SCIENTIFIC ABSTRACT WEISS, Z. - WEISSER, O.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001961520006-1
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 1, 2001
• Sequence Number: 6
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

23892
P/046J61/666/oni/ooi/oo
A.method of determining... D226/D301,
are giver.a ainst T from vihic',~t it-is clearly seen that the optimal
9
.ratio. 1~o/G6 is 1. The dependen-.e of sensitivity of-thc:.---phase angle
method on parameters g 'arida permits determination of the
usefulness',of the resultant signal method for measuring oscillator
parameters.for.various typew of reactors. As an example'of appli
cation of the above methods certain numerical.data are.given, which
are thought to be r.equired and known before the actual construction
of the oscillator begins. These numerical.data are worked out from
.,,the experimental-material obtained during the dynamic-measurements
of-the oscillator installed at Chatillon and,quoted by.D. Breton
(Ref.. 3: MateriaZy I Konferencji Genewskiej,t. 4 ref. 356); the
original Breton notation is used. There are 7 figures, I table and
7 references: 2 Soviet-bloc and 5 non-Soviet-bloc. 'The reference
to.the'English-language-publication reads.as follows: A.M. Weinberg,
Schweinler: Phys. Rev. 74,,:8-51 (1948).
ASSOCIATION: Instytut badaA jgdrowych PAN, War~zawa, zaklad in:ky-
nierii reaktorow~;'j (Institute of Nuclear Research, PAS
Warsaw, Reactor Engineering Laboratory)
C/
SUBMITTED November, .1960

22073
~P/04.6/61/006/004/001/002
D22 1/D306
AUTHOR: Weissj.Zbigniew
"..~-,.:TITLE: Neutron spectrum.tomperature distribution in hetero-
geneous systems with constant absorption
PERIODICALrNukleonika, v. 69 r.o. 4P 1961P 243 259
:TBXT-.~In.this paper the first-of a series of four on neutron tem-
perature.distribution, the, author presents-a.more general.formula-
tion of the method of. D.A. Kottwitz.(Ref. 6: Bull.Am.Phys.Soc. 3,
1 (1958), Abstr. A-7) for deteimining the effective neutron tempe-
rature which enables the calcu'.ation of the distribution of effec-
tive temperaturein a. finite o:? infinite homogeneous assembly with
or external epithermal neutron sources. The basic assump-
tions are: (I) Validity of the P1 approximation for spatial neutrons
distributions; (II) Representation of ener transfer probability
in the 1/M heavy gas,model approximation; M) Isotropic scatter-
system;:(IV) Energy independence of the ab-
inglin the laboratory
Card 1/13

22073
P/046/61/006/004/001/002
Neutronspectrum, temperature D221/D306
sorption cross-section. These :-educe the general Boltzmann equation
to~the form
DV2 V S(F, E) [21 (2)
whereIP(r, EY is the neutron spectrum,distribution, D the diffu-
the macroscopic scattering cross-sectio
sion.coefficierit, Z: 13
the mean logarithmic energy decrement,
E(, 0.0253 eV
2 T111
0
is the macroscopic absorption.cross
-section at energy Eol leff
P_
the effective neutron temperature, A=TE T is the tempe-:
we +EFE+l
rature of the. mediumi and S(rj,E) represents external sources..Ex--
panding Y(r, E) in terms.of Laguerre polynomials.and substituting
in (2) gives a set of equations for the moments fn Of the expansion,
Card 2/13

22073
P/046/61/006/004/001/002
Neutron, spectrum temperature D221/D306
~for the same value of A and.for a typical uranium-graphite lattice
~:,`,.is.shown.in,Fig. 6..There are divergences for high andlow modera-
tor-uranium:volume !,atios, although in the.region normal for graphi-
rated.reactors# there is quite good agreement. Eq. (.22) is
te: mod e
-ate the temperature of the neutron gas in the
also,used to calcul,
middle of the fuel elemen.ts in the W17R-S 11EIVA" reactor (Institute
:of Nuclear,Sciencest Warsaw),core, The numerical values are Lm
111 .80 cm, D V49 Cm (aireraged over the fuel composition), and,
L 2.72 cm. D(2,) 0.164.cm,.a 0-05 cm, effective b 0.15
(2)
L For 3200K Eq., (22) gi-
cM 1.78 Ltw =.'.0.629 cm. T
ves Teff ~4150K in good agreement with'the.value 4000K given in
11 "BWAII reactor dbeuraentation ./Abstractorls.note: No reference for
this7. Cohen's 35000. The author thanks Dr.R.
ation gave T 1;~
eff
4
.,Zelazny,of the'Reactor Theory Groupp Institute of Nuclear.Research
Card.,10/13-

m

II
11--.1

26029
11/040/61/006/007/001/008
Neutron spectrum temperature D240/jmon
ZAbs tracto rl a no te: 'not A o f I.n-e d.2 having 2(N+I) ro o ts for -VIO The solu-
solution of the -homo gone c.u s equation.3 may_then be~-writton
f-N
fS (r) Eq. (12)
~A+ C.4)(vjr)4 A- CJ 0
+ J-0 -.0
~Ixc re AA are arbitrary constants. aoliondent on boundary conditionsp cuid CJ
j . .:~ I I I II n
2 2
cottpl ing constantso From Eq. (11)j products ~) I and the coefficients CJ
n
are indcpIendent of geome try and may lie tabulated. Also, the product 2L2
depends only on the order of approximetion and on 6, so that
J/L (A Eq. (13)
From Eq.-(IP) and the fact' that an or,thogonality relation
Ajk GJ
(I+n)CI.C.
,S established, a particular solution. of the inhomogencous equations (9)
:be dotermined, A solution
m
ay..
td

-Joko6l)
E. Z+3 F42;.15_~ EqO (30)
114 So"
-7. f;.+3 4
Th for:
e *qua ions -are evaluated 'L 'BO eme L 6,cm., and the diffusion
t
ium~ 1 14 cm. and Qe',calculated flux abd me
I ength in uran an energy dim-
tributiong' are shown..~. IComparison with'the results of Ref. 1, (OP-. cit.)
shown -that more :detailed investigations are required. For high N9 the
applicability ofAlie, arproximatiowis limited by the approximation,
LN
~i A.,

30579
P/046 61/006/011/ool/oo4
D216)D304
00
AUTHORs eisso Zbigniew
~W
TITLE: The transport,the.)ry of thermal neutrons in a heavy gas
moderator
PERIODICALt Nukleonika, v. 6p no. 11, 1961, 691 701
This is the third:-in.a series of-fourpapers by the author
onneutron temperature distribution. The solution of the multivelocity
Boltzmann equation is reduced to.solving set of single-velocity Boltzmann
-.equations for the ener
~gy moments of the expansion.of-theldistribution func-
tion:in Laguerre polynomials. Th(! requirementfor more exact information
about neutron spectra has arisen with the development of the sperical har-
monies approach to reector theonr.. The Boltzmann equation is written in
the form
IA-grad,~+T dE' ff dA: + S (1)
tol
0
Card .1/10

30 79
F/04616IA06/01/001/004
The transport theory of ... D21671)3o4
-Withly - (v,AX: representing the neutron distribution; 16 (E) the
tot
totil macroscopic cross-section;.< 6(Z'+ EISX'II')> T the energy transfer
cross-section; and the coVine'of the angle through which'the neutron
is.scattered. Expressing the ene3-gy-:transfer cross-section bnalytically,
and,i-n the 1/A approximation,
(E) 6- (E) :+ 41E~1 2 T + 6 (E) (E) (5)
tot a, + ;2 -ME -60 a 0
where 6'0is the bound. atom scatl;ering cross-seotion, &a the absorption
cross-section, 1/M, and le;i~,(E) ~, (2 - T hE). Also, putting the ex
pression for the energy,-transfer cross-section in the right-hand side of
'Eq., (I the equation,becom-es
grad + [1 +
0 E a (E) 1f
t1. X6, (EL1 (1 + 2ra) 2AAI.A(a d-W+ S (I')
41;
Card 2/10

30579
P/o46/61/006/011/oo1/oo4
The, transport theory of ... D216/D304
A 2
withCK representing the operator ET E ~E + 1 so long as the
E7- +
~reBtriction to the first order of the 1/X approximation is observed. Eq.
1') may further be rewritten
A A
(Io I,)-f (r,(19E) ;3(rjIIE) WO
where the operatorsIC and TI a-re given by
0 1
A grad + &a 4-60 (7a)
I - 0 + dk
0
6
19, (E 1 d _W] -'[6, (E) -,eaj /X
0
A
A-Ir ... dA! (7b)
and the absorption cross-sooticns are-assumed to be small. The equation fbr
the zeroth urder approximation in
~Card 3/101 0 YO S (8)

30579
P/o46/61/006/011/001/004
-6/I)3o4
The transport theory of D211
givfe the isotropic i3onstant crDss-eection. approximation. The eigenfunctions
o.f4% orm a complete set of Lagaerre ploynomials which are, in vector no-
tation,
L' (E T)> (9)
j>4 T7- exp T
The solution of Eq. (8) may then be represented as an infinite expansion
yo (r, E) J> 2
and their conjugates , and their conjugates 4 k I - (.1A + 1
Lk (E/T) . All the problems involved concern the general solution of 'he
Anhomogeneous one-velocity transport equation, and this is next found. In
the vectdr notation, the equation-to be solved.is
< N,k I I JIM> < M,jJV > N,k F> (k
MIJ 0 0,1,2,...)
with F an arbitrary function of xqU E, and I is a transport operator de-
fined in the author's previous pa, Iaer(Nukleoniga, 696919 1961). The solution
of the homogeneous equation in PN:approximation may be written
Y CJ exp (-a X) (10)
Card 3/ 13. n

30580
P/04V61/006/011/002/60
The PWL iapproximation of ... D216/D304
where CJ-are column vectors, theelements Ci of which are simply -numbers.
M
Since the matrix elements4N,k I Ij j,M> are-diagonal with respect to ell-
ergy variablef and since, from the recurrence formulae of Legendre polyzo-
mial 9 < N X > may be written
NIIAIM > 2N + I E(N 1) GN+)'M + M& n-1,M] -E-N T I
.,then the homogeneous equation to 'be oolved.becomen
j
0 OJ + (61e
where
*j OJ (6r
j2M + 1) (
CM j OM M
and c c (1 -2j/X) ' The. -mat_rix,Cj. so that there are Y* I
~ i tyj * 9 jI
(for odd N4 eigen'values for V - VP 1 9 (N+1)12 "d also the
2
Cj (Vr) vectors are orthogonal tCL each other. Thus the general solution of
Card 4/ 13

I
a

0
P/046/6 1/000111/002/004
7. ,The %L, approximati.on..of ... D216/D304
thus
0

' 1
+
-)
(
'
k
[DFOI floc
3 IDPI j2~bl
5pO'tAC2c7VIx
~
5#00AC2et-"
-
VU
7P.AC
3e 7flotAC36
Pro m- (17), and using; the boundary conditions of the problem, the'fir'st
component (total 2lux) is giv en by