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