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AE-166UDC 621.039.538
UJ The Transmission of Thermal and Fast Neutrons
in Air Filled Annular Ducts through Slabs
of Iron and Heavy Water
J. Nilsson and R. Sandlin
AKTIEBOLAGET ATOMENERGI
STOCKHOLM, SWEDEN 1964
AE-166
THE TRANSMISSION OF THERMAL AND FAST NEUTRONS IN AIR
FILLED ANNULAR DUCTS THROUGH SLABS OF IRON AND
HEAVY WATER
J Nilsson and R Sandlin
Abstract
An investigation has been carried out concerning the trans-
mission of thermal and fast neutrons in air filled annular ducts
through laminated Fe-D~O shields. Measurements have been made
with annular air gaps of 0. 5, 1. 0, 1. 5 and 2. 0 cm, at a duct length
of half a meter. The neutron fluxes were determined with a foil
activation technique.
The thermal flux was theoretically and experimentally
divided into three components, a streaming, a leakage and an
albedo component. The fast flux was similarly divided into a
streaming component and a "leakage" component. A calculational
model to predict the components was then developed and fitted, to
the data obtained by experiments.
The model reported here for prediction of neutron attenua-
tion in ducted configurations may be applied to straight annular
ducts of arbitrary dimensions and material configurations but is
especially designed for the problems met with in short ducts.
Printed and distributed in December 1964
Contents
1. Introduction Page 1
2. Experimental Details 1
2. 1 The R2-0 Research Reactor 1
2. 2 Experimental Set-up 2
2. 3 Measurement Technique 2
2.4 Experimental Results 3
2. 5 Discussion of Experimental Errors 3
3. Theoretical Interpretation of Results of Thermal
Flux Distribution Measurements 4
3. 1 Definition of Components of the Thermal Air Gap Flux 4
3. 2 Streaming Component 6
3. 3 Leakage Component 6
3.4 Albedo Component 7
3. 5 Parameters Necessary to Describe the
Thermal Air Gap Flux 7
3. 6 Discussion of Errors 9
4. Theoretical Interpretation of Results of Fast Flux
Distribution Measurements 10
4. 1 Definition of Components of the Fast Air Gap Flux 10
4. 2 Streaming Component 10
4.3 Leakage Component 11
4. 4 Parameters Necessary to Describe the Fast Air Gap Flux 11
4. 5 Discussion of Errors 12
5. Conclusions 12
References 13
Appendix I: The Relation between the Leakage Component
and the Surface Source Density of the Duct Walls 14
Appendix II: The Geometry Dependent Leakage Component 16
Fig\xres
- 1 -
]_. Introduction
All kinds of power and research reactors inevitably contain
ducted configurations due to the need for coolant lines, control lines,
control devices, charge and discharge access, gaps between different
parts of the shield and entrances to shielded regions. However, the
prediction of the attenuation of neutrons and gamma radiation in
ducted shields still offers a serious problem to the shield designer.
The most elaborate bulk shielding calculations lose a great deal of
their validity when the shield contains many channels.
As regards the neutrons, the fast component forms the most
important part since it causes not only the fast dose but also the main
part of the thermal dose at the duct outlet. However, the streaming of
low energy neutrons to distant parts of the shield may there produce
secondary gamma radiation with high escape probability in the outlet
direction.
In the present report an investigation has been carried
out partially along new lines regarding the transmission of thermal
and fast neutrons in air filled annular ducts through laminated Fe-D^O
shields.
The air gap flux was hypothetic ally divided into components
suitable for analysis. These components are a streaming, a leakage
and an albedo component in the thermal case and a streaming and
a "leakage" component in the fast case. This partition is further
justified by the fact, that it is possible, in the thermal case, to
measure the components experimentally using Cd-sheets. A calcula-
tional model to predict each of the components was then developed
and fitted to the data obtained by experiments.
2_. Experimental Details
2. ] The R2-0 Research Reactor
The experimental part of this investigation was performed
at the R2-0 reactor at the Studsvik research center of the Swedish
Atomic Energy Co.
- 2 -
The reactor (Fig. 1) is a 1 00 kW, light water moderated,
swimming-pool reactor with natural circulation cooling. The core is
movable on a trolley along the two horizontal axes, and can be turned
toward any side of the pool wall by a simple lift with the overhead
crane, and thus be placed in front of any of the shielding facilities
around the pool (Fig. 2).
The facilities available are one large irradiation window (Nl)
(2 m x 2 m) and four small windows (02, S3-5) (0. 5 m x 0. 5 m). Each
facility consists of an inner room, where a set-up can be built up and
tested, and an outer concrete shielding plug. The set-up and the plug
may be removed together.
2. 2 Experimental Set-up
The experimental set-up was built up in the irradiation window
Nl as shown in Fig. 3. The laminated Fe-D_O shield was composed
of Fe-slabs and Al-tanks filled with heavy water, as can be seen from
the figure. All slabs and tanks were penetrated by a hole of 15 cm
diameter. Together these holes formed a channel of 51. 5 cm length
through the configuration. In the channel were placed cylindrical
Fe-plugs of various diameters. Thus annular ducts were obtained
with air gap widths of 0. 5, 1.0, 1. 5 or 2. 0 cm. In some experiments
0. 5 mm Cd was placed in front of the annular duct mouth, and in
others a 0. 5 mm Cd-sheet was also wrapped round the Fe-plug.
In all experiments the reactor core was positioned to give
a 20 cm HLO-reflector between the core and the pool lining, which
was 2 cm aluminium. Outside this lining in the window there is a
stiffening construction, consisting of two I-beams, which forms an
air gap of about 30 cm between the lining and the set-up.
2. 3 Measurement Technique
The neutron fluxes were measured with foils. The fast flux
was determined with cast sulfur pellets and the thermal and epi-
thermal fluxes with foils of gold and copper activated in pairs.
Pertinent details of this activation technique have been presented
earlier [ l , 2].
- 3 -
Foils were activated both in the air gap at various distances
from the duct mouth and at various distances from the duct axis.
The activities of the exposed foils were determined by
measuring the rate of 3-decay in a sample changer equipped with a
scintillation counter and a punch tape device. The tape without any
modifications was then fed into a computer and the activity values
were reduced to flux values.
2.4 Experimental Results
The experiments were performed at reactor power levels of
20 kW and 100 kW and with activation periods from 1 to 6 hours. All
results have been normalized to 100 kW.
The experimentally determined fast and thermal air gap flux
distributions in different configurations and geometries are presented
in Figs. 6-10. The epithermal flux is not dealt with in this report.
In the figures are indicated errors relating to uncertainties
in foil data and counting statistics.
2. 5 Discussion of Experimental Errors
2. 5. 1 Reactor power, reactor positioning and activation time
To eliminate uncertainties in reactor power, reactor
positioning and activation time, normalization foils were activated at
a point 3 0 cm from the duct centerline at the front of the set-up, where
the flux was assumed to be independent of the annular air gap width
and the different configurations. The relative errors in the saturated
activity (dps/g) of these foils were less than 1 %.
2. 5. 2 Foil data and counting statistic^
The errors in the neutron fluxes relating to uncertainties in
cross sections, calibration constants, etc. are generally about 3 %
for the thermal flux, 11 % for the epithermal flux and 5 % for the
fast flux. These errors and the counting statistics were obtained from
the computer for each measuring point.
- 4 -
?L'~L']L _F°^ positioning
An assumption of an approximate inverse square law attenuation
in the duct, and an uncertainty in foil positioning of less than 5 mm at the
end of the duct gives an error in the flux of less than 2 %.
2. _5_. 4_ _Duct radius
The inner surface of the annular duct was formed of the turned
Fe-plug with well determined radius. An error in the outer radius was
caused by the displacement of the slabs and tanks in relation to each other.
The displacement was less than 1 mm» which means an error in the outer
radius of about 1 %.
3_, Theoretical Interpretation of Results of Thermal
Flux Distribution Measurements
In this section the thermal air gap flux will be theoretically
divided into three components, in order to make the above results
suitable for analysis. A notation will be developed for the components
and a theoretical model for the calculation of the components will be
presented. The results of a comparison between theory and experiments
are shown in Figs. 11-14.
3. 1 Definition of Components of the Thermal Air Gap Flux
The thermal flux at a point in an annular duct may be resolved
into three components [3j according to Fig. 5,
3. 1. 1 thermal neutrons entering through the annular duct entrance
and attenuating geometrically. This is the streaming
component (S)
3. 1. 2 neutrons of all energies which, having entered the annular duct
mouth, travel into the duct walls before diffusing back into the
duct again as thermal neutrons. This is the albedo component (A)
3. 1. 3 neutrons of all energies which penetrate to the duct wall
arriving as thermal neutrons without having previously passed
the annular duct. This is the leakage component {!_.).
- 5 -
Notations
In Fig. 4 each configuration investigated has been listed
together with an identification symbol. The symbols are
wCd for the configuration without Cd
CdM " " " using Cd at the duct mouth
CdMP " " " using Cd at the duct mouth
and on the plug
und " " unducted configuration
Let n be an arbitrary identification symbol of those given
above. Then (ft (x) is defined as the experimental thermal
flux in the air gap at the distance x from the duct mouth in the
configuration denoted by n. Let <̂ (x), be the corresponding
fast flux. Let V * h e o ^ a n d ^ t h e o ^ b e theoretically
determined analogies. Using these symbols we are ready to define
a) the experimentally determined thermal streaming component
cth r v [wCdj^th , , [CdMj^th , >S (x) » @ (x) - Q (x)expv ' r exp^ ' r expv '
b) the experimentally determined thermal albedo component
Ath ( u ^ ( ) ^ {
exp^ ' * expv ' expx
c) the experimentally deterxnined thermal leakage component
th (x y (expv ' r exp*
Then we have
s th ( x ) th ( x ) A thexpv ' expx '
In the following, a method of calculation of the components
S, L and A is presented and these are designated theoretically
calculated thermal components
«th ».« Tth t \ J A t h t \S., (x), L,, (x) and A., (x).theo* ' theov ' theov '
- 6 -
3. 2 Streaming Component
The estimation of the streaming effect has been
investigated in ref. [4] and all the expressions referred to
here originate from this paper.
The well-known formula [5, 6] for the fltix due to
streaming, is correct only at large distances(x » R). However,
from the integral (13) in [4], here written as
f ( c + l ) x P P -, 1 j I - Iov ' 2 r ! dr1 ctco'- • -. j J —5 - , -̂ -X-s - " ( ? , x ) » - " 2TT - J r 2 y — m ^ r <5>
* (x + r + r - Zr r'coscp1)1 *
a general solution can be obtained.
r and x are the radial and axial coordinate of the dose point
respectively, c is a parameter of the angular source distribution
function, R and r are the outer and inner duct radius respectively
and Y the surface source density in neutrons cm s at x « 0,
The domain of integration, A, is given by (9) in [4], i. e.
r £ r* < R
0 < cp' < (^cos -i- + cos" ~ J (6)
r
The integral (5) was solved by means of a computer program
and the solution was then fitted to the experimentally measured stream-
ing component by a least squares technique. The parameters utilized
in this fitting were c and Y . The special solution obtained was by
definition put equal to S , (x). The corresponding values of c and
Y are given in table 1.
3. 3 Leakage Component
The thermal leakage contribution to the air gap flux at a
certain point was assumed proportional to the flux at the same point
in the unducted shield, i. e. proportional to <j#, (x). Thus we
define
~ I n r \ g L UIxU. J -J L.Q / v / « \
_ 7 -
In the comparison between theory and experiments given in
Fig. 12 "0 (x) has been used for 0«.T_ (x) and the0 r expv ' r theov
constant of proportionality (-t) was chosen to fit the experimentally
determined L, (x). See also Appendix I and II for another, more
detailed, approach to the calculation of the leakage flux.
3.4 Albedo Component
The albedo contribution to the thermal air gap flux at the
distance x from the duct mouth may obviously be expressed in
terms of streaming and leakage contributions by
AjJ (X) * or. (x) I*? fx) + a, (x) S* (x) (8)theo^ ' 1 v ' theo* ' 2 v ' theov ' x '
In this relation the functions a., (x) and or_(x) are character-
istic for the whole geometrical and material configuration and of
course of the type of radiation involved.
Another interpretation, making it possible to calculate
a. (x) and ff_(x), is to regard them as albedo-coefficients aver-
aged over different angular distributions and materials. The lack
of information of these distributions is the reason for putting
a\ (x) ss cc?(x) ss as which is a constants, and we get
A (x) * CM J-Ui. Cx) + S,, (x) (9)' L theo v ' t h e o v 'J x '
In the comparison given in Fig. 13 between theory and
experiments the constant a was chosen to fit the experiments.
3. 5 Parameters Necessary to Describe the Thermal
Air Gap Flux
By definition we have
[wCdj,_fth / ^ oth f \ , r th r \ , A th / %rtheov ' theov ' theov ' theov '
Putting together the theoretical data given in (5), (7) and (9) we can
write
(10)
5» [
Y Q (C + l ) x C -,+ -2—£__ _ G(rs x, rs R, c) J (11)
where G(r, x, r, R, c) is the integral in S (r, x) i.e.
i (x 4- r + T1 - 2r r
The radial dGse point coordinate r satisfies r ••£ r £ R and was
chosen to give the average flux in the manner described in [4j .
Thus necessary parameters are, disregarding the geometrical
ones and those involved in the bulk .shielding calculation of
the albedo-coefficient, a
the leakage proportionality factor, -£•
and the flux parameters
the angular source distribution constant, c
the surface source density, ¥ ,
The calculations! model presented is intended to predict the air
gap flux, provided that the parameters c, Y , a and t- are
available. The error in the air gap flux due to a given error in any
of the parameters can be calculated by means of equations (13) - (l 6)
given below.
In this paper* however, the inverse problem was solved, i. e.
the values of the parameters were determined by fitting the calculated
air gap flux to the one experimentally found by a technique of least
squares. This "least squares fitting" was performed by means of
computer programs which also calculated the errors in the para-
meters caused by errors in the experimentally measured fluxes.
The values are given in table 1 and were used in the com-
parison between theory and experiments given in Figs. 11-13.TV [undl-jth r \ i - x i J7 [und],jth * v .However, " <3 (x) was used instead of G , (x) m
r expv ' T theov 'expv
order to keep the errors connected with bulk shielding calculations
out of this investigation.
- 9 -
Table 1. Values of the parameters necessary to
describe the thermal air gap flux.
äI
c
o
0.
0.
3.
(1
74
211
2
. 8
±
±
•k
±
0. 06
0. 006
2. 0
0. 6) • 109
3. 6 Discussion of Errors
Expressions relating the error of a parameter to the
corresponding error of the air gap flux are given below. The
quantity fJ given in expression (13) is a distance (its magnitude
is about half the duct length) and is equal to
1 6GG ' "6c"
A0 S • c f 1.™*i-=1» as ... —,I,...I..MM.. [ — — ™
g> L + s Lc ++ In Ac
c (13)
A o (14)
ål (15)
(16)
Table 2 shows the relative error in the air gap flux (gap
width 1. 5 cm) calculated with the parameter values of table 1
inserted in the above expressions and assuming a relative error of
10 % in each of the parameters.
4.
- 10
Table 2. Errors in the air gap flux caused by 10 %
relative errors in the parameters.
{Gap width 1. 5 cm)
10 % relative error
in the parameter
a
I
c
Yo
Relative error in
the air gap flux
5 %
5%
15 %
5%
Theoretical Interpretation of Results of Fast Flux
Distribution Measurements
In this section the fast air gap flux will be theoretically
divided into two components and the calculation of these components
discussed.
4. 1 Definition of Components of the Fast Air Gap Flux
In the case of fast neutrons the albedo effect is negligible since
it involves energy degradation. As for the "leakage" contribution at a
certain point, we simply state this to be equal to the flux in the unducted
configuration at the same point. Finally, the streaming contribution is
ruled by the same laws as in the thermal case.
4. 2 Streaming Component
The discussion in the thermal case (3.2) is, slightly modified,
also relevant to the fast case.
The fast streaming component could not be experimentally
isolated from the fast "leakage" component, thus the sum of the two
was measured. In agreement with the thermal case, the parameters
Y and c were chosen to fit the above mentioned sum to the measuredofast air gap flux.
The values of the parameters used in the comparison between
theory and experiments are given in table 3.
- 11 -
4. 3 Leakage Component
As mentioned above the assumption will be made that in-
ferring the air gap in the shield does not greatly affect the unducted
flux. Thus we get
Thus the parameters necessary are, disregarding the
geometrical ones and those involved in the bulk shielding calculation£ [undl^f fOf ^ C
the angular source distribution constant, c
the surface source density, ¥ .
In table 3 are given the values of c and Y used in thecomparison between theory and experiments given in Fig. 14. However, <& (x) was used instead of Qi,, (x) for the
™ expv ' * theov 'same reasons as in the thermal case.
Table 3. Values of the parameters necessary to
describe the fast air gap flux.
c
o
48
( 1 . 8
±±
7
0. 1) . io9
As in the thermal case <$tl (x) was replaced byr ,-i , * t h e o v ' f J
<$ (x) in the comparison between theory and experiments
made in Fig. 14.
4. 4 Parameters Necessary to Describe the Fast Air Gap Flux
By definition we have
* (x) + lA (x) (18)theov ' theo* ' v '
Putting together the theoretical data given in (5) and (17) w©
can write
C d V L C d ] 4 + ! 4 ^ O(i.*.r.R.c, (19)
- 12 -
4. 5 Discussion of Errors
What was said in the "Discussion of Errors" in the thermal case
also holds in the fast case with the exception of the expressions and the
table that relate the parameter errors to the flux errors.
Thus in the fast case we have
* c (20)
(21)
Table 4. Errors in the air gap flux caused by 10 % relative
errors in the parameters (gap width 1. 5 cm).
c
Y
15 %
10 %
5. Conclusions
The model reported here for prediction of neutron attenuation
in ducted configurations may be applied to straight annular ducts of
arbitrary dimensions and material configurations.
The model reduces asymptotically to the simple streaming case,
i .e. to the well-known attenuation formulae [5, 6], at distances where
these formulas are supposed to work. However, it is evident from this
report that neglecting wall contributions to the air gap flux may, in
both the thermal and the fast case, give rise to very large errors in
the prediction of the air gap flux attenuation in the part of the duct
nearest to the source. Thus the model presented is designed especially
for the problems met with in short ducts.
The model was tested against the experiments described above
and works satisfactorily when applied to the configurations investigated.
- 13 -
References
1. J Braun and K Randen
Neutron Streaming in D_O Pipes. 1962 (AE-98)
2. E Aalto and R Nilsson
Measurements of Neutron and Gamma Attenuation in
Massive Laminated Shields of Concrete and a Study
of the Accuracy of Some Methods of Calculation.
19 64 (AE-157)
3. DC Piercey
The Transmission of Thermal Neutrons along Air
Filled Ducts in Water. 19 62 ( A E E W / R - 7 0 )
4. J Nilsson
Geometrical Attenuation of Particle Streaming in
Annular and Ordinary Ducts. Nukleonik 6_ (l 964} p. 285
5. T Rockwell (ed)
Reactor Shielding Design Manual. Van Nostrand,
Princeton, N. J. , 1956, 472 p.
6. B T Price, C C Horton and K T Spinney
Radiation Shielding, Pergamon Press, London, 1957, 350 p.
- 14 -
APPENDIX I
The Relation between the Leakage Component and the Surface Source
Density of the Duct Walls
Consider an annular duct of inner radius r and outer radius R
and let x be the axial coordinate with respect to the duct mouth. On the
duct wall, we assume a rotational symmetry around the duct axis for
the surface source density that provides the leakage component. Let
the inner surface source density be Y (x) and the outer surface source
density YR{x). Assume further that the angular source distribution
function may be put proportional to an arbitrary non-negative power,c -1
|i , of the cosine of the emission angle, cos ^. The latter being
the angle between the emitted particle' s direction and the normal to
the duct surface in the emission point.
We can now derive the flux due to leakage through an arbitrary
point (r,x) in the duct (r ^ r £ R) and (0 ^ x ^ xxJ-
An element of inner source area rdcp'dx' at the point
(r,cp',x') contributes with dL (r,cpf,x' ^ r, 0, x) to the
leakage flux, L (r,x) at the point (r, 0, x). The subscript r
indicates leakage through inner duct surface. It is easy to show that
the following relation holds between dL (r, tp',x' > r, 0, x) and
dL (r, cp', x' > r, 0, x) * dL (r, x)
C + 1 [i,_ . yr ̂ xj . _ rdcp'dx1 (22)
TT r D 2r
with
D r2 * (xf - x)2 + r2 + r 2 - 2rrcos.9( (23)
and
rcoscp' - r^r * 15
r
Integration over those parts of the inner duct walls that
contribute gives
- 15 -
-Ir
x l X M C O S 7
r x) » Ji-L r F * (x) • C'coa^-r) r rdcp' dx'o o v '
In the same way we can derive the contribution from the outer
duct wall and the resu l t will be:
c-R+1 I*™ R
(R, cp!, x' » r , 0, x) * dL-pCr, x) * -5— • Y^x) - -2^- Rdcp' dx'" D R
with
D R2 at (x' - x ) 2 + R2 + r 2 - ZRrcoscp'
and
R -u, D R
Integration over those parts of the outer duct walls that can
contribute gives
, ! S ! 1 f FY (X) . (R-rcoscpQ^Rdcp'dx-J J R(} 2 2 2o o
Thus we can write the- relation between the leakage component
and the surface source density on the duct walls:
c + 1
L(r,x) « Lr(r,x) + LR(r,x) « -L_- Jo o
/ -1 r . - l rx M ( c o s
(rcoscp'-r) r rdcp'dx' A _±v___ , , ^
( R - r c o s y J )
[ (x ' -x) 2+R 2+r 2 -2Rrcoscp J
- 16 -
APPENDIX II
The Geometry Dependent Leakage Component
An improvement of the assumption made in section 3. 3 would
be obtained if the surface source density of the duct walls (instead of
the flux due to leakage) was assumed to be proportional to the flux in
the unducted configuration. In order to compute the leakage flux the
source should then be inserted in eq. 29 of "Appendix I".
Making use of the symbols defined in "Appendix I" we can
thus write for the leakage through the outer duct surface:
oo DR
The leakage through the inner duct surface should be treated
analogically.
However, the errors in the flux measurements are too large
to give preference to the more detailed approach in the above
appendices over the one given in section 3.3 at the calculation of
the leakage component.
and inserted in eq. 29 of Appendix I
xM(cos g + coe ? )1 tv.
LR(" r ' x 'S -F- J J ^R [ U n dVW- —2 * R<V dx' (32)D
List of Figures
1. The R2-0 Reactor
2. Shielding Facilities
3. Arrangement of Experimental Set-up
4. Investigated Configurations
5. Model for Air Gap Flux Calculations
6. Experimental Flux Distributions - Gap Width 0.5 cm
7. " " " - " " 1.0 cm8. " n >; _ i. it L 5 c m
9. " " " - " " 2.0 .cm
10. " " " - Undue ted Configuration
11 . Thermal Flux Comparison - Streaming Component
12. " M ti • -Leakage "
13. " " " -Albedo "
14. Fast Flux Comparison
Fig.1 The R2-0 Reactor
S3 S5
R
o
o o o o_. _ _ „.
0 0 0 0
0 0 0 0 d|*5
5m
.2 The R2-0 shielding facilities.
Reactor pool Borated lucite
1
1/
1
1\
Fuel element Control rod
Al
Scale V.5
Fig.3 Arrangement of Experimental Setup
Borated tucite
>R D2O iii - D Ö O -
KW1
wCd
CdM
CdMPL
und
Fig.4 Investigated Configurations
Fig. 5 Model for air gap flux calculations.
1010
(n
10'
8̂
10'
Conf.
Thermal flux o [wCd]
Fast flux x [wCd]
D20 D20
0 10 20 30Fig.6 Experimental Flux Distributions. Gap Width 0.5 cm
(cm) 50
Thermal flux o [wCd]
0 20 30 40Fig.7 Experimental Flux Distributions. Gap Width 1.0 cm
(cm) 50
1010
(n cm2s1)
10-
10.8
10'
Conf.
Thermal flux o [wCd]• [CdM]v [CdMP]
Fast flux x [wCd]
\ D20 D20
0 10 20 30 40
Fig.8 Exper imental Flux Distributions. Gap Width 1.5 cm
(cm) 50
10,10
(n cm s)
10"
10'
Conf.
Thermal flux o [wCd]Ö [CdM]v jCdf
Fast flux x [wCd|
10c
\\>K\\ D20
0 10 20 30Fig.9 Experimental Flux Distributions. Gap Width 2.0 cm
(cm) 50
1010
(n cm V )
1CT
108
10 '
Thermal f luxFast flux
Conf.
x [und]o [una]
10s
D20 D 20i
10i
3020 30 40 — > (cm) 50Fig.10 Experimental Flux Distributions. Unducted Configuration.
Gap Width (cm) 2.0 15 1.0 0.5th
D A
10
Fig. 11 Thermal Flux Comparison.Streaming Component.
1oio
f (n cm2s"1)
108
10'
10*
0
Gap Width (cm) 2,0 1.5 1.0 0.5i thL e x p O O A
ththeo
10 20 30
Fig.12 Thermal Flux Comparison. Leakage Component.
(cm) 50
Gap Width (cm) 2.0 1.5 1.0 0.5
10
o 20 30 40
Fig. 13 Thermal Flux Comparison. Albedo Component.
(cm) 50
1010
f
108
Gap Width (cm) 2.0 1.5 1.0 0.5
01theo
10'
101
U21
20
D20
0 10J
30Fig.U Fast Flux Comparison.
(cm) 50
LIST OF PUBLISHED AE-REPORTS
1—90. (See the back cover earlier reports.)
91. The energy variation of the sensitivity of a polyethylene moderated BFjproportional counter. By R. Fräki, M. Leimdörfer and S. Malmskog. I962.12. Sw. cr. 6:—.
92. The backscattering of gamma radiation from plane concrete walls. ByM. Leimdörfer. 1962. 20 p. Sw. cr. 6:—.
93. The backscattering of gamma radiation from spherical concrete walls.By M. Leimdörfer. 1962. 16 p. Sw. cr. 6:—.
94. Multiple scattering of gamma radiation in a spherical concrete wallroom. By M. Leimdörfer. 196/. 18 p. Sw. cr. 6:—.
95
133. Studies of water by scattering of slow neutrons. By K. Sköld, E. Pilcherand K. E. Larsson. 1964. 17 p. Sw. cr. 8:—.
134. The amounts of As, Au, Br, Cu, Fe, Mo, Se, and Zn in normal and urae-mic human whole blood. A comparison by means of neutron activationanalysis. By D. Brune, K. Samsahl and P. O. Wester. 1964. 10 p. Sw. cr.8:—.
135. A Monte Carlo method for the analysis of gamma radiation transportfrom distributed sources in laminated shields. By M. Leimdörfer. 1964.28 p. Sw. cr. 8:—.
136. Ejection of uranium atoms from UOj by fission fragments. By G. Nilsson.1964. 38 p. Sw. cr. 8:—.
137. Personnel neutron monitoring at AB Atomenergi. By S. Hagsgärd andC-O. Widell. 1964. 11 p. Sw. cr. 8:
I. The paramagnetism of Mn dissolved in a and fi brasses. By H. P. Myers 138. Radiation induced precipitation in iron. By B. Solly. 1964. 8 p. Sw. cr.ana R- Westin. 1962. 16 p. bw. cr. 6:—. 8:—.
96. Isomorphic substitutions of calcium by strontium in calcium hydroxy-apatite. By H. Chrislensen. 1962. 9 p. Sw. cr. 6:—.
97. A fast time-to-pulse height converter. By O. Aspelund. 1962. 21 p. Sw. cr.6:—.
98. Neutron streaming in D2O pipes. By J. Braun and K. Randen. 196241 p. Sw. cr. 6:—.
99. The effective resonance integral of thorium oxide rods. By J. Weitman.1962. 41 p. Sw. cr. 6:—.
100. Measurements of burnout conditions for flow of boiling water in verticalannuli. By K. M. Becker and G. Hernborg. 1962. 41 p. Sw. cr. 6t—.
101. Solid angle computations for a circular radiator and a circular detector.By J. Konijn and B. Tollander. 1963. 6 p. Sw. cr. 8:—.
102. A selective neutron detector in the keV region utilizing the "F(n, y)!0Freaction. By J. Konijn. 1963. 21 p. Sw. cr. 8:—.
103. Anion-exchange studies of radioactive trace elements in sulphuric acidsolutions. By K. Samsahl. 1963. 12 p. Sw. cr. 8:—.
104. Problems in pressure vessel design and manufacture. By O. Hellströmand R. Nilson. 1963. 44 p. Sw. cr. 8:—.
105. Flame photometric determination of lithium contents down to 10-3 ppmin water samples. By G. Jönsson. 1963. 9 p. Sw. cr. 8:—.
106. Measurements of void fractions for flow of boiling heavy water in avertical round duct. By S. Z. Rouhani and K. M. Becker. 1963. 2nd rev.ed. 32 p. Sw. cr. 8:—.
107. Measurements of convective heat transfer from a horizontal cylinderrotating in a pool of water. K. M. Becker. 1963. 20 p. Sw. cr. 8:—.
108. Two-group analysis of xenon stability in slab geometry by modal expan-sion. O. Norinder. 1963. 50 p. Sw. cr. 8:—.
109. The properties of CaSOjMn thermoluminescence dosimeters. B. Bjärn-gard. 1963. 27 p. Sw. cr. 8:—.
110. Semianalytical and seminumerical calculations of optimum materialdistributions. By C. I. G. Andersson. 1963. 26 p. Sw. cr. 8:—.
111. The paramagnetism of small amounts of Mn dissolved in Cu-AI andCu-Ge alloys. By H. P. Myers and R. Westin. 1963. 7 p. Sw. cr. 8:—.
112. Determination of the absolute disintegration rate of Cs"?-sources by thetracer method. S. Hellström and D. Brune. 1963. 17 p. Sw. cr. 8:—.
113. An analysis of burnout conditions for flow of boiling water in verticalround ducts. By K. M. Becker and P. Persson. 1963. 28 p. Sw. cr 8:—.
114. Measurements of burnout conditions for flow of boiling water in verticalround ducts (Part 2). By K. M. Becker, et a l . 1963. 29 p. Sw. cr. 8:—.
115. Cross section measurements of the s8Ni(n, p)'äCo and "Si(n,r\ n-)«Mg reac-tions in the energy range 2.2 to 3.8 MeV. By J. Konijn and A. Lauber1963. 30 p. Sw. cr. 8:—.
116. Calculations of total and differential solid angles for a proton recoilsolid slate detector. By J. Konijn, A. Lauber and B. Tollander. 1963. 31 p.Sw. cr. 8:—.
117. Neutron cross sections for aluminium. By L. Forsberg. 1963. 32 p.Sw. cr. 8:—.
118. Measurements of small exposures of gamma radiation with CaSOj:Mnradiothermoluminescence. By B. Bjärngard. 1963. 18 p. Sw. cr. 8:—.
119. Measurement of gamma radioactivity in a group of control subjects fromthe Stockholm area during 1959—1963. By I. O. Andersson, I. Nilssonand Eckerstig. 1963. 19 p. Sw. cr. 8:—.
120. The thermox process. By O. Tjälldin. 1963. 38 p. Sw. cr. 8:—.121. The transistor as low level switch. By A. Lydén. 1963. 47 p. Sw. cr. 8:—.122. The planning of a small pilot plant for development work on aqueous
reprocessing of nuclear fuels. By T. U. Sjöborg, E. Haeffner and Hulr-gren. 1963. 20 p. Sw. cr. 8:—.
123. The neutron spectrum in a uranium lube. By E. Johansson, E. Jonsson,M. Lindberg and J. Mednis. 1963. 36 p. Sw. cr. 8:—.
124. Simultaneous determination of 30 trace elements in cancerous and non-cancerous human tissue samples with gamma-ray spectrometry. K. Sam-sahl, D. Brune and P. O. Wester. 1963. 23 p. Sw. cr. 8:—.
125. Measurement of the slowing-down and thermalization time of neutronsin water. By E. Möller and N. G. Sjöstrand. 1963. 42 p. Sw. cr. 8:—.
126. Report on the personnel dosimetry at AB Atomenergi during 1962. ByK-A. Edvardsson and S. Hagsgård. 1963. 12 p. Sw. cr. 8:—.
127. A gas target with a tritium gas handling system. By B. Holmqvist andT. Wiedling. 1963. 12 p. Sw. cr. 8:—.
128. Optimization in activation analysis by means of epithermal neutrons.Determination of molybdenum in steel. By D. Brune and K. Jirlow. 1963.11 p. Sw. cr. 8:—.
129. The Pi-approximation for the distribution of neutrons from a pulsedsource in hydrogen. By A. Claesson. 1963. 18 p. Sw. cr. 8:—.
130. Dislocation arrangements in deformed and neutron irradiated zirconiumand zirca!oy-2. By R. B. Roy. 1963 18 p. Sw. cr. 8:—.
131. Measurements of hydrodynamic instabilities, flow oscillations and bur-nout in a natural circulation loop. By K. M. Becker, R. P. Mathisen, O.Eklind and B. Norman. 1964. 21 p. Sw. cr. 8:—.
132. A neutron rem counter. By I. O. Andersson and J. Braun. 1964. 14 p.Sw. cr. 8:—.
139. Angular distributions of neutrons from (p, n)-reactions in some mirrornuclei. By L. G. Strömberg, T. Wiedling and B. Holmqvist. 1964. 28 p.Sw. cr. 8:.
140. An extended Greuling-Goertzel approximation with a Pn-approximationin the angular dependence. By R. Håkansson. 1964. 21 p. Sw. cr. 8s—.
141. Heat transfer and pressure drop with rough surfaces, a literature survey.By A. Bhattachayya. 1964. 78 p. Sw. cr. 8:—.
142. Radiolysis of aqueous benzene solutions. By H. Christensen. 1964. 40 p.Sw. cr. 8:—.
143. Cross section measurements for some elements suited as thermal spect-rum indicators: Cd, Sm, Gd and Lu. By E. Sokolowski, H. Pekarek andE. Jonsson. 1964. 27 p. Sw. cr. 8:—.
144. A direction sensitive fast neutron monitor. By B. Antolkovic, B. Holm-qvist and T. Wiedling. 1964. 14 p. Sw. cr. 8:—.
145. A user's manual for the NRN shield design method. By L. Hjärne. 1964.107 p. Sw. cr. 10:—.
146. Concentration of 24 trace elements in human heart tissue determinedby neutron activation analysis. By P.O.Wester. 1964. 33 p. Sw. cr. 8:—.
147. Report on the personnel Dosimetry at AB Atomenergi during 1963. ByK.-A. Edvardsson and S. Hagsgård. 1964. 16 p. Sw. cr. 8:—.
148. A calculation of the angular moments of the kernel for a monatomic gasscatterer. By R. Håkansson. 1964. 16 p. Sw. cr. 8:—.
149. An anion-exchange method for the separation of P-32 activity in neu-tron-irradited biological material. By K. Samsahl. 1964. 10 p. Sw. cr.
150. Inelastic neutron scattering cross sections of Cu'" and Cu" in the energyregion 0.7 to 1.4 MeV. By B. Holmqvist and T. Wiedling. 1964. 30 p.Sw. cr. 8:—.
151. Determination of magnesium in needle biopsy samples of muscle tissueby means of neutron activation analysis. By D. Brune and H. E. Siöberq.1964. 8 p. Sw. cr. 8:—.
152. Absolute El transition probabilities in the dofermed nuclei Yb1" andHP". By Sven G. Malmskog. 1964. 21 p. Sw. cr. 8:—.
153. Measurements of burnout conditions for flow of boiling water in vertical3-rod and 7-rod clusters. By K. M. Becker, G. Hernborg and J. E. Flinta.1964. 54 p. Sw. cr. 8:—.
154. Integral parameters of the thermal neutron scattering law. By S. N.Purohit. 1964. 48 p. Sw. cr. 8:—.
155. Tests of neutron spectrum calculations with the help of foil measurmentsin a D2O and in an HzO-moderated reactor and in reactor shields ofconcrete and iron. By R. Nilsson and E. Aalto. 1964. 23 p. Sw. cr. 8:—.
156. Hydrodynamic instability and dynamic burnout in natural circulationtwo-phase flow. An experimental and theoretical study. By K. M. Beck-er, S. Jahnberg, I. Haga, P. T. Hansson and R. P. Mathisen. 1964. 41 p.Sw. cr. 8:—.
157. Measurements of neutron and gamma attenuation in massive laminatedshields of concrete and a study of the accuracy of some methods ofcalculation. By E. Aalto and R. Nilsson. 1964. 110 p. Sw. cr. 10:—.
158. A study of the angular distributions of neutrons from the Be' (p,n) B'reaction at low proton energies. By B. Antolkovic', B. Holmqvist andT. Wiedling. 1964. 19 p. Sw. cr. 8 : - .
159. A simple apparatus for fast ion exchange separations. By K. Samsahl.1964. 15 p. Sw. cr. 8:—.
160. Measurements of the FeH (n, p) MnH reaction cross section in the neutronenergy range 2.3—3.8 MeV. By A. Lauber and S. Malmskog. 1964.13 p. Sw. cr. 8:—.
161. Comparisons of measured and calculated neutron fluxes in laminatediron and heavy water. By E. Aalto. 1964. 15 p. Sw. cr. 8:—.
162. A needle-type p-i-n junction semiconductor detector for in-vivo measure-ment of beta tracer activity. By A. Lauber and B. Rosencrantz. 1964.12 p.Sw. cr. 8:—.
163. Flame spectro photometric determination of strontium in water andbiological material. By G. Jönsson. 1964. 12 p. Sw. er. 8:—.
164. The solution of a velocity-dependent slowing-down problem usingcase's eigenfunction expansion. By A. Claesson. 1964. 00 p. Sw. cr. 8:—.
165. Measurements of the effects of spacers on the burnout conditions forflow of boiling water in a vertical annulus and a vertical 7-rod cluster.By. K. M. Becker end G. Hemberg. 1964. 15 p. Sw. cr. 8:—.
166. The transmission of thermal and fast neutrons in air filled annular ductsthrough slabs of iron and heavy water. By J. Nilsson and R. Sandlin.1964. 33 p. Sw. cr. 8:—.
Förteckning över publicerade AES-rapporter
1. Analys medelst gamma-spektrometri. Av D. Brune. 1961. 10 s. Kr 6:—.2. Bestrålningsförändringar och neutroratmosfär i reaktortrycktankar —
några synpunkter. Av M. Grounes. 1962. 33 s. Kr 6:—.3. Studium av sträckgränsen i mjukt stål. Av G. Ostberg och R. Attermo.
1963. 17 s. Kr 6:—.4. Teknisk upphandling inom reaktorområdet. Av Erik Jonson. 1963. 64 s.
Kr. 8 r - .
Additional copies available at the library of AB Atomenergi, Sludsvik,Nyköping, Sweden. Transparent microcards of the reports are obtainablethrough the International Documentation Center, Tumba, Sweden.
EOS-tryckerierna, Stockholm 1964