
c be suitably described with the value the G
3 C
... 14
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
does not depend on the nucleus concentration and on the rea-
ctor spectrum but it is function of resonance parameters.
Among all the resonance absorbers hafnium (j=1.56) tanta-
lum (4 X1.4) indium (6=1.04)t antiniony (6=1.07), europium
(( =1.02)j -rhenium (6=0.92) are those which have the best
correlation between absorption in the thermal and in the
resonance regions. For 1/v-cross section this characteris-
tic is equal to zero. Cadmium and gadolinium have the
worst energy-dependence for the absorption cross section,
the "smooth" part of their absorption cross sections decre-
asing more quickly than 1/v-absorption. The contribution of
their epicadmium resonances is neglected and as a result
the value < for these element should be written as negative
one.
In Fig.6 the plate optical width Po for neutron energy
E0=0.025ev is plotted as a function of value 6 which has to
compensate the water reactor (ration of hydrogen nuclei to
U235 nuclei is about 200, the square lattice pitch is 10cm).
The dependence of the thermal neutron flux max-average ra-
tio "K" for elementary cell is shown in this figure too.
Using the optimum composition mixtures we can achieve
the value 6 considerably exceeding that one for a single ele-
ment. In this case the optimum composition L is found so as
to provide the maximum resonance absorption in the plate
I _Z T L under extra conditionZhi= P ~
If the element resonance levels evels are assumed to be over -
lapped and non-shielding absorption to be caused only by 1/v-
cross section d= const, i=1, 2, ... , n) this problem can
be solved analytically by Lagrangian undefined multipliers
method. The optimum weight content of i-th element (atomic
weight Ai and thermal cross section 6 ~) will be described
by the expression
2
66 A i /67C
riK`GV_ (2.4)
and maximum total resonance ab1so-r t ion is
Ima-x = C~o-2. E? 4 61)"CLK ~1 Po ~Omax ~oK (2.5)
354 Eze - 15 - K
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
The optimum compositions and values d'moxfor mixture
of some resonance absorbers are given in the table below.
* 16 -,
Material
In-Ag
Hf-Ta
Hf-Ta-W Hf-Ta-Eu
P1%
37 63
26.3 73.7
91,1 59.1 19.8
27 73 0.2
&~
1.01 0.78
1.57 1.14
1.57 1.14 0.64
1.57 1.14 1.0
& max
1.30
1.94
2.04
2.18
REFERENCES,
X11 A.P.Aleksandrov et al. "Atomic ice-beaker Lenin".(P/2140
Pro c . 2nd Ult C onf , on Atomic Energy-Genera (1958)
L21 A.Radkowsky. Theory and Application of BurnablePoisons
(P/1900 Proc. 2nd ?TN Conf, on Atomic Energy--Geneva
(1958)),
~31 V.S.Volkov et al,. "Use of burnable poisons in power reac-
tors" , "Atomic Bnergy " V,111 1961 ,
~4I The Physics of IntermedLal :Spectrum Reactors. USAEC,1958,
t5l G.I.Toshinsky, A.G.galashniko-r. "Methods for calculating
burn up of absorbers In power reactors", "Theory and
methods for calculation nuclear reactors". Gosatom-
isdat , 1962.
~61 L.N.Ussachev, r'Equa t L.)n for neutron importance, reactor
kinetics and .pe.e nirbation theory" , (P/2 Proc, It UN
Conf.. on Atomic E:le:rgy-(", ne-ra, 1955).
?,71 I.V.Gordeev, D.A.Rardashe , A.V.Talyshev. "Iaderno-?Pizi-
cheskie constanti". Gosatomisdat, 1963.
c 81 A.I.Leipunsky et alp Experimental investigations of some
physical features of Intermediate spectrum reactor
with berillium moderator. (P SM 18/80 International
symposium on physics of fast and intermediate spect-
rum reactors. Vienna. 1962.) o
Approved
2
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
5 10 15 20 L~ 95
X
Fig. I. The initial absorber plate
optical width providing the
maximum reduction of the use
of mechanical control devi-
ces as a function of the ab-
sorber lifetime Xn .
z - to
cduo t
qqo scP
nq
?
~s
11
Q
S .1
.
5 Q
0 Q2
5 .-.0
Fig. 2. The maximum reactivity mismatch
(1) and non-burnable re-
sidual poisoning )i /p,*, (2) as a
function of absorber lifetime
with the optical width being
optimum.
0 02
I
ae 1,0- Xr
Pig. 3. The maximum reactivity mismatch for absorbers of
infinite cross section in plane (1) and vylindrioal
geometry as a function of fuel burnup during the
reactor lifetim. (1/i,. )
6
2
-
- 17 -
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7
I -Aorrr, of x
' o 0 of ux
a y- f
Fig. 4. The steady distribution of
absorber nuclei in transient
region.
44
O
Fig. 5. The rod efficiency in the
reactor /!'-4 as a function
of europium oxide content
in Re-Eu203 izixture.
Fig. 6. Optical plate width to compensate the reactivity
excess of water reactor and max-average ration for
the thermal neutron flux in its elementary as a
function of 6 .
- 18 -
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110002-7