AE-157UDC 539.1.074.8

62! .039.538

UJ Measurements of Neutron and Gamma

Attenuation in Massive Laminated Shields of

Concrete and a Study of the Accuracy

of some Methods of Calculation

E. Aal to and R. Nilsson

AKTIEBOLAGET ATOMENERGI

STOCKHOLM, SWEDEN 1964

, v u

ERRATA

To report AE-157

Measurements of Neutron and Gamma Attenuation in Massive LaminatedShields of Concrete and a Study of the Accuracy of some Methods ofCalculation

E. Aalto and R. Nilsson

Page 17, line 1 reads analysis, should read compositionsPage 24, line 20 reads (iS90 per cent), should read (&90 per cent)Page 25, line 26 reads the run of, should read the sum ofPage 26, line 6 reads phosphorus foil, should read phosphorus foils

Back cover: The correct price for AE-157 is Sw. cr. 10:-

AKTIEBOLAGET ATOMENERGI

STOCKHOLM, SWEDEN 1964

AE-157

MEASUREMENTS OF NEUTRON AND GAMMA ATTENHATION IN

.MASSIVE LAMINATED SHIELDS OF CONCRETE AND A STUDY

OF THE ACCURACY OF SOME METHODS OF CALCULATION

E. Aalto and R. Nilsson

Summary

Extensive neutron and gamma attenuation measurements have

been performed in magnetite and ordinary concrete up to a depth of

2 metres in order to study the accuracy attainable by some shield

calculation methods. The effect of thin, heavy layers (Pb) has also

been studied. Experimental facilities and instrumentation, especi-

ally the foil detection methods used for thermal and epithermal

neutrons, are described in some detail. Great weight is laid upon

a thorough error analysis. The fluxes measured are compared to

those calculated by an earlier version of the British 18-group re-

moval method (RASH B_), by an improved removal method (NRN)

developed at AB Atomenergi, and by numerical integration of the

Boltzmann equation (NIOBE). The results show that shielding cal-

culations with the newer methods give fluxes that are generally

within a factor of 2-3 from the true values. A greater accuracy

seems to be difficult to obtain in practice in spite of possible im-

provements in the mathematical solution of the transport problem.

The greatest errors originate in the translation between the true

and calculation geometries in the uncertainty of material proper-

ties in the case of concrete, and in approximations and inaccuracies

of radiation sources.

Printed and distributed in Sept. 1964.

Table of contents

™~ " Page

List of tables iii

Figure captions iiii

INTRODUCTION

1,1. General remarks 1

1 „ 2, History 1

1.3. Scope of the report 2

1.4. Acknowledgements 3

EXPERIMENTS

2. Experimental facilities 4

3. Methods of measurements, instrumentation 5

3 ,1 , General remarks 5

3. 2. Neutron measurements 6

3.3. Gamma measurements 11

4. Composition and properties of the concretes studied 16

50 Configurations studied 17

5 .1 . Magnetite concrete 17

5. 2. Ordinary concrete 18

5O3. Other configurations studied 18

6. Experimental procedure 18

6. 1. Ranges of measurements and instrumentation 18

6, 2. Experimental runs 19

7'. Sources of e r ror and their effects on the results 19

7 .1 . General remarks 19

7. 2. Reactor power and irradiation time 20

7. 3. E r ro r s in the spatial coordinates 21

7. 4. Variations in the materials studied 22

7. 5. Summary of the e r ro rs 25

8. Summary of the measured values 26

8a 1. Neutron fluxes 26

8. 2. Gamma exposure rates 27

CALCULATIONS

9. Introduction to the calculations 27

9 . 1 . General remarks 27

9. 2, Methods 28

- 11 -

Page

10. Calculations based on. the 18-group removal method(RASH) 28

10.1. Removal source 28

- 10. 2. Neutron diffusion and slowing-down 30

10. 3. Gamma exposure rate 31

11. Calculations based on the improved removal method(NRN method) 32

11.1. Introduction 32

11.2. Removal source 33

11.3. Neutron diffusion and slowing-down 34

11.4. Gamma exposure rate 34

12. Neutron penetration calculations by numericalintegration of transport equation (NIOBE) 35

12.1. Introduction 35

12,1. Calculations 36

12.3. Results 36

13. Concluding remarks about the calctilations 3?

COMPARISON OF THE RESULTS, CONCLUSIONS

14. Quantities to be compared and their presentation 38

14.1. Neutron fluxes 38

14. 2. Gamma exposure rates 39

14.3. Presentation of the results 39

14.4. Explanation of tables and figures 40

15. Discussion of the results 41

15.1. Neutron fluxes 41

15.2. Gamma exposure rates and source distributions 42

16. Conclusions, recommendations 45

16.1. Attenuation measurements 45

1 6. 2. Comparison of measured and calculated fluxes 46

REFERENCES 48

APPENDICES

I. Effective flux level in an open channel 55

II. Radiation heating in concrete 56

III. Effective gamma sources for a dose point onthe outside of the shield 60

IV. Experiments in the use of nuclear emulsions

for fast neutron detection 62

TABLES

FIGURES

- Ill -

List of tables

1. Data for the foil detectors

2. Composition and properties of magnetite concrete

3. Composition and properties of ordinary concrete

4. Compositions of the real and calculation concretes,weight per cent

5. Shield configurations studied

6 Macroscopic Removal Cross-Sections for the Concretes

7. R2-0 Core parameters for RASH calculation

8. Energy Groups for RASH calculation

9. RASH Multi-Group Parameters for Various Concretes

10. Data for the gamma calculations

11. Relative gamma sources for the GASLIT

12. Taylor build-up factors used in GASLIT

13. R2-0 Core parameters for NRN calculation

14. Fission source density for NIOBE calculation

15. Neutron Fluxes in configuration 1

i / ™ f Thermal and epithermal fluxes | , c. _ o

16 - 29. J > for configs. 2 - 8} P(n, p) and gamma exposure ratesj

- 1 1 1 1 -

Figure captions

1. R2-0 reac tor with shielding facili t ies

2. R2-0 core loading

3. The R2-0 shielding faci l i t ies . Plane view

4. Configurations for the bulk shielding study

5. Usable ranges vs . exposure for neutron detectors inconfig. 3

6. Usable ranges vs exposure for gamma detectors inconfig. 3

7. Removal source in config. 3' as a function of thedensity and water content of the concrete

8. Determinat ion of the effective core radius forspher ica l geometry from isoflux l ines

9. Relative the rmal fluxes in configurations 3 and 2as a function 'of the core radius

10. P r inc ip l e s for neutron slowing-down in RASH B andNRN methods

11. Neutron spec t ra in config. 2 at z a 35 cm by NRN and NIOBE

12. Explanation of the signs

13. Neutron fluxes in config. 1 (water)

f Thermal and epi thermal fluxes ">14 - 27. 1 „ / v , f in configs. 2 - 8

{ P(n, p; and gamma exposure r a t e s ) &

28. Definitions of the coordinates for a detector in a channel29. Flux dis tr ibut ions in an open vs . filled channel in

magneti te concrete

30. Thermal flux distr ibution in channel 3, config 3

31. Observed and predic ted heating r a t e s in config. 2

32. Observed and predicted heating ra t e s in config. 7

33. Gamma exposure ra te originating pe r 10 cm shieldthickness for a dose point on the outside of config. 2

34. Gamma exposure ra te originating per 10 cm shieldthickness for a dose point on the outside of config. 5

35. Gamma exposure ra te originating per 10 cm shieldthickness for a dose point on the outside of config. 6

3 6. Gamma exposure ra te originating per 10 cm shieldthickness for a dose point on the outside of config. 7

37. Relative fast flux in config. 3 by nuclear emulsion method

- 1 -

INTRODUCTION

1.1. General remarks

The radiation shields form a considerable part of the civil en-

gineering costs of a nuclear power plant. The most impoitant shield

unit is normally the main biological shield of the reactor.

The design of radiation shields is not yet an exact science. A

large amount of theoretical work has been done during the last decade,

but much of the practical design work is still based on empirical

methods or on plain guess work. Often one necessarily has to safe-

guard against the uncertainties inherent in the calculating methods by

using large safety factors. These extra, factors add, of course, to the

cost of the plant. It has been estimated, for instance, that savings of

about £ 100.000 per reactor could be achieved by really reliable

methods of calculation in the British natural U-graphite reactors. Ten

years ago the Hänförd K reactors needed about $ 6 million lower

shielding cost per reactor ' than the old Hanford types.

A comparatively small part of the nuclear energy efforts in

various countries has been, directed to shielding, and the development

of accurate shielding calculation methods has been rather slow. One

reason for this may be that shielding has been treated as a kind of

fringe area, and hence the main efforts in reactor physics have been

concentrated on the core.

1.2. History

Before I960 little data were available on the reliability of the

existing design methods for biological shields. The most important

unciassified comparisons between the measured and calculated

attenuations in massive shields were presented by the Harwell and3-6}the Hanford groups. In 1961 and 1962 the Hanford report series

7 8)

was followed by two more reports ' . Only the Harwell group re-

ported measurements for about 300 cm penetration, while the reports

from Hanford treated penetrations up to 125 cm only. The latter re-

sults were compared with attenuations calculated by single group re-

moval cross-sections.

After the nucleus of the present shielding group at AB Atom-

energi had been set up in 1956, it was felt that a thorough understand-

ing of the attenuation properties of laminated shields in simple geo-

metries should be the basis for all subsequent shielding research. On

this account, and because of the gains that would ensue from better

and more accurate design methods, a study of the basic, massive

biological shields- was initiated. This report is an effort to sum up

the results of this work.

Preparations for the work started in 1958, but the first main ex-

periments were performed in I960 after the R2-0 reactor with its faci-

lities was completed. Preliminary results, compared to the British1) 9)

multigroup-method that was new at that time, were presented ; at*

the EAES Symposium on "Nuclear Reactor Shielding, Theory and Ex-

periments" in March 1 961 . Thereafter the experiments went on till

the summer of 1962.

The bulk shielding studies concluded with a study of laminated

shields of Fe and D_O reported elsewhere . After these studies the

main effort of the small experimental groups was directed to the study

of "voids and ducts".

The publishing of the results of the measurements in massive

shields has regrettably been delayed, partly because of other more

urgent problems in connection with the Swedish reactor programme,

and partly because we wanted to include results obtained with the NRN

design method (chap. 11).

1 . 3. Scope of the report

This report is divided into three main sections. The first

describes the penetration measurements. The evaluation of the discre-

pancies between the measured and the calculated results has been the

main purpose of this report. Therefore our aim has been to eliminate

or minimize errors of all kinds in the measurements and to produce

reliable results that are accurate in their absolute values. As will be

seen, we are able to measure radiation after penetrations up to about

200 cm. However, biological shields for power reactors are about 300

- 3 -

cm thick. The necessary extrapolation of possible trends of divergen-

ce to great penetration depths demands accurately measured data in

order to give reliable results.

Economic points of view normally determine the material to

be used in biological shields. Usually the cheapest solution is ordi-

nary concrete made from materials available near the reactor site.

Lack of space sometimes necessitates heavier aggregates and in

special cases some expensive, exotic materials have been used.

Owing to this trend towards locally available materials, or-

dinary and magnetite concretes are studied in this report.

The description of the experimental work starts with a pre-

sentation of our facilities. This is followed firstly by a short descrip-

tion of the instrumentation used, secondly by other required physical

data, about the materials, then by some notes on the experimental

procedure, and finally by an error analysis and a summary of the

results of,the measurements.

The second part of this report, describes the main calculation

methods used, which are the well-known British 18-group removal

method , an improved removal method and a Monte Carlo code for

gamma, the last two developed at AB Atomenergi, Besides, some

calculations were performed by direct solution of the Boltzmann

equation by means of the programme NIOBE .

Finally, in the third part of the report, a comparison is made

between the theoretical and the experimental results and conclusions

are drawn about the accuracy attainable in the shield design work.

1.4. Acknowledgements

A study of this extent would not have materialized without the

co-operation of a great number of colleagues at the company's re-

search centres at Studsvik and in Stockholm. The authors thus wish

to express their gratitude to all concerned at the Swedish Atomic

Energy Company, and especially to Dr. J. Braun, who initiated the

work and followed it with great interest, and to our co-workers in

- 4 -

the Experimental and Theoretical Shielding Groups, who kindly assist-

ed us throughout the whole investigation.

Further-we want to thank Dr. M. Leimdörfer at the Swedish

Research Institute of National Defence for valuable discussion and for

kindly assisting us with the NIOBE calculations.

The concrete analyses and tests were performed by Mr. G. Eke-

värn at the Swedish State Power Board and Dr. I. Bergström at the •

Swedish Cement and Concrete Research Institute, whose assistance we

gratefully acknowledge.

Outside Sweden, we. are especially grateful to the late Dr. K.T.

Spinney and to Dr. J. Butler and Dr. A. F. Avery at. the Harwell Shield-

ing Group for acquainting us with the methods developed and the results

obtained in Great Britain.

EXPERIMENTS

2_. Experimental facilities

The experimental shielding facilities are located around the pool

of the R2-0 reactor situated at Studsvik. •

The reactor (fig. 1) is a 100 kW swimming-pool reactor primari-

ly intended for shielding experiments and critical studies. It has a ma-

ximum of 1 0 x 1 0 positions for MTR type fuel elements (90 % enriched)

in a closepacked array. The loading used for the shielding experiments

and giving a reactor face of 60 cm x 60 cm is shown in fig. 2. The ca-

libration, including the determination of the power distribution of the

reactor, has. earlier been described . The reactor is movable on a

trolley along the two horizontal axes and can be turned toward any side

of the pool wall by an overhead crane, this operation taking in practice

about 15 minutes. The shortest distance between the reactor face and

the pool wall is 10 cm.

. The shielding facilities available (fig. 3) are:

a) the large .experimental window (N I), about 200 cm square

- 5 -

b) the massive pool wall (marked M) of magnetic concrete

c) small windows (Ö 2, S 3-5), 50 cm square.

The lines and circles in fig. 3 indicate a system of channels (diam.

6 cm) in which detectors can be placed. In the N 1 window and pool

wall these channels form a 40 cm x 40 cm matrix.

In the N 1 window the lining (here 2 cm Al) is supported by

two pairs of crossing aluminium beams, the height of which is 25 cm.

Because of these beams, and an extra plexiglas shield, the shortest

distance between the wall and the experimental set-up is approx. 30

cm. At the slightest pressure the plexiglas shield disconnects the

driving machinery of the plug. This is to prevent anything from being

sqeezed between the set-ups and the pool wall. The pool lining at

the small windows has no extra support, so that these windows can

be filled up to this lining. Plugs in the small holes are moved manu-

ally.

When comparing the R2-0's large window to the shielding fa-

cilities at the English LIDO reactor, the most important difference

is in the stiffening structure of the window. At LIDO, the window is

a 10 cm thick sandwich construction filled with water, so that there

are no large air gaps between the reactor and the experimental set-

up. At the R2-0 there is the hardly avoidable gap of -30 cm air.JThis

air gap has presented some difficulties in the evaluation of the ex-

perimental results, mainly because none of the one-dimensional

shielding codes can accurately cover the lateral leakage in this kind

of slot.

3_. Methods of measurement, instrumentation~ ~ "*""«?— — ™~ — " * ™— * — ™" ' — — ' " " " " • •—"•* ~™ "™~ ~ " * ""•"** - " " * - ~ - " " " ****** " " - " ~ ~ ~ ~™

3. I . General remarks

One main principle was followed in the measurements, and

turned out to be a suitable one. The movable part of the instrumen-

tation was made as simple as possible and, whenever practicable,

all necessary, calibrated electronics were permanently installed in

undisturbed laboratories. There the equipment was much better

6 -

sheltered from mechanical and electrical disturbances than in the

reactor hall itself with its two reactors.

:. The principle led to the. choice of the foil technique for the

neutron measurements, and this method was predominantly used.

Routines were worked out both for cadmium ratio measurements and

measurements with paired foils.

3.2. Neutron measurements

The neutron flux spectrum has been approximated with a Max-

wellian and a l/E spectrum distribution for the thermal and epithermal

parts. The definitions used are

©,, = nv the conventional thermal flux where n is the den-•' th o

sity of neutrons in the Maxwellian distribution

0 . = epithermal flux per unit interval In E'ep i r ^

Thus the thermal and epithermal parts of the spectrum can be

written

° " E / E m + | ] <* 0)m

T is the neutron teraperature and T the temperature correspond-

ing to the velocity v = 2200 m/s. E = kT, where k is the Boltz

mann constant. A is a joining function, which can often be approxi

mated by a. step-function with an upper and a lower (ET = y kT)

limit of tKe l/E spectrum.

14)The authors, like Stoughton and Halperin , have preferred

to use these conventions instead of those recommended by Westcott

et al. . Westcott's "total flux" 0 W includes a Maxwellian and an

epithermal component, and the connection between his notation and

ours is

- 7 -

E is the energy corresponding to the velocity 2200 m/s . The ratio

between 0 . and 0 , , here defined as d , is related to Westcott's' ep i ' t h

r-value through the expression

In the fast neutron energy region the spectra have usually been

calculated and tested against the disintegration rates obtained from

threshold reactions: no special shape of the fast neutron spectrum

has been assumed.

This and the following section describe in some detail two de-

tection methods for thermal and epithermal neutrons. The reader not

particularly interested in this subject may proceed to section 3.5.

The thermal and epithermal neutron fluxes can be obtained by

simultaneous irradiation of two foils, one with an approximate l/v

cross-section and one with a strong resonance peak in the epithermal

region. The induced saturated activities can be written

. I ( i ) i =1.2 (2)epi corr K '

E is the 2200 m/s cross-section, g is the Westcott g-factor which

corrects for non-l/v cross-section in the thermal region.

Corrections for detector efficiency, flux depression and self-

shielding of thermal neutrons due to the finite thicknesses of the

foils are assumed to have been applied in the A-value in eqs. (2).

The .larger self-shielding .of neutrons at the resonance energies

is accounted for in eq. (2) by using a "corrected resonance integral"

I , calculated according tocorr 6

I = G \l + 21 V E / E T + 2E (1-G) KE / E T -VE / E - , J , | (3)corr I res o o' L J ov . L ' P' L. . . o' Cd'J v '

Here £ is the excess resonance integral,res °G is a resonance self-shielding factor determined by means of cad-

mium measurements on thin and thick foils, a method described by

Greenfield et al. . E~ , , is the F-corrected (see below) effective

energy corresponding to the Cd thickness used in determining G .

17)A programme FLUDUF ' for the Mercury computer has been

prepared and used for solving eqs. (2.3). The programme also cal-

culates relative errors due to counting statistics and absolute errors

due to.uncertainties in resonance cross-sections, shielding factors

etc.

_ ^ ^ ^ 2 j ^ ^ j j _ _ _c adinium_-cove re_d .foils

The thermal and epithermal fluxes have also been measured by

means of the commonly used Cd ratio method. Saturation activities,

A ' and A ' , from foils activated bare and cadmium-cove red res-

pectively have been used to calculate 0 •, and 0 . given by

V - F X

a n d

A(Cd) (b)0 . = A

t ' ^A- (5)6P1 1 ^ ^ ) / ^

I« T is the corrected resonance integral for Cd ratio measureCd-corr te

ments and is defined by

I_ , . = § ' ( E + 2 S VE / E « ,,) (6)C d - c o r r F K f*<»« « ^' r:^»' \ '

G is the resonance shielding factor described above. X is the

transmission factor of thermal neutrons for the cadmium

covers and is usually small enough to be put equal to zero in eqs.

(4.5).

- 9 -

The thickness of the cadmium cover determines the effective

cadmium cut-off E« , . But if, as above, the activities from cadmium-O et

covered foils are F-corrected according to a method described by(1 8)Martin , a new activity value independent of the Cd-thickness is

obtained, at least for thick enough covers. The new activity actually

corresponds to a new corrected effective energy cut-off. This energy,

E« , , , is also independent of the cadmium thickness and is fairly

constant for different foils, provided that the only resonances are well

above 1 eV, A constant, designated H , is the ratio between the total

epithermal activation and the epithermal activation above E~, , t .

Assuming a 1/E distribution down to the energy ET and a resonance

energy well above E_, , f , one can write

HJoto

FECd

'MlE

• d E

-

- dE

Eres

Eres

h 2E /E /E TO o 1 f

Y 2X /E /E „o o Cd

The necessity for this correction in eqs. (4.5) is due to the fact that

a Maxwellian thermal flux has been used instead of the Westcott flux

or a subcadmium flux.

A programme FLUCAD for the Mercury computer using

the eqs. (4-7) has been prepared and used for calculating 0 , and

0 . . Relative errors due to counting statistics and absolute errors^epi &

due to errors in cross-sections and other parameters are also cal-

culated by this programme.

3. 2. 4. Fast neutron measurements

Threshold detectors have been used for testing the calculated

fast neutron spectra. Saturated activities have been measured and

compared with the corresponding activities A calculated according

to

A = <p(E)E(E)dE

o

- 10 -

The cross-section for phosphorus has been taken from Hughes and

Schwartz arid from Cuzzocrea et al. . If a fission spectrum is

assumed, the "fission spectrum neutron flux" 0 f can be calculated

from the P activities in tables 15-28 by means of

0 f = A ' i (9)

where — = 1570 g/cm .Z

Some measurements have also been made by means of pro-

portional counters and neutron films. The use of neutron films is

discussed in Appendix IV.

Foils of Au, Cu, Mn and In have been used for determining

0 , and 0 . . Pertinent constants, most of them experimentally de-

termined, are given in table 1 . The detector efficiency for the Au

foils was measured by a beta-gamrna coincidence method. The other

foils were calibrated by irradiating them in a constant neutron flux

simultaneously with the measurement of the thermal flux by means of

Au foils.

Beta scintillation set-ups equipped 'with anthracene crystals

were used as detectors. One set-up was equipped with a 30-position

automatic sample changer which punches out all necessary informa-

tion directly on tape. The essential long time stability was checked• . . 2 0 4 j - 1 4 ,

with a Tl and a C sample.

Two Mercury computer programmes, FOMAK ' and SOD AC ,

for the manual and the automatic set-up, respectively, were prepared

and used for the reduction of raw data to saturated activities correc-

ted for dead time, decay, foil weight, reactor power etc.

31As threshold detectors we mainly used the P(n, p)Si reaction.24The efficiency was determined by injecting absolutely calibrated Na

solution into unirradiated foils and correcting for the small difference24 31

in beta energy between Na and Si . The result from this thres-

hold reaction has also been compared with results from four other

- 1 1 -

27)ones with independent calibration . The agreement has been within

1 4 per cent.

A Mercury programme STREKO ' has been developed and

used for analysing complex decays (three exponential components

and background) directly from raw data.

å.'Jz •J'JJ^JLO-E f_ 15- iy5§ ?_ measured

The errors in the thermal arid epithermal fluxes determined by

the foil measurements depend very much on the shape of the neutron

spectrum. In most cases the systematic errors in the thermal and

epithermal fluxes*have been estimated at 3-5 per cent and 5-10 per

cent respectively. It,should be observed that the systematic error

in the thermal flux also goes into the calibration of the reactor and

thus, for the most part, is eliminated in the final result.

The errors in the phosphorous activities have been estimated

at about 15 per cent.

Statistical errors due to counting statistics have usually been

negligible compared with the systematic errors.

In an investigation of this extent it is difficult to avoid isolated

sporadic errors, for instance because of some mix-up with foils. To

eliminate these errors, the points presented here have been measured

at least twice, except some P-values. In addition to this,- horizontal

and vertical flux traverses were made to check the smoothness of

the flux distribution.

3. 3 t Gamma measurements

For the gamma measurements, instruments indicating ioniza-

tion according to the definition have been used, viz.:

- ion chambers: Landsverk Roentgen Meter, L-64 (0.01 -100 R)

Philips Universal Dosemeter, 37470/03 +

+ heads 37486 and 37488 (1 -300 R/h).

- gamma pens: Landis & Gyr (0.2 R)

Bendix (0.2, 600 R)

- 12 -

Secondary methods have also been applied, viz . :

- gamma f i lms: Du Pont , type 558 (= 508 + 1290)

- Nal scint i l la tor : 1 l / 2 " x d iam. 1"

- G.M. ins t ruments .

The ion chambers a r e , of course., the most accurate i n s t r u -

ments , but the use of them is l imited by availabil i ty. Two types of

heads for the Phil ips Universal Dosemeter were used; one had a wall

of 0. 5 cm, the other a wall of 0.2 cm. The aluminium walls of the

Landsverk chambers were > 0. 1 cm, and they could be surrounded by

bakelite s l eeves , 0.5 cm thick. Results from Landsverk condensator

chambers and gamma pens were compared with those obtained with

the Phil ips ins t rument , and an agreement within about 10 per cent '

was found.

Most of the gamma pens have been cal ibra ted individually in

o rde r to obtain a bet ter reproducibil i ty than - 10 per cent . The low

dose range (0-200 mR) of the pens available at the beginning of the

exper iments l imited their u s e . The walls of the Bendix pens consis t of

a 0. 1 cm plast ic enclosure surrounded by 0. 1 cm aluminium, while

the plastic wall of the Landis & Gyr pen is about 0, 1 cm thick.

F i lms have been used for the majori ty of the m e a s u r e m e n t s .

They can be conveniently exposed simultaneously with the foils , and

a great number of points can be m e a s u r e d per exper iment . Some

cha rac t e r i s t i c s of the Du Pont 508 film have been investigated in

order to facilitate the in terpre ta t ion of the r e s u l t s .

3_._3 «_2. S_ou_rc_e_s Jp.^jY.P.L

In-shielding measu remen t s of this kind there a re three main

difficulties in gamma detection to be taken care of, v iz . a) the neutron

sensitivity of the gamma detector , b) the influence of the hard gamma

spect rum and c) the predominant fission and activation product gamma

at low reac to r power.

Gamma detectors are sensit ive to ail ionization including that

originating from the neutron flux at the position of the detector . As a

rule of thumb one may say that in our measu remen t s the rat io between

r- 1 3 -

4 _2 -1 -1

the fast neutron and gamma fluxes lias been 10 n cm s R h. The

same order of magnitude applies to the thermal and intermediate

neutron fluxe s.

Gamma spectrum in concrete is quite hard (E •** 7 MeV)

Because the methods of measurement are energy-sensitive and the

highest calibration energy easily available is from Co (E «* 1.25 MeV),

their calibration is difficult.

On the whole the neutron flux is directly proportional to the

reactor power,, but the gamma dose comes partly from long-lived

fission and activation products in the core. This gamma source has

been comparable to the fission gamma level of a core running at a

power between ones watt and one hundred watt, This constitutes a vary-

ing background level to be determined during each experiment.

In the following sections the effects of the above points a) and

b) upon the different detectors are discussed.

Neutron sensitivity is the most important source of e r ror . A

correction for neutrons has not generally been indicated in published

shielding measurements. The ionization measured has been directly

given as the gamma exposure dose rate at the point of measurement.

On the other hand, in some shielding calculations the energy deposi-

tion by fast neutrons cannot be neglected. It may amount to a few per

cent of the total energy deposition. As regards the biological dose

rates, it is well known that, in the inner parts of the shield, the fast

neutron flux gives dose rates that are of the same order of magnitude

(in rem) as the gamma exposure rates. In view of this, the fast

neutron sensitivity of the Landsverk chambers and gamma pens has29 30)

been studied with a Pu-Be source ' . The result arrived at is

approx. 0. 10 roentgen unit indicated per rem dose of neutrons. Since

in our experiments the calculated ratio gamma exposure (R)/ fast

neutrons (rem) was ®* 1, about 10 per cent of the ionization measured

is estimated to originate from the neutrons. This ionization originates

mainly from recoil atoms released from the chamber walls by fast

neutrons,

- 14 -

As regards the inelastic scattering and absorption of neutrons

and the disturbance due to these reactions, one may point out that the

neutrons are less scattered in the chamber than in the heavier materi-

als surrounding it. The thermal absorption, cross-sections are also

much smaller in the chamber walls of Al and C than in the surround-

ing materials.

The energy dependence of the sensitivity is the second factor to

be considered. Ion chambers and pens are constructed for a certain

energy range, normally from about 0. 1 to 3 MeV.

As regards the lower end of the energy range, the instruments

used are guaranteed to be energy-independent down to 100-200 keV.

Since the number of photons below these energies decreases rapidly31)

with energy , this error in energy sensitivity can be neglected.

The energy sensitivity at the upper end of the energy scale (> 3 MeV)29)is a more serious question. It has been shown that when measuring

with zero-wall chamber, the energy absorption would be maximally

over-estimated in magnetic, concrete by a factor of 1.4. It can be shown32)

by further calculation that the upper limit of this over-estimation is

^.5 per cent for a wall thickness of 4-5 mm and tt 15 per cent for 2 mm.

These results are arrived at by considering the outside disturbance,

which is seen from the gas volume in the chamber. The upper limit is

obtained by taking an undegraded energy for the secondary electrons.

In accordance with the calculations, no effects originating from

electron non-equilibrium were experimentally found. Extra sleeves

(0.6 g cm ) did not cause an observable change (> 5 per cent) compared-2

with the measured values obtained from bare chambers (0. 3 g cm ).

Thus it is deduced from calculations and experiments that the error due

to electron non-equilibrium is less than 10 per cent even for chambers

with 1 -2 mm walls.

films

The interference due to neutrons has proved to be negligible. While

using films especially intended for fast neutron monitoring, it was found

that the tracks disappear in the general blackening caused by the gamma

1A \

flux (App. IV). On the basis of theoretical calculations ' the effect

of the thermal and epithermal neutrons was estimated to be of the

order of one per cent of the gamma dose. These results have been35)

verified in experimental work . ,In addition, film and ion chamberresults were compared. Agreement within f20 per cent was found.

The energy dependence is a more serious source of error.

Because of the lack of space we have exposed films without any filters

in most cases. Doses are then read as open-window values from a

Co calibration curve measured in air. Various authors ' have

discussed the energy sensitivity at the low end of the energy scale

(< 0.4 MeV). The sensitivity of a bare film increases with decreas-

ing energy below 200 keV. In the heavy elements the relative number

of photons below 200 keV is less than in equilibrium in the air. There-

fore we should read too low doses.

The effect of the high average photon energy is more difficult

to estimate. The data of the energy sensitivity above 3 MeV is.meagre.34)

Becker ' gives a qualitative indication of an increasing sensitivity

between 3 to 10 MeV (in electron equilibrium). A quantitative theore-

tical study along the same lines as that performed for the ion chambers

results in an over-estimation of the absorbed dose by a factor ofÄ T. 05 when compared with the dose with electron equilibrium. (Note

the heavy materials Ag, Br in the film emulsion.)

Thus the errors in the low and high ends of the energy scale

work in opposite directions and probably even each other up.

In the final results (tables 17-29) the ratios of exposure rates

from films and ion chambers fall both below and above 1 . The average

is 0.8 ± 0 . 1 .

A third source of error in the film measurements is the

exposure rate dependence In our measurements it can be dis-

regarded because of the relatively low rates.

The reproducibility in film measurements has been within

1 5-20 per cent in the dose ranges 0. 1 -4 R and 50-500 R.

- 16 -

^ ^ ^ ^ ^ _ ^ ^ _ ^ ^ ^ ^ ^ _ G._M_. and scintil lation detectors

The G.M. ins t ruments were ordinary health physics i n s t r u -

ments ca l ibra ted against Ra and Co sou rce s . These ins t ruments were

used on the outer surfaces of the configurations. A check was made

against JLandsverk 10 m r chamber and the agreement was within JO-20

per cent. Neutron and energy sensi t ivi t ies of the G.M. ins t ruments

have ,not been especial ly studied.

F o r relat ive measu remen t s in very weak fields (< 5 m r / h ) a

scinti l lat ion detector was constructed, consist ing of a 1 l / 2 " dia x 1"

Nal c rys t a l coupled to a DuMont 6199 photomultipl ier . Reproducibi-

lity was - 15 per cent, p r bet ter than the absolute accuracy for this

ins t rument , - 40 per cent.. Thermal neutron sensit ivi ty was studied

and could be el iminated by avoiding unnecessa ry activation of the de -

tec tor head.

4k Composition and proper t i es of the concretes studied

As accura te m a t e r i a l s data as possible a re given (tables 2-3),

since some of the e a r l i e r m e a s u r e m e n t s presented are of little value

because of incomplete data. Analysis of the bal last ma te r i a l is included

in its original form for ordinary concre te . In order to re ta in as much

water as poss ib le , our concre tes have a high quantity of cement

(300-330 kg m ' 3 ) .

— 3

T h e d e n s i t y u s e d f o r t h e m a g n e t i t e c o n c r e t e ( 3 . 7 4 g c m ) i s

lower than the experimental values given in table 2. It is slightly

higher than the values (3. 27 to 3. 62 g cm } given for this type of37)concrete in a compilation by Walker and Grotenhuis . We have arrived

_2at the value 3. 74 g cm starting from the water-saturated density3. 83 . The density 3. 9 g cm from the crushed drill core is most

probably obtained from large single pieces of ore surrounded by a

layer of finer material, and thus this figure is of little value. The

most probable water content of the magnetite concrete is 133 kg m

The density of the ordinary concrete is 2.43 g cm , and the_3

water content! 65 kg m

Table 4 gives the chemical analysis arrived at on the basis of

the material analysis. The small percentages (< 0.01) given for some

elements in the magnetite concrete are the result of an activation•i • 3 9 )analysis

The possible errors in the densities and analyses are discussed

in chap. 7.

5_. Configurations studied

We have made measurements, in water in 5 configurations of the

magnetite and in 2 of the ordinary concrete. The layers of these are

presented in table ,5 and fig. 4 for comparison. The configurations

are also shown in the lower part of the figures presenting the results.

Configurations 3 to 6, containing layers 2 cm Al - 26 cm air -

1 cm plexiglas - 2. . . 8 cm air, were all studied in the large window

Nl . Streaming effects in the narrow slots (w 1 cm) around the concre-

te blocks fitted to the window have been studied. Rather extensive ver-

tical and horizontal flux traverse measurements with foils and Co

wires have shown them to be negligible for the centreline measure-

ments .

5.1. Magnetite concrete

Configuration 2 is the pool wall of magnetite concrete, designated

M in fig. 3. The shortest possible wall-reactor distance is 1 7 cm.

Instead of this, 20 cm was used in the experiments.

Measurements with magnetite concrete have also been made

with two large concrete blocks (thickness 60 and 108 cm). The only

difference between configurations 3 and 4 is that the Pb-B plastic

plate between the two plugs is removed in 4. Configuration 6 is ob-

tained from 5 by adding a second Pb-B plate on the front of the inner-

most concrete plug. Finally, the only difference between 3 and 5 is

that the water layer has been decreased from 1 5 to 10 cm. This was

done in order to demonstrate the influence of small variations in the

geometry. However, no major effect was found, and so the gap was

increased by 40 cm between the ordinary concrete configurations 7

and 8.

- 18 -

5.2. Ordinary concrete

A single plug, 168 cm deep, was used. The difference between

configurations 7 and. 8 lies in the increase of the thickness of the

v/ater layer, from 10 to 50 cm.

5.3. Other configurations studied

Measurements have also been made in one of the 50 cm x 50 cm

'windows. Because of streaming via the narrow (< 1 cm) slot around

the plug, results were usable to a depth of approx. 60 - 70 cm only.

These results will not be presented here.

Measurements have also been performed in a 90 cm deep plug

of barytes concrete. Agreement with calculations was satisfactory,

but because shallow penetration experiments do not prove anything

about the accuracy of the methods at deep penetration, no results are

presented in this report. Besides, barytes is not of interest for

shielding purposes in Sweden.

6>_. Experimental procedure

In this chapter a few remarks concerning the experimental pro-

cedure are given which may be of interest to the unexperienced ex-

perimenter.

6.1. Ranges of measurements and instrumentation

Shielding experiments are often characterized by the extremely

large range of the quantity to be measured. In our experiments the to-Q

tal range is larger than 10 . The reactor power can be changed by a"" 4

factor of 10 and by varying the exposure time a factor of, say, 504

may be obtained. The rest, about 10 , must be covered by means of

the methods of measurement, whose ranges are very individual, e.g.4 1

10 for certain types of foils and about 10 for a single component of

a gamma film or an ion chamber. Thus no single method usually

covers the whole thickness of the shield. The useful penetration for

some routine neutron and gamma detecting methods in magnetite con-

crete is indicated in figs. 5 and 6, and these estimates proved to

agree pretty well with the observations. The Landsverk instrument

with its six ion chambers (0. 01 to 1000 R full scale) is the only one

that spans the whole thickness of the set-up.

6.2. Experimental runs

Careful planning has been needed in order to obtain the maxi-

mum amount of information from an experimental run, especially

when more than one or two types of detectors have been used. The

reactor power, the irradiation time, the number and the positioning

of the detectors have been chosen with due regard to the difference

in half-lives of the several activation detectors, the maximum capa-

city of the sample changer, and the usable range of the gamma detec-

tors etc.

For the exposure, the detectors are first taped on thin (0. 2 mn

pure Al-strips. With the prefabricated strips and holders, the loading

and unloading is done within one hour.

The unloading of the set-up after an experiment can normally

be done rather soon after the exposure. The Al window itself has

proved to be so pure that, even after a high power run, the activity

level from the window is very low, a few tens of milliroentgens per

hour, as soon as the 2.3 rnin. Al activity has decayed. In some cases

the activation of the concretes restricts access. During the first day,

after a short decay time, the Mn and Na activities are the dominating

ones in magnetite and ordinary concretes, respectively.

7_. Sources of error and their effects on the results

7.1. General remarks

The errors originating from our particular set-ups and confi -

gurations are discussed below. The errors in the detection methods

were discussed in chap. 3. The other sources of error in our mea-

surements may be arranged in three groups according to their origin:

a) Reactor power and irradiation time

b) Spatial dimensions and coordinates

c) Variations in the materials studied.

- 20 -

7.2. Reactor power and irradiation time

The possible error in the absolute reactor power has been cal-*» ' 13)

culated to "•* 5 per cent . This enters as a systematic, error.

-To control the reproducibility of the power levels a better check

"than the reactor instrumentation was needed. Therefore a monitor

copper foil was activated in each experiment in a special holder on the

top of the core. Thus the position of the foil was accurately reproduced.

For the full power runs the foil could be activated only for 10 minutes,

because longer irradiations'prevented counting within six days, and

after that disturbance from the long-lived impurity activities starts.

The error in the timing for all runs was estimated at < 5 sec, giving

a negligible error (< 1 per cent). The reactor effects were, on the40)

average, below the nominal ones . About 90 per cent of the values

fell between. - 10 and + 2 per cent of the nominal power.

The error in the relative power level thus corrected is < 2 per

cent assuming constant flux distribution in the reactor. The power, as

determined by the monitor foil, has been checked three times at various

levels by means of more extensive foil measurements

The agreement was within 3 %. The standard deviation in the

saturation activity determined by our foil handling methods was approx.

1 per cent. The 2 per cent error enters into the measured values as a

random error.

7_._2 jj^£,radiation_ time

Irradiation time or the effective time of a run was determined

from the point of reaching 1 /Z of the prescribed power to the moment

of the shut-down. The reactor was run up to the power level required

with as constant a period (. S 50 sec) as possible. The minimum length

of a run was about 20 minutes. It is easy to show that the error due

to starting the activation time from the l/2-power level is thus negli-

gible .

Ion chambers and pens were also exposed long enough or on

repeated occasions to give errors less than a few per cent in timing.

7.3. Errors in the spatial coordinates

The reproducibility and absolute accuracy of the reactor posi-

tion were checked both when the pool was empty and the fuel trans-41)

ferred into a storage pool , and with a contact instrument under

water. The position of the reactor can be adjusted according to a

millimetre scale on the trolleys. The reproducibility of the position

at the depth of the core is a few millimetres. Since the error arising

here is theoretically 1 (Z - 1 per cent per millimetre, it can be neglec-

ted. The unevenness of the pool wall is oS the same order of magnitude

as the positioning error.

The coordinates of the measuring channels in the direction from

the reactor (z-axis) have been measured as accurately as possible. Be

cause of the unevenness of the surfaces of the plugs and the possible

bowing and slanting of the channels, the maximum error in the penetra

tion depths has been estimated at 1 cm. Since the attenuation of the

fluxes to be measured is of the order of e " (x in cm), we get a

max. error of about 10 per cent. Assuming that this corresponds to

two standard deviations, we obtain 5 per cent as a standard deviation.

This error is of random type when the plug is considered as a whole.

For a single channel it is a systematic error.

In the x- and y-coordinates the standard variation is "- K 5 cm

according to our methods of placing the foils. With the known flux

distribution this gives an error in the measured fluxes near zero on

the centre line, - 4 per cent at a distance of 40 cm, and - 6 per cent

at a distance of 80 cm,

The total standard deviation from the errors in the positioning

of the detectors will thus be - 5 per cent on the centre line, - 6 - 7

per cent 40 cm off, and - 8 per cent 80 cm off the centre line.

- 22 -

In the magnetite concrete the measurements were made mostly

in open channels.

The channel matrix in the ordinary concrete, as in the magne-

tite concrete, was made of aluminium tubes to,avoid disturbances in

the thermal flux. However, for the flat detectors in ordinary concrete

a special set of plugs was prepared. An aluminium tube that fitted in

the channels was furnished with a rectangular slot. The cross-section

of"the slot was appröx. O. 8 cm x 3. 8 cm. The space between the slot

and the tubes was filled with a sand-cement mixture.

Thus the coordinates of the detectors in the ordinary concrete

are more easily defined than in the magnetite concrete and the possible

effects of the channels on the average density are eliminated. In both

cases the centre-line of the channel has been used as the effective z-

coordinate. How one arrives at this conclusion even in the case of an

open channel is discussed in App. I.

7.4. Variations in the materials studied

Of the variations in the materials studied only the uncertainties

concerning density and water content are discussed here., because they

are clearly the dominating ones. Yet they have been discussed very

little in reports of this type. Density errors can be divided into local

variations and variations in the average values. The latter may depend

both on voids and on density errors in the concrete mass. The water

content is of minor importance compared to the density.

^.^^J^Ijocal va_riati_qns_

The density of the concrete may have small local variations. In

the worst case this might lead to the situation where the maximum flux

values were not at the centre of the plug cross-sections (on the z-axis).

Extensive flux traverses perpendicular to the z-axis were made

with: foils and with Co wires. These showed asymmetry up to 20 - 30

per cent at distances of 80 cm from the z-axis. Of course it is im-

possible in these cases to distinguish the error originating from un-

certainty concerning the detector positions (7. 3. 2) from the one ori -

- 23 -

ginating from the variations in density. Anyhow, these transversal

measurements have shown that the fluxes measured on the centre line

are the maximum fluxes at the corresponding distance from the reactor.

_ j § ^ ^ _ _ y _ e_:rj*o_r_due__to_ the_ channel matrix

The 40 cm x 40 cm matrix of 6 cm id. channels decreases the

average density of the concretes. For the plugs in the big window this

decrease is & 1.6 per cent. The two extreme effects are:

a) it does not increase penetration at all

b) it increases penetration as much as does a homogenously

distributed decrease of 1 . 6 per cent.

Case b) gives rise to a 30 per cent increase in the fluxes on the out-

side of the experimental plugs in the large window. It should be ob-

served, however, that there are only three lines of channels in front

of the line T5 (fig. 3), which is the last line where neutron measure-

ments, are possible. Thus the homogenization of the channels into the

whole plug probably overestimates the errors involved.

The measurements in the magnetite concrete were mostly made

in open channels. In order to check the effect discussed above, during

some runs the channels were plugged, with steel tubes filled with the

same type of concrete. The wall thickness of the tubes was selected

so that their total weight gave the density of the surrounding concrete

to the channel volume.

The measurements with all the channels plugged had to be made

in the outer regions of the shield where the relative accuracy was

lowest. The results indicated that after 170 cm magnetite concrete

the difference in the doses due to unplugged and plugged channels

amounted to:

< 20 per cent for neutrons

< 10 per cent for gammas

In the subsequent discussion this source of error is disregarded.

- 24 -

The estimate of the error in the density of the magnetite con--3

crete ( p = 3. 74 g cm ) has been based upon the results from the test

cubes; they gave a standard deviation of - 0.04 g cm" . Because of

other uncertainties, a final maximum deviation of - 0.09 g cm" was

obtained. This is a deviation within which the true value occurs with

a high confidence level {>_ 90 per cent), and thus it is comparable to

twice the standard deviation. The water content has been estimated at

130 - 140 kg m"3 .

Later a diamond drilled core, with a diameter of 10. 1 cm, was

taken from the outer (108 cm) concrete plug, when it was about one

year old. Parts of this core were dried to 900 C, giving an average+ + -3

weight loss of 3.23 - 0.07 per cent, equal to 121 - 3 kg m . Assum-

ing the amount of water still bound to the cement to be < 2.5 per cent

of its weight, a value of 1 29 ^ 3 kg m~ was obtained. In these mea-

surements a significant drying effect of the concrete surface was ob-

served. The total weight loss of the concrete at 105 °C increased from

1 . 9 per cent at 15 cm depth to 2. 3 per cent at 1 1 0 cm depth. Consider-

ing all these effects the most probable water content was taken as

1 33 - 7 kg m with a high confidence level (< 90 per cent).

At a penetration depth of 1 70 cm the errors in density, - 0. 09

g cm , and water content, - 7 kg m , cause errors in the removal

source of about - 50 and * 10 per cent, respectively (fig. 7). After

210 cm penetration the corresponding figures are 65 and 14 per cent.

These values hold good approximately for the neutron fluxes and for

the gamma dose rates, too. However, for neutron fluxes additional

effects may occur; besides the change, for instance, in the attenua-

tion of the thermal flux, a change in water content also affects the

thermal-fast flux ratio. The standard deviations due to variations in

density and water content are estimated to be within the order of 30 and

40 per cent after 170 and 210 cm penetrations, respectively.

Z\4:J jJ?J£P_E?_i&^^B tyJ^Qdjw&teY^ content_of_o_rdinary concrete

The measurements with the ordinary concrete were partly per-

formed immediately after it was taken out of the form, and partly a few

months later. Thus it is assumed that no water losses had taken place

, 25 -

and all of the water, 165 kg m , that went into the mixture was left.

The densities of the test cubes showed a very small deviation, giving

P = 2. 43 ^ 0. 02 g cm " . The error in water content, too, was certainly

smaller than in the case of the magnetite concrete. Proportioning to

the densities yields a standard deviation due to the errors in density

and water content of < 20 per cent after 1 70 cm penetration; a value

of 15 per cent has been used.

7. 5. Summary of the errors

A summary of the approximate errors is given below, includ-

ing the errors discussed in chap. 3.

Z-JÉ •— To the group of systematic errors belong:

a) errors in absolute reactor power (5 per cent)

b) errors from the uncertainties concerning density and water

content of the concretes (30 and 15 per cent for magnetite

and ordinary concretes, respectively, after 1.7m penetra-

tion)

c) local density variations and errors in foil positions .{5 per

cent)

d) certain errors in the detection methods (2, 10, 15 and 10

per cent when measuring thermal neutron, epithermal

neutron, fast neutron and gamma fluxes, respectively).

Point c) is a systematic error at a certain point only, and should be

disregarded when considering the shield as a whole.

Thus, assuming that all components act in the same direction,

the run of all systematic errors after 170 cm penetration is estimated

to be 25 - 55 per cent, depending on the quantity and material in

question. Usually the systematic errors are considerably less.

The random errors are

a) errors in reactor power and irradiation time (3 per cent)

- 26 -

b) statistical errors in the detection methods of varying magni-

tude .

Repeated measurements of 0 , and 0 . have shown deviations from* XJjL 6 TJX . •

their average values which are explainable with regard to these errors.

Thus there appear to be no other significant random errors. The result

from the phosphorus foil showed a somewhat poorer reproducibility.

Additional deviations of 4 - 8 per cent were found, probably originating

from an uncertainty in the beta absorption factor, recently experimen-

tally determined to < 5 per cent for the 30 foils used.

8_. Summary of the measured values

8.1. Neutron f luxe s

The results of the measurements (columns "EXP") are presented

in the tables 15 - 29 together with the calculated values.

The definitions of the fluxes are given in section 3.2.1. Usually

foils have been activated repeatedly at each position. In calculating the

average values x , the N results x. are then given weights

x.

where Ax. is the standard deviation based on the counting statistics.

The deviations given are the standard deviations of the mean

value:

^ ( 1 0 )( N - l ) Z p .

Normally the number of measurements have been 3 - 1 0 for the

nd 0 . determinations, while usually on

measurements have been made in each position.

0 , and 0 . determinations, while usually only 1 - 3 phosphorous

- 27 -

8.2. Gamma exposure rates

The gamma resxalts are also to be found in the tables mentioned

above. The values given for ion chambers have been corrected for

neutron sensitivity by multiplying the values observed by a factor of

0. 90 (section 3. 3.4).

Deviations for the gamma dose rate are estimated on the same

principles as for the neutron results. In some cases {e.g. a single

measurement with a gamma film) the deviation is more a matter of

personal judgment and experience. Even then we have tried to reach a

deviation corresponding to the standard one.

CALCULATIONS

9. Introduction to the calculations

9.1. General remarks

In the following the calculations and the methods will be presented

in a short form. Only the special properties of the various methods are

mentioned. On the other hand the "trivial" data and details are presen-

ted to an extent which should enable the reader to reconstruct the cal-

culations performed. This is because the results are in many cases

very sensitive to small variations in the input parameters. As we wish

to present a detailed comparison between the results, we consider it

necessary also to give a detailed picture of how the programme was

applied in every specific problem. In our opinion an explanation that

"calculations were performed using programme XX" would make a re-

port of this type completely valueless.

In making the calculations we have tried to avoid any tinintentional

fitting of the calculated to the measured results. In view of the many-

parameters used, and especially because of the fairly wide potential

range for some of them, a mental fit to the measured values is an ever-

present danger. We have used the experimental parameters in some

immaterial cases, e.g. to effect the geometrical transformation from

the theoretical calculation geometries to those actually used. Other-

wise the theoretical results are, with one exception, produced from the

best available data without considering the experimental results. The

- 28 -

exception is the neutron penetrat ion par t of the improved removal

method ' . This method has one pa rame te r which de termines the

penetrat ion 'and which was a r r ived at by using our exper imenta l r e -

sults (see chap. 11.2) .

9 . 2 . Methods

The methods used a r e :

1) The well-known Br i t i sh mult igroup removal method , also

called RASH method

2) The NRN m e t h o d 1 2 '

3) NIOBE (Numerical Integrat ion of Boltzman Equation) ;

The reason for present ing resu l t s obtained by an older (RASH B,)

vers ion of method 1) in these compar isons is that this method has been

used to design the main shields of the R-3 (Ågesta) power r eac to r . We

may point out that there exis t la te r , improved vers ions of this

method, even though they have not been used in this study.

10. Calculations based on the 18-group removal method (RASH)

Calculations according to 1) a re based on an 18-group removal

concept. After the f i rs t coll is ion all of the neutrons end up in the

highes t -energy diffusion group. For the slowing down, an ordinary

mult igroup diffusion theory is used.

10. 1. Removal source

In the removal par t of this sys tem the fission source is divided

into 18 intervals of 1 MeV each. The removal c r o s s section for each

of the groups is defined as

r ( E . ) = 'z . ( E ) + Z ( E ) + 2: ( E ) [ i - i T ] = z ' ( E . ) - M E . ) S . ( E . ) ( 11 )rerrr r irr ' av ' scv J totx r y r e l v r v '

- 29 -

The removal cross sections used for the calculations are based

on the cross sections recommended in except the hydrogen cross

section. We have taken the latter to be equal to 0. 9 times the total42)

cross section, as recommended in ref. . The macroscopic removal

cross sections used for the concretes are presented in table 6. For the

magnetite concrete, four sets of values are given to permit a study of

the effects from small variations in the density and water content (see

fig. 7).

The removal source term is found by a "brute force" treatment,

i.e. the core is divided into 2 L ' 2 M * 2 N cells. The total removal

source density S at the dose point P is then obtained by summing up

the contributions over all of the 8 (L ' M * N) cells and all 18 energy

groups, using a removal flux kernel,

exp~£.[s (E.i)r.lg[s (1,m,n)l =F(E) • S(l,m,n) • * - | - (12)

1 C

where F(E) is a normalizing factor for the fission spectrum18£ F(E) = 1 and Y, (E,i) is the macroscopic removal cross section

E-l r

in the shield layer (i) and r. the part of r in the same layer.

The integration is performed tising the removal programme43)

LIDO . This programme requires a symmetric flux distribution in

all three directions, whereas the R2-0 core is as symmetric. The

"effective symmetric source distribution" has been calculated using44)

the real flux distributions . The effective source distribution can

be defined as a symmetric distribution that gives at the core face a

removal flux equal to that given by the actual assymmetric flux distri-

bution .

The programme calculates the absolute values S(l ,m,n) of the

fission source distribution in the core cells using a given reactor

power and a given relative power distribution. The core parameters

are presented in table 7. To save computer time, (L + M + N) should

be kept as small as possible. It was determined experimentally that

further out the deviation in S by using L = M> 4, N>' 8 is < 4 per

cent, compared to S (L - M = 4, N = 8).

_ 30 -

10.2.. Neutron diffusion and slowing-down

Using the removal source term thus obtained, the multigroup

diffusion system is solved by the RASH programme. Six groups, five

intermediate and the thermal one, have been used with the energy

ranges recommended in (see table 8), Table 9 shows the group pa-

rameters used. They have been obtained by using the MENDIP program-45)

me

In solving the multigroup diffusion equation, one has to consider

the geometry to be used. Plane, cylindrical and spherical geometries

are all possible in the RASH programme. It is clear that, in an R2-0-

like shielding facility, spherical geometry gives the most satisfactory

description, especially further out in the shield.

In determining the effective radius (R ) of the core face, one may

follow three different lines of thought.

A) In the first place one may try to make the calculational and

real geometries eqxial further out in the shield. In this case the air

space in the N 1 window has the effect of "flattening" the flux distribu-

tion compared with the distribution without the air space. We have de-

termined the "effective radius" of the core face from both removal cal-44)

culations and experimental flux distributions ' . This concept of "effec-

tive radius" (R ) is described in fig. 8. The centre is obtained by de -

termining the apparent centre of the isoflux lines. This method gaveR = 80 cm for the core face. Because R = 100 cm is easier to use as

e e »a coordinate, it has been used in some earlier calculations ,

B) Another method that is more often used to determine R is

to approximate the reactor with a sphere of equal volume. In our case

this gives R =31 cm (30 cm has been used),

C) A third possibility is to use plane geometry and an experi-

mental buckling term in the z~ and y-directions. When fitting a cosine

or J curve into the middle parts of the measured flux distributions,° 2 - 3 - 2

one gets B = ( 1 . 3 , . . , 1 . 1) x 10 cm ) in the concrete, depend-to

ing on the z-coordinate.

Some examples of the effect of varying R in the solution of the

diffusion equation with RASH code are given in fig. 9 for the configura-

tions 2 and 3.

It is seen that the variations a re , as expected, largest near the

core. Especially in the N 1 window with its air space, the variations9)have a *>» 2:1 ratio when R (°°—> 31 cm). In R =100 cm was used,

while the best possible flux values were sought further out in the

shield.

The R has been taken as 30 cm in the calculations presented

in this report. This was done for three reasons:

1) the variations of R = (30—>°» cm) have no particular effect on

the fluxes further out in the shield (see fig. 9)

2) R = 1 00, crn gives too disadvantageous a picture of the design

method in this very special geometry

3) with large R and with too high neutron fluxes closest to the

core, the gamma sources are also too high at the same place.

The gamma dose rate on the outer surface of many of the con-

figurations is determined mainly by the capture in the inner-

most regions in the shield (see App. III). Too high a neutron

flux inside the shield would thus give an unnecessarily disad-

vantageous picture of the reliability of the gamma calculations.

While it may be argued that, by using R =30 cm, some ad-

justment towards the measured values is made, we feel that this ad-

justment is justifiable mainly because of point 3).

10. 3. Gamma exposure rate

According to the method described in , the gamma dose rates

are calculated by using an analytical expression for infinite plane

sources with Taylor build-up factors and by summing up the contribu-

tions from each of the source planes. The planes are defined by the

mesh-point intervals of the neutron diffusion code.

In a research reactor, calculations based on an infinite geometry

would, of course, give too high doses. This is avoided by dividing the

plane into a number of concentric discs. The source density decreases

from disc to disc the further from the z-axis. The dose rate is then

obtained by integrating over these discs. The system and the code,

- 32 -

46)

GASLtIT, for the calculations are described in . The relative sour-

ces have been determined from the experimental neutron distribution

curves (see 10, 2. C) and are given in table 1 1 . The error due to dis-

regarding the dose from the regions outside the largest disc is $$ 1 -2

per cent at z ss 1.6m concrete. This figure is valid for three discs.

Two regions would be enough if well selected (error < 10 per cent).

Computer time outside the core is proportional to the number of

annular discs, and therefore one should use as few discs as possible.

The other relevant data and energy groups for the gamma cal-

culations are given in tables 10 A and B. Build-up factors for mag-47)

netite concrete were calculated from the build-up tables given for

aluminium by Goldstein . For ordinary concrete the build-up fac-48)

tors are taken from Rockwell . The reason for using the Al build-

up factors for the magnetite concrete instead of the factors for iron,

for instance, is that factors for Al have been used in the calculations

for the R3 power plant. These two sets of factors actually give re-

sults that, at 1 -2 m penetrations, are within 10-20 per cent from one

another. Build-up factors for iron would increase the results pre-

sented by 25 per cent in the worst case.

Gamma dose rates are calculated for a clean core and include

only prompt and delayed fission gamma from the core, and thermal

and epithermal capture gamma from the shield. Fission product de-

cay and activation gamma sources can be disregarded because of the

short on-power times (< 2-3 h).

11. Calculations based on the improved removal method (NRN method)

11.1. Introduction

As will be seen, the method described in chap. 10 cart predict

neutron fluxes in the thermal and low epithermal range with a rather

good accuracy. Using experimental corrections for the removal cross

sections, this accuracy could be further increased. This method is,

however, not capable of giving sufficiently detailed information on the

neutron spectrum for prediction of, for instance, radiation damage

rates. Spectrum calculations of this type have required the use of

codes that need at least one order of magnitude better machine per-

formance .

- 33 -

A code system based on an improved removal method has

been developed at AB Atomenergi. In this code system, called NRN,

neutron transport and slowing down are handled by an improved'multi-49)

group removal-diffus ion method ; and the gamma penetration is cal-

culated by a Monte Carlo code. In the following, the most important

differences compared with the RASH method in chap. 10 will be pre-

sented.

11.2. Removal source

In this method the removal cross section is defined as

i

(E.) sE, ,(E.) - 2 * w(l*)£ ,(E. j*)d*t (13)v r tot/ 1' J x ' elv 1, ' ^ \ /

-iwhere' w(fci) is a weight function, for which a Heaviside function has

been chosen.

o The parameter Rfco is a boundary

cosine, in the laboratory system of reference, defining a cone into

which the virgin neutrons may be scattered without losing their charac-

ter of being (virtually) unscattered. The rest of the notation is self-ex-

planatory.

The penetration is thus determined by a single parameter for all

materials. This cosine has actually been experimentally determined in50)connection with this work ; , The once collided neutrons with real

energy losses are fed into the right levels in a set of multigroup diffu-

sion equations. The difference between this and the method in chap. 10

is described in fig. 10. .

In this study we have used the version (REBOX) comparable to

the LIDO code, written for a box geometry. This code is distinguished

from LIDO' by the fact that the division of the core can be selected at

will and the power density distribution need not be symmetric.

The core divisions and thermal fluxes are given in table 13. It

was determined that the 6x6x12 divisions used give sources which are

- 34 -

within 10-15 per cent of the sources given by a "»x» x » " number of

divisions. An accuracy plateau was found to begin from t$ 8 x 8 x 20

divisions. To save computer time, 6 x 6 x 12 divisions with a running

time "of w 0.5 h per configuration was used. The energy groups are

those recommended in for maximum accuracy, i.e. 30 groups.

11.3. Neutron diffusion and slowing-down

In the NRN programme slowing-down between the diffusion groups

is treated by a discrete-collision formalism in which the correct aver-

age energy loss is taken into account, including inelastic scattering.

Slowing-down between all groups is permitted (see fig. 10). The 24

energy groups are those presented in . The groups in this system

have an approximate width of 0. 25 - 0. 30 lethargy units above 0. 3 MeV,

1 unit between 0. 3 and 0.01 MeV, and 2. 3 units below 0,01 MeV. Phos-

phorus reaction rates have been calculated using "dose factors" in the

code and correcting for direct (removal) flux manually. The epithermal

flux is an average from the fluxes 1-10 and 10-100 eV.

For the diffusion part the same geometry has been used (spheri-

cal, with R =30 cm) as for the RASH calculation, and thermal constants

have been the same too. The results are presented in table 15 -29 (co-

lumn marked "NRN").

11.4. Gamma exposure rate

The method for gamma penetration is based on the Monte Carlo

technique with various departures from direct numerical simulation to

accelerate the convergence of the calculation process. The essential

"trick" is the application of a modified exponential transformation which

improves-the forward penetrability of the sample photons and alters

the spatial dependence of the source density to make it more favotirable

for Monte Carlo treatment ' ' . At present, only an one-dimen-

sional plane geometry version of the associated programmes exists

(SALOME on the Ferranti Mercury and SALOMON on the IBM 7090), but

spherical as well as cylindrical versions will be ready in the future.

We see that the main difference between the normal build-tip

method and the Monte Carlo treatment is that the build-up factors in

the last mentioned case are calculated (with a lower statistical accuracy)

r 35 -

for every single problem, while in the build-up t rea tment they have

been calculated for homogeneous ma te r i a l s with a high s ta t i s t i ca l

accuracy or solved for exactly. The attenuation of the uncollided c o m -

ponent is determined, in pr inciple \ by the same density dependent r e -

laxation lengths in both c a s e s , and thus the e r r o r s in density en te r in -

to both se ts of r e su l t s in the same way.

As regards the data for these calculat ions , the number of

photons per react ion (absorption), and per energy in terval is the same

as in the GAS LIT calcula t ions . The source (react ion rate) outside the

core is given by the neutron pa r t of the NRN method. Inside the core

an average z-dependent value is used. This value is approx. 0 .5 t imes

the source on the centre l ine (z -ax is ) . This was because the ca lcu la -

tion in the infinite plane geometry would otherwise have given much

too high values on the outside of the shield. As will be seen from the

r e su l t s , the values obtained in this geometry can, anyway, not be d i -

rect ly compared with the m e a s u r e d va lues .

The output of t he ' p rog rammes provides the penetrat ing dose -

r a t e , with a specification of the contributions from photons born in

var ious predefined spatial reg ions , and the energy deposition ra te in

the same reg ions . Thus this code does not give exposure r a t e s inside

the m a t e r i a l . The ra t e s p resen ted a re based on the energy deposition

ra t e s (chap. 14.4).

12. Neutron penetra t ion calculat ions by numer ica l integrat ion of

t r anspor t equation (NIOBE)

1 2 . 1 . Introduction

The numer ica l integration of the Boltzmann t r anspo r t equation

for some of our configurations has been per formed using the NIOBE

code ' for the IBM 7090 computer . This code can be used to ca lcu la -

te angular ^distributions, total f luxes, and cu r r en t s for neutrons (or

photons) as a function of energy in a finite, mul t i layered , spher ica l ly1 2)

symmet r i c configuration. According to the authors of ' "this p r o g r a m

rep re sen t s the most accura te calculation to date of the solution of the

energydependent Boltzmann t r anspo r t equation in a relat ively compl i -

cated geometry" .

- 36 -

The angular distribution of the neutrons can be calculated at 16

angles to the radius vector, where the cosines of the angles are given

by the zeroes of the Legendre polynomial of degree 16. In calculating

the sources of scattered neutrons, this distribution of the angular flux

is fitted to Legendre polynomials up to an order of 12. The angular

distribution of elastic scattering is fed into the programme also as an

expansion in Legendre polynomials, the order of which is iisually 8, so

that anisotropic cross sections can be well represented.

The Boltzmann equation is solved for the angular flux as a func-

tion of distance by successive iterations at a number of discrete ener-

gies at equal lethargy spacing. The source of neutrons slowing down

from higher energies is obtained by numerical integrations using the

fluxes calculated at the higher levels and making simple assumptions

about the variation between levels. The number of energy levels which

can be used is 200, giving a very detailed neutron spectrum.

The programme is restricted to spherical geometry and requires

a considerable amount of computer time. Thus it is not suitable for

production runs. The running time for our problems with 50 energy

groups, and energy down to .o 0. 1 eV, was «• 2.5 hours.

12.2. Calculations

In this case as well the configuration to be studied has to be trans-

formed into the spherical geometry. The core radius is put at 30 cm,

which gives approximately the right volume of core. The core is divided

into ten spherical layers of 3 cm thickness. The fission source density

for these is given in table 14, starting from the centre of the core. As3

the other relevant data in the form of the numbers of atoms per cm are

easily obtainable from table 4, they are not reproduced here.

The programme calculates fluxes in a given (i) number of equal

lethargy intervals. I = 50 and 200 have been used. The calculations

using 200 energy groups were performed only down to 3 0,1 MeV energy.

12.3. Results

The results were plotted as a flux per lethargy interval to check

the form of the spectrum. The phosphorus reaction rates are calculated

.- 37 -

using the 200-point results. The 0 . are the fluxes at 4.5 eV. The© pi

values given are combined from the I = 50 and I = 200 results in thefollowing way.

It was found that the I = 50 'and 200 results agree in the form

of the spectra, but the absolute values diverge with increasing penetra-*

tion, the I - 50 results being a factor" of 3 above the I = 200 results

on the outside of configurations 2 and 3. As the 200-point results should

be considered more reliable, we determined the f> . by normalizing

the 50 point spectra to the absolute values of the 200-point results at

E & 0, 1 Me?. This method is used throughout the configurations, ex-

cept near the air space in configuration 3, where the I = 50 results

showed a great "spectral error. There the form of the approximately

l/E part of the spectrum has been assumed. The spectral error is pre-

sumably due to the not-so-suitable geometry for this code, as .it is

known that disturbances do appear in certain geometries with air spaces.

Using this method of two systems of energy points, about 50 per

cent of the computer time for a complete 200-point calculation was

saved, by calculating only the 50 highest energies in the 200-point

system. This means approx. 3-4 hr savings per configuration.

13. Concluding remarks about;the calculations

The calculations have been performed, as far as possible, with

equal input data in all of the methods. Thus the values obtained can be

directly compared. The following points should be mentioned:

a) The core was divided into approximately equal numbers of volume

elements in the RASH and NRN methods for the "box" geometry

handling of removal sources (8 x 8 x I 6 vs. 6 x 6 x 12 elements).

b) In NIOBE a core with R - 30 cm and with 10 radial layers was

used.

c) The geometry for the diffusion parts of RASH and NRN also has

a core radius of 30 cm . Tliis actually gives the best overall,

agreement between measurements and RASH results nearest to

the core.

- 38 -

ct) The s a m e t h e r m a l neu t ron cons tan t s have been u s e d in RASH

and NRN.

e) The same numbers of photons born per absorption and per

energy interval have been used in gamma calculations.

f) The same relaxation lengths at source energies are used for

both methods of gamma calculation.

g} The neutron cross sections used in NRN calculations are based

mainly on those used in NIOBE by Troubetzkoy and Goldstein,

United Nuclear Co.

The neutron spectra obtained by NRN and NIOBE after a pene-

tration approximately equal to that from a core to the vessel wall in

a power reactor are compared in fig. 1 1 . No normalizing of the ab-

solute values has taken place. It should be pointed out that the effec-

tive computer times have a ratio of ss 1:100.

COMPARISON OF THE RESULTS, CONCLUSIONS

14. Quantities to be compared and their presentation

14. 1 . Neutron fluxes

The qtiantities that are easily measured are not the ones that are

easily calculated, and vice versa. Various activation rates and thermal

fluxes, especially those of the Westcott type, are the quantities most

simply measured and most often given.

The predicted thermal flux, and hence the activation of a certain

detector, is very sensitive to small variations in the input parameters

for the codes. Thus the comparison of experimental and predicted

thermal fluxes may give too disadvantageous a picture of the reliability

of the method in other energy regions. Of course, an accurate predic-

tion of thermal flux is in principle reqxiired because of the secondary

gamma production. However, the quantity of interest is not actually the

flux but the reaction (absorption) rate. As the diffusion length of neutrons

belowO. 1 eV is short in normal, highly absorbing shield materials, the

absorption rate at a point is determined by the number of neutrons

slowed down in the vicinity. This applies to shields composed of rather

thick, homogeneous layers.

,- 39

Thus, instead of detecting thermal flux, it would be more pro-

fitable to measure the epithermal neutrons in the l/E range, where

the newer methods (NRN, NIOBE) give theoretically more reliable

•results. Accurate measurements are more difficult in this range, but

we think that we have a very useful tool in our-paired foils and Cd- •

ratio methods.

In the fast region, say 0. 1 -10 MeV, threshold reaction rates

have generally been measured but they have been very difficult to pre-

dict before the appearance of more advanced methods of calculation.

The new methods, however, make it possible to calculate the spectrum

and reaction rates accurately.

We have made measurements in all three energy ranges. Thermal

neutron detectors have the highest sensitivity, and the thermal flux mea-

surements penetrate deeper into the shield than the other two compo-

nents do.

14.2. Gamma exposure rates.

The exposure rates (in roentgen per hour) are normally used

when describing the gamma field, and the measured quantities are

usually determined according to the definition, i.e. as the ionization in

air. This method has also been used here, supported by measurements

with secondary instruments (section 3.2).

14.3. Presentation of the results

We have chosen to present the results both as absolute values in

tables 15 - 29, and as relative results in figs. 13 - 27. The latter re-

presentation shows more clearly small variations between calculated

and experimental values than do the attenuation curves, whose logarith-

mic scales often hide rather large deviations. All of the neutron fluxes

are normalized to those obtained by the NRN method. Because the RASH

method does not permit the calculation of P activity, the quantities

compared in this case are the total fluxes in the interval 0. 3 to 2 MeV.

Gamma exposure rates have been normalized to those predicted by the

small geometry gamma code GAS LIT. This is because the gamma code

available in the NRN method so far works in infinite plane geometry

only (chap. Tl). .

- 40 -

14.4. Explanation of tables and figures

The thermal and epithermal fluxes are given in the first table

for each of the configurations. The deviations given for the measured

values are standard deviations (chap. 8). All values are normalized

to 100 kW. Coordinates are given in cm from the reactor face, and

the "Sign" column gives the positions of the detectors in the configura-

tion:

F = interface between two materials

Tl to T5 = centre row of vertical channels in NT (fig. 3}

01 to Ö 5 = horizontal channels in configuration 2

No "sign" = point in the material (water)

The values used for epithermal fluxes are from group 0.07 - 100 eV

in the RASH method, from groups 1-10 and 10 -100 eVin NRN, and the

flux at 4. 5 eV in the NIOBE calculation (section 12.3).

The phosphorus reaction rates are calculated using published cross-

sections ' that give F =* 32. 8 mb for fission spectrum by Cranberg '

(cf. 3.2.4). For the RASH method the total flux between 0.3-2.0 MeV is

used in comparisons.

The measured gamma exposure rates are given for all three types of

instruments: films, ion chambers including gamma pens, and indicating de-

tectors, including G-M instruments and scintillation detectors. The ion

chamber results observed have been multiplied by 0. 9 to correct for the

neutron dose (section 3. 3. 2). The result that is considered most accurate

for each coordinate, and used in the figures, is \mderlined. Normally it

is the ion chamber result, if available.

As regards the calculated gamma values, the GASJLIT results are

the ones obtained directly by the code. In the gamma part of the NRN

method, the energy deposition rates per cm in 1 0 - 20 cm thick layers

were plotted and a curve giving the integrated value was drawn. Values

with their statistical variations were read from this curve. For transla-

tion into exposure dose, a factor of 0.9 * 10 R h W cm was used.

This value is actually valid for 6 MeV photons in magnetite concrete. In

addition, the last NRN value in brackets is the exposure rate calculated

directly by the code for the outer surface of the shield. In this way we

have been able to check the error produced by the fairly rough averaging

procedure for the energy deposition, based on a single translation factor

and on a single-term exponential attenuation in each layer. The agree-

ment between the two values is satisfactory within the statistical accuracy.

- 41 -

In the figures both the measured and the predicted values are

joined by straight lines. The resulting zig-zag lines are, of course,

not the most probable curves, but this time-saving method has 'been

used as the variations between the spatial points of measurement are

of less interest in this report.

15. ' Discussion of the results

15.1. Neutron fluxes

For comparison of the neutron flux results the reader is re-

ferred to figs. 12-to 27. The values obtained in the range from z = 0

to about z = 50 cm in configurations 3 - 8 are of less value because

of difficulties in the translation of the geometry (section 10.2 and fig. 9).

Therefore these values are normally excluded from the following discus-

sions.

JMxJ J.._t^e_rmal_:tl£'ié^?l?S£

The thermal fluxes measured in configurations 2 - 8 are in ge-

neral slightly below those predicted by the NRN method. In configuration

1 (water), on the contrary, the detected flux is twice the predicted value

at z = 50 cm. The hardly significant rise observed in this configura-

tion at z ">_ 1 70 cm may be due to the photoneutron production, which

is known to determine neutron fluxes in this kind of set-ups after 180 -

200 cm penetration.

The relative attenuations of the predicted and measured fluxes

seem to agree quite well, since a constant ratio is obtained in the fi-

gures. The only exception is configuration 2, where the measured

values indicate a higher attenuation than predicted. This fact is also

repeated in the other fluxes. The explanation may be a minor devia-

tion in the properties of the concrete of the pool wall compared to data

used. In principle we have the same magnetite concrete in configura-

tions 2 - 6 .

The values predicted by thjold RASH method are after 200 cm

penetration about 0.2 - 0 . 3 times the values observed in magnetite

concrete, and tend to diverge further with increasing penetration. In

- 42 -

ordinary concrete the ratio is 0.5 - 0.8. The zig-zag form in confi -

guration 1 originates from errors in the exponents for the source term.

To sum up, the measurements have shown that the NRN method

is able to predict the thermal fluxes with an accuracy equal to or better

than a factor of 2 at penetration depths of 80 - 200 cm.

The agreement between the NRN- or NIOBE-predicted and ob-

served epithermal fluxes is very good in configurations 2 - 8 , the dis-

crepancies being ^ 5 0 per cent of the values observed. The RASH

results show approximately the same ratios as in the case of the ther-

mal fluxes. For the NRN method the greatest discrepancy is observed

in water, where the observed values are 2 - 3 times the predicted

ones. The reason for this discrepancy has not yet been studied. The

disturbances from the air space are smaller in the epithermal than in

the the rmal f luxe s.

IAJ• 3. Fast neutrons

The agreement between the P reaction rates measured and pre-

dicted by the NRN method is also good in configurations 2 - 8 . The r e -

sults have generally the same tendency as the epithermal results and

the discrepancy is less than a factor of 2. The results obtained by

NIOBE in configurations 2 and 3 also agree very well with the measure-

ments. The point at z = 167 cm in configuration 2 is a value obtained

by a recoil counter relative to the value at z = 127. The greatest dis-

crepancy is observed in configuration ), where the reaction rate is

overestimated by a factor of 2 - 3. The ratios of the fluxes between

0.3 - 2 MeV by the RASPI and NRN methods have approximately the

same values as the respective thermal and epithermal flux ratios, i .e .

they have an increasing discrepancy in heavy concrete, and an approxi-

mately constant ratio in ordinary concrete. Only in water is the 0 . 3 - 2

MeV flux by RASH higher than the one by NRN.

15.2. Gamma exposure rates and source distributions

Considering the gamma exposure rates, the configurations can

be divided into two groups:

-43 -

a) Configurations in which the major part of the dose originates

from the core and from the inner regions of the shield (App. Ill),

i.e. configurations 2, 4, 7 and 8.

b) Configurations with one or more heavy-layers: 3, 5 and 6. A

great part of the dose in them originates from the outer regions

of the shield.

JA?:J •^!o£IIli*i h°JF£ §J?Eej2 Lf _shie Ids'

Configurations in group a) get the right gamma source indepen-

dently of the neutron flux calculations further out, and being r a the r

homogeneous they a re suitable for the t r ea tmen t based on build-up fac -

t o r s . In these configurations the GAS LIT resu l t s agree with the m e a -

surements within a factor of l ess than 2. The discrepancy in coisfig. 2

at z = 207 cm is probably caused by s t reaming via the slot around the

Nl window to the open end of channel 05 (fig. 3).

with Jae_a_yy_ lay_e r_s_

In the second group-(b) the GASLIT resu l t s a r e sat isfactory

between the core and the heavy l ayer . Outwards from the heavy l aye r s

the predicted values a re too low by a factor of 3 to 10. Dis regard ing the

points on the outer surface the maximum ra t io , extrapolated from the

points in the shield, s eems to be somewhere between 5 and 7. The d i s -

crepancy can be explained by consider ing the e r r o r in the e r roneous

neutron fluxes (and absorpt ion ra tes) between z = 1 15 and z = 226 cm

as obtained by RASH. As shown before, these were too low by a factor

of about 5. F igs . 34 and 35 (App. Ill) show that even with this sou rce ,

which i s too low, approx. 55 and 70 per cent of the exposure ra te on

the outer shield surface in configurations 5 and 6 originate from the

region mentioned. When these ra tes by GASLIT a re co r r ec t ed for the

observed neutron fluxes they increase to 86 and 92 per cent, r e s p e c -

t ively, i . e . in real i ty the outer region completely de te rmines the e x -

posure rate outside the shield.

These la t te r percentages a re cert if ied by the NRN resu l t s (dotted

lines in figs. 33 - 36). A geometr ica l cor rec t ion of the form (~~-)R

with R =100 cm has been applied to the infinite plane r e s u l t s . Wesee that the exposure originating from the outer region of concrete in

- 44 -

configs. 5 and 6 is 91 and 95 per cent, respectively, as against 86

and 92 estimated above. These considerations apply, of course, to

config. 3 also (fig. 17),

The exposure originating from the concrete in config. 2 (fig. 33)

has grown from 69 by GAS LIT to 80 per cent by NRN, but the most

remarkable fact is the re -distribution of the source. It is practically

evenly distributed in the concrete. The results are due to the rela-

tively greater attenuation of the neutron fluxes in the RASH results

(fig. 14). The NRN result, with its too high neutron fluxes, over-esti-

mates in this case the contribution from the outer regions.

The relatively high values on the outside of configurations 5 and

6 may probably be explained by a streaming and scattering effect;

between the floor and the set-up there is a straight slot of 1 - 2 cm

width. The measurements in configs. 5 and 6 were made in the earlier

part of the experimental series, and no special precautions were taken

against this streaming. On the other hand, for config. 3, one of the

most thoroughly studied, the streaming had been blocked by using lead

bricks.

Finally, it should be noticed that the points at z = 41 . 4 and 47

cm in config. 6 are based on very uncertain film measurements and

are thus of less value.

The absolute results by the NRN method are difficult to compare

in our geometries. In the first group of configurations (2, 4, 7 and 8),

the results could apparently be brought into agreement by a suitable

spherical correction. Such adapted absolute values depend on the trans-

lation factor and the source assumed in the core, and are of less in-

terest here. As pointed out in section 11.4, we have not used the ma-

ximum source on the centre line of the core.

In configs. 3, 5 and 6, on the other hand, the infinite plane

geometry used should give rather accurate results on the outer shield

surface. The results seem to agree in config. 5, but both in 3 and 6

the measured values are about twice the predicted. At this point we

wish to draw attention to the absolute values of the NRN results. As

pointed out in section 14.4, the values plotted are based on a rough

- 45 -

approximation in the translation factor. The dose calculated directly

on the outside is based on photon current , not on the flux. When the

flux is- considered, the results should be multiplied by a factor of

1.5 - 2. With this correction the predicted values agree with the

measured values corrected for scattering in configs. 3 and 6, and are

higher but still within a factor of 2 in config. 5. In spherical geometry,

outside exposure rates predicted would be lower by 10-20 per cent.

Thus we have seen that in these configurations (3, 5, 6), where

absolute results obtained in infinite plane geometry are meaningful,

the predicted exposure rates agree with the measured ones within a .

factor of 2 or better. On the other hand, these are the configurations

where the RASH-GASLJT method failed because of erroneous neutron

attenuation.

16. Conclusions, recommendations

16.1. Attenuation measurements

Attenuation measurements can be done in two main ways:

a) measurements in the shields of large power reactors

b) measurements in smaller geometries with research reactors.

In the research reactor measurements described, one has the

advantage of a flexible, dry facility and possibilities of running the

reactor in the desired way.

The greatest disadvantage is the not so easily defined geometry

(section 10.2). Another one is the source strength, which does not allow

measurements at penetration depths equal to those in actual reactor

projects.

The shields of large power reactors would offer a rather clean

geometry and a source strong enough for really deep (300 -400 cm)

penetration measurements. The latter fact is also very valuable because

a singleexponent attenuation model is capable of predicting fluxes up to

about 100 cm from the core, and only after this penetration length do

greater discrepancies appear. The disadvantage is, of course, the

impossibility of running the reactor in the desired way. However, more

- 46 -

measurements ought to be made in the cheapest laboratories, i .e. in

power reactor shields.

The foil techniques developed for the neutron detection have

proved to be very practical and have given relative and absolute

accuracies within better than - 15 per cent, which is adequate for

this type of measurements. A disadvantage was the relatively low

sensitivity.

In the gamma measurements the use of primary methods is to

be recommended as the calibration of secondary methods is difficult

owing to the unusual energy spectrum in question. A large number of

miniature condensator chambers would probably be the ideal solution

for this type of measurements. The neutron sensitivity and the energy

dependence of the chambers must be kept in mind.

16.2. Comparison of measured and calculated fluxes

J___J j _ _ _ s _of_e_rror

We believe that this type of comparison between measured and

calculated values gives a much better picture of the actual reliability

of the design methods than a comparison between calculated results

in some of the more or less idealized configurations. This statement

is based on the following conclusions about the sources of error.

The greatest errors no longer come from the microscopic

cross-sections or from the solution of the transport problem by the

methods available. They originate from

a) the translation of the real geometry into the one used in the

calculations,

b) inaccuracies in the radiation source, both in the number of

photons produced per reaction and in the shape of the most

energetic part of the fission spectrum

c) uncertainties in material data (in the case of concrete).

- 47 -

Point a) includes, besides the approximations used in the spa-

tial integration of a small source and the other difficulties discussed

in chap. 10, also the homogenization of the core in the case of large

reactors. One may question, for instance, whether the homogeniza-

tion is allowable in the case of a D?O-mode rated reactor with a 25 cm x

x 25 cm grid and 25 cm reflector. This question ought to be given more

attention.

Point b) has not been discussed in this report, as the same data

have been used in all the calculations (chap. 13). In the course of the

work it has been observed that in very deep penetrations the error may

be considerable.

Point c) was discussed in chap. 7 and was found to cause the

greatest uncertainty on the outside of the shield.

Even though the accuracy of the design methods has improved

during the last years, we should not expect any of them to give results

for power reactors that could with great probability be closer than with-

in a factor of 2 - 3 from the true values. This applies throughout the

shield. The accuracy is limited by the points presented in section 16.2. 1

and thus could not be improved by developing new codes for the mathe-

matical solution of the transport problem.

The NRN code developed seems to offer an economical way of

solving neutron penetration problems, giving an accurate fast spectrum

at the same time. As for the gamma penetration, the build-up concept

works excellently in fairly homogeneous shields, but the NRN - Monte

Carlo method offers a possibility of solving problems in configura-

tions made of thin laminae for which build-up factors are not available.

- 48 -

References

1 . AVERY A F et al

Methods of calculation for use in the design of shields for

power reactors

AERE-R 3216 (Feb. I960)

2. BUNCH W L

Radiation shielding program at Hanford

HW-78274 (Aug. 1963)

3. BUNCH W L

Attenuation properties of high density Portland cement

concretes as a function of temperature

HW-54656 (Jan. 1958)

4. WOOD D E

The effect of temperature on the neutron attenuation of

magnetite concrete

HW-58497 (Dec. 1958)

5. PETERSON E G

Shielding properties of ferrophosphorous concrete as a

function of temperature

HW-64774 (July I960)

6. PETERSON E G

Shielding properties of ordinary concrete as a function of

temperature

HW-655 72-(Aug. I960)

7. BENNETT C L

Shielding properties of As-cured barite concrete

HW-71 113 (Sept. 1961)

8. PETERSON E G

Shielding properties of iron serpentine concrete

HW-73255 (Apr. 1962)

9. AALTO E and NILSSON R

Measurements of neutron and gamma fluxes through thick shields

of magnetite and baryte concrete. A comparison with calcula-

tion. Presented at the EAES-Symp. on "Nuclear Reactor Shielding",

Studsvik, March 1961

- 49 -

10. AALTO E

Comparisons of measured and calculated neutron fluxes in la-

minated iron and heavy water

Trans. Am» Nucl. Soc. ]_, 1964 No. i

1 1. HJÄRNE L (ed.)

User's manual for the NRN Shield Design Method

AE-Report 145 (May 1964)

12. PREISER S et al

A program for the numerical integration of the Boltzmann

transport equation - NIOBE

A R L - T . R-60-314 £Dec. I960)

1 3. NILSSON R and RANDEN K

Neutron flux measurements and power determination in the

R2-0 Swimming-Pool Reactor

Presented at the EAES-Symp. on "Nuclear Reactor Shielding",

Studsvik, March 1961 (= Internal report AE -RSA-57, 1961)

14. STOUGHTON R W and HALPERIN J

Heavy nuclide cross sections of particular interest to thermal

reactor operation

Nuclear Sci. and Eng. 6_, (1959), p 100

15. WESTCOTT C H, WALKER W H and ALEXANDER T K

Effective cross sections and cadmium ratios for the neutron

spectra of thermal reactors

Proc. Second U.N. Conf. on the Peaceful Uses of Atomic Energy

lib 0958), P 70 (A/Conf. 15/P/202) .

16. KOONTZ R L, GREENFIELD M A and JARRET A A

Absolute thermal neutron determination P. 1 -2

NAA-SR-1 137 (1955)

17. NILSSON R

FLUDUF - a program for the determination of the thermal and

epithermal flux with double foil method

Internal AE-RS A-report 51 (Oct. I960)

- 50 -

18. MARTIN D H

Correction factors for Cd-covered foil measurements

Nucleonics 1_3 (1955) p 52

1 9'. DeJUREN J A and PASCHALL R K

Thermal neutron transmission through cadmium covered foils

Trans. Am. Nucl. Soc. 6 (1963) p 28 or NAA-SR-7770 (l 963)

20. SVENSSONS

FLUCAD - a program for calculating thermal and epithermal

neutron fluxes by the cadmium-ratio method

Internal AE-RSA-report 55 (Jan. 1961)

21 . HUGHES D J and SCHWARTZ R B

Neutron cross sections

BNL-325, 2 ed. (1958)

22. CUZZOCREA P, PAPPALARDO G and RICAMO R31 31

Cross section for . P(n, p) Si reaNuovo Cimento (10) 1_6_ 0 960) p 450

31 31Cross section for . P(n, p) Si reaction up to 5 Me v

23. BE AU GE R

Sections efficaces pour les detecteurs de neutrons par

activation recommandées par le groupe de dosimetri d'Euratom

Centre d'Etudes Nucléaires, Fontenay-aux-Roses 1962

24. GRANBERG L, FRYE G, NERESON N and ROSEN L

Fission neutron spectrum of U

Phys. Rev. 103 (1956) p 662

25. NILSSON R

FOMAK - a program for calculating the saturated activity in

foil measurements

Internal AE-RSA-report 27 (Oct. 1959 + 1 compl. , in Swedish)

26. SVENSSON S

SODAC - a program for processing data from an automatic

sample changer

Internal AE-RFA-re port 69 (Nov. 1961, in Swedish)

27. NILSSON R

Neutron dose monitoring for irradiation of materials in reactors.

Neutron dosimetry II

IAEA, Vienna 1963 p 275

- 51 -

28. NILSSON R

STREKO - a program for analyzing an experimental decay curve

with three components

Internal AE-RSA-report 31 (Dec. 1959, in Swedish)

29. NILSSON R

Gamma dose measurements with ionization chambers in mixed

radiation fields

Internal AE-TPM-RFA-468 (Sept. 1963)

30. WIDELL C O

(AB Atomenergi, personal communication)

31 . GOLDSTEIN H and WILKINS J E

Calculations of the penetration of gamma rays

NYO-3075 (June 1954)

32. AALTO E and MÅLEN K

Gamma dose measurements with ionization chambers. Energy

sensitivity

Internal AE-TPM-RFA-526 (Jan. 1964)

33. Selected topics in radiation dosimetry

Proc. of a Symposium in Vienna, June I960

IAEA Vienna 1961

34. MERCER T T and GOLDEN R

Response of photographic emulsions to thermal and epithermal

neutrons

USN-RDL-TR-493 (Dec. I960)

35. SMITH R J and BENCK R F

Thermal and fast neutron effects on dosimeter films

Health Physics, _9_, (1963) p 473

36. HINE G J and BROWNELL G L (ed.)

Radiation dosimetry. Academic press, New York 1956

37. WALKER R L and GROTENHUIS M

A summary of shielding constants for concrete

ANL-6443 (Nov. 1961)

•r 5 2 -

38. AALTOE

Vattenhalten hos magnetitbetong (Water contents in magnetite

concrete)

Internal AE-TPM-RSA-166 (Dec. I960, in Swedish)

39. NILSSON R

Neutroninducerad aktivitet i järnmalms betong för R2-0

(induced activity in magnetite concrete)

Internal report AE-RSA-23 (Oct. 1959, in Swedish)

40/ AALTOE

The R2-0 reactor. Variations between the nominal and real

reactor powers

Internal AE-TPM-RFA-256 (March 1962)

41 . RANDEN K

Avståndsmätningar: R2-0 härden-bassängväggen

(Distances: reactor to pool wall)

Internal AE-TPM-RFA-1 96 (June 1 961, in Swedish)

42. A VERY A F

The theoretical prediction of neutron penetration in shields

for marine reactors

NPS/4 (Nov. I960)

43. BENDALL D E

Private communication (June 1959)

44. AALTO E

On the application of the LIDO and RASH-GASH programs for

the R2-0 shielding facility

Internal AE-TPM-RSA-169 (Dec. I960)

45. SYNGE M J

MENDIP, a digital computer programme for calculating, neutron

diffusion parameters

SWP/P.67 (Sept. 1960)

46. ACRAMAN WE

GAS LIT. A programme for calculating the gamma dose rate in

the shield of a small reactor

AERE-R 3442 (Sept. I960)

53 -

47. ROOS M

Kärnfysikaliska egenskaper hos R3/Adams tunga betong

(Nuclear properties of the R3's heavy concrete)

Internal report AE-RSA-1 7 (Apr. 1959, in Swedish)

48. ROCKWELL T (ed.)

Reactor shielding design manual

Me Graw-Hill New York 1956

49. HJÄRNE L and LEIMDÖRFER M

A new method for predicting the penetration and slowing down

of neutrons in reactor shields

(to be published 1964)

50. AALTO E and FRÄKI R

The experimental determination of the boundary cosine

in the NRN-shield design method

(to be published 1964)

5 J. LEIMDÖRFER M

A Monte Carlo method for the analysis of gamma radiation

transport from distributed sources in laminated shields

Nukleonik 6_ (l 964) p 58

52. LEIMDÖRFER M

On the transformation of the transport equation for solving deep

penetration problems by the Monte Carlo method

FOA 4 Report A 4361 -41 1 (l 964) or

Trans. Chalmers Univ. of Technology 286 (Apr. 1964)

53. LEIMDÖRFER M

On the use of Monte Carlo methods for calculating the deep

penetration of neutrons in shields

FOA 4 Report A 4366-41 1 (1964) or

Trans. Chalmers Univ. of Technology 287 (Apr, 1964)

54. BECKER K

Filmdosimetrie . Grundlagen und Metoden

Springer Verlag Berlin 1962

- 54 -

55. WESTCOTT C H

Effective cross section values for we 11-moderated, thermal

reactor spectra. 3 ed. corr.

AECL-report HOI f 1 960)

56. JIRLOW K and JOHANSSON E

The resonance integral of gold

, J. Nucl. Energy-

Part A Reactor science _M (1 960) p 101

57-. DAHLBERG R, JIRLOW K and JOHANSSON E

Measurements of some resonance activation integrals

J. Nucl. Energy

Part A/B Reactor science and technology j_4 (1961) p 53

58. JOHANSSON E, LAMPA E and SJÖSTRAND N G

A fast chopper and its use in the measurement of neutron

spectra

Ark. Fys. J_8(I960) p 513

59. GOLDSTEIN H

Fundamental aspects of reactor shielding

Pergamon press New York 1959

60. BENDALL D E

RASH D - A Mercury programme för neutron shielding calculations

AEEW-M 261

61. RANDEN K

Power calibration of R2-0

Internal AE-TPM-RFA-256 (May 1962, in Swedish)

62. NILSSON R

Gamma dose measurements with DuPont 508 film in mixed

radiation fields.

Internal report AE-RFA-487 (1963).

- 55 -

APPENDICES

L. Effective flux level in an open channel

To find the effective coordinate at which the calculated flux of the--Cfzform p = p e "" can be compared to the flux measured in an open

channel penetrating the material perpendicular to the z-direction. The

following assumptions are made:

1 . the channel does not disturb the flux distribution in the surround-

ing material

2. the detector is a point detector and does not disturb the flux in

the channel

3. axial streaming in the channel is negligible

4. the flux in the surrounding material is isotropic.

With these assumptions and the signs in fig. 28, and following59)

the treatment in , we may define the average flux a detector sees in

the channel as

dA(z)2R

dA 2* RL( i )

z - 0

w e

By noting that dA = R d t • L, z = R - R cos f, 0(z) = 0oe~Q'Z

get <j5= 0 e" a R I (aR), which must equal 0 e ~az , where i" is the

value that is sought. By solving for ~z and dividing by R we get

-f I n J

Defining a new function ——5 we get for (o?R) <

16(3)

- 56 -

It is seen that eq. (3) is a good enough approximation starting

from J®~R) & 1 . In ^ only the first term is given.

In our experiments aR ® 0. 1 • 3.0 = 0.30, giving g ** 0.075, i.e,

• R - z" s 0.23 { cm], which is negligible. Thus we may use the calcu-

lated fluxes at the centre of the channel in our comparisons.

An effort was made to check this experimentally and a typical

result, is shown in fig. 29 for the channel T2, the diameter of which is

7.5 cm, giving R - z" = 0. 35 cm. Thermal and epithermal fluxes were

determined:

a) as an average of five measurements in open channel

b) a distribution with points spaced 1 cm apart in an open channel

c) on the front and back walls of a filled channel.

As can be seen, the statistical errors (10 - 20 per cent) make

definite conclusions difficult, but the best values that were obtained

point to a z % 81 - 82 cm or to the centre line, as expected.

The effective z-value is more difficult to determine for the

channel T3 in configurations 3, 5 and 6. These channels are separated

by about 2 cm concrete from the borated lucite . The neutron spectrum

is rather abnormal in the vicinity of this absorber. This gives fairly

large variations when our standard methods are used (fig. 30). In the

same figure we have plotted the calculated flux. We assumed that the

real thermal flux curve has the same form as the calculated one, and

thus got the z , , = 1 19. 5 cm. Because of the great disturbances in and

near channel T3, the measured fluxes at this point are of less value.

II. . Radiation heating in concrete

There are two regions in massive shields where the accuracy of

the flux calculations is of greatest interest. These are:

a) outer face of the shield (biological dose)

b) innermost regions of the shield, including thermal shield and

pressure vessel (radiation damage rates and heat generation).

57 -

This report has mast weight as regards questions that affect

point a). Excluding the radiation damage rates (neutrons) there is a

great interest in the heat generation rates, originating mostly from

gamma absorption, in the innermost region of the biological shields.

We saw that because of the high dose rates and background, the

measuring of the gamma exposure rates- with "biological response"

detectors was difficult on the innermost face of the concrete. In these

regions calorimetric measurements become useful.

Measuring with a calorimeter is rather difficult because of the

great attenuation (l 0~ in 30 cm) of the heat generation in relation to

the finite size of the calorimeter with insulation etc. Besides, flux dis-

turbances would be rather large.

Another way of determining the heat generation would be to heat

the shield to a steady state value and determine the heating rate from the

known material constants. The results could be compared with the pre-

dicted values.

It is easy to show, however, that a time of the order of one week

would be needed to reach a nearly steady state temperature distribution.

Thus the steady state experiments must in practice be excluded with our

reactor..

There remains an interesting possibility of using the material it-

self as a non-steady state calorimeter.

We consider the differential equation of heat conduction in plane

geometry:

k ^ + q r "

qM ' ~ heat generation per unit volume, t = temperature and T = time

and p , c and k have their usual meanings.

2We assume that when f < t , t(x) = T and — = §-4r = q i ' i a o

ST S X 2

58 -

When applying a heat source qf ' '(x) at T = x , after a short

time2

T ' —- 4 0, t * T , and ^ - ^ » 0.

W e g e t | L . 8 ijlll (Air.z)

In our experiments this equation is valid within the measuring

accuracy until at least T £5 T +30 min.

Experimental procedure

Thermocouples were placed in the pool wall (config. 2) and in the

plug of ordinary concrete. In the latter, measurements were possible

in config. 7, . i .e . with the smallest possible water thickness between the

core and the pool wall.

In config. 2 there are 5 rows of elements, 3 in each row, at the

height of the midplane of the core. As, with this placing, only lines of

elements at 3 and 18 cm depth gave usable results, the distance between

the couples was decreased and only one row was used in ordinary concrete.

Sources of error

Depending on the accuracy of the recorder, 0 . 5 - 0 . 8 C h was« 4-

the smallest usable value of -— . This was obtained at 20 - 25 cm depth

in the concrete. Besides, the usable measuring time deeper in the mate-

rial is limited by the wave character of the heating.

We consider the heating phenomen as it is seen from a point 30 -

40 cm in the concrete. Because of the exponential nature of the heat

source, it can be approximated with a plane source switched on and off

on the concrete surface. This step function causes a temperature wave

which moves in the z-direction with speed and attenuation determined by

the material constants. This wave is a disturbing factor deeper in the

material. It would of course be possible to solve the heat conduction

equation for unsteady state even deeper in the material, but this has

not been attempted because the accuracy is anyhow estimated to be too

low.

- 59 -

The drift of the zero point of the temperature indicated is another

source of error. Irrespective of the origin of this drift, it has an effect

lt-1

on the results as soon as it exceeds 0. ] C h . The observed rate was

» 0.5 C h

The only material constant involved in this study is the specific

heat. It depends greatly on the water content of the concrete.

Results

The results are presented in figs. 31 and 32 for configurations 2

and 7. It is seen that the measured and GAS LIT-calculated values seem

to agree well in config. 2. In this case the pool lining has certainly pre-

vented any drying effects of the concrete. The low value from the first

couple (z = 23) may depend on contact with the pool lining. It is seen

that the sensor at z = 68 cm can give only an upper limit of the heating

rate.

In config. 7 the predicted values seem to fall below the original

measured ones. In the November experiment one of the recorder channels

was unconnected. A drift of + 0. 5 - 0. 1 C h was observed in this

channel. It is seen that the observed values show exponential attenuation

only after this correction has been applied.

Measurements about 3 months.later indicate a 20 - 30 per cent

change in the heat capacity. This could be explained if it is assumed that

the drying effect from the uncovered surface has removed 50 per cent of

the water from the first 10-15 cm. The value 5 - 6 C h for th"e first

3 sensors is probably due partly to some sort of radiation damage, be-

cause the plug has received a rather high accumulated exposure between

these experiments. In these runs no unconnected channel was recorded,

thus the discrepancy from, the earlier results may equally well be due to

the drift of the instrument. The' first set of measurements should thus be

considered the most reliable.

Comparison with the NRN method

Because this method does not give any distinct curve for the energy

absorption, the curve given is fitted to the total absorption in 1 0 - 20 cm

thick layers. It is seen that these curves have, of course, the same ten-

dency as the respective exposure rate curves, i.e. they start at lower

- 60 -

rates than the GASLIT results and with a smaller attenuation because

of the infinite plane geometry; they cross the GASLIT curves further

in the concrete. The absolute ratios are not exactly the same for the

heating and exposure rates, but this is because.of the approximate

translation factor from energy absorption to exposure rate .

In the GASLIT calculation the energy absorption was determined

individually for all of the energy groups, while in the NRN results the

exposure rate was determined with an averaged translation factor from

-the summed-up energy deposition. No correction has been applied for

the energy transport by neutrons. This correction is estimated to be

max, 10 per cent (see chap. 3.3.3).

As regards the geometrically correct GAS LIT calculations and

the measured rates, they have, within the error limits, the same ratio

as the observed and calculated biological exposure rates. This is, of

course, to be expected if the measured values are correct.

Conclusions

We may conclude from this study that the determination of gamma

exposure and heating rates is entirely feasible by the transient tempera-

ture method. It could be easily applied to difficult-to-reach high-dose

points outside the reactor, as the laying of the necessary thermocouples

is very easy during construction.

III. Effective gamma sources for a dose point on the outside of the

shield

Besides calculating and measuring the gamma exposure rates on

the outer surface of the shield, it is interesting to study from which

regions this gamma exposure comes. This will enable one to

a) make a closer study of the causes of discrepancies between the

measured and calculated values

b) get a general feeling of the effective gamma sources in various

configurations

c) obtain a basis for possible shield optimization and improvements.

- 61

Even though the configurations studied are not comparable to

those found in power reactors, gamma source distribution is presented

in histogram form in figs. 33 - 36. The vertical scale gives the per-

centage of the gamma exposure rate originating per 10 cm thickness of

the shield. The partial exposure rate is assumed to be evenly distributed

over the whole calculational region, as the programmes do not give any

distribution inside the regions. The figures given indicate the total per-

centage originating from the whole region.

Figs. 33 and 36 of configurations 2 and 7 show the well-known

fact that in ordinary, and even in heavy concrete, the gamma exposure

rate originates from the core (in power reactors from the thermal shield

and reactor tank) and from the innermost regions of the shield. Thus the

required accuracy of the neutron flux and reaction rate calculations is

highest in these regions, the outer regions of the shield being of minor

importance. The accuracy of the biological dose predictions depends on

the accuracy of the deep penetration gamma calculations.

The discrepancies between the two sets of results presented ori-

ginate in differences in neutron fluxes, and were discussed in chap. 15. 2.

On the other hand, if we have a shield with one or more still heavier

layers (configurations 5 and 6 in figs. 34 and 35), the picture changes

markedly. These configurations have an average density of 4. 0 and 4. 3~3

g cm , respectively, when considered as a whole. In these shields ** 90

to 95 per cent of the gamma exposure rate on the outer surface originate

from the last metre of thickness (NRN results in figs. 34 and 35), i .e.

from neutrons that have penetrated on an average one metre of material.

The RASH-GAS LIT system gives only 58 and 68 per cent from the outer

region, but these values are due to too low neutron fluxes. When corrected

to the actual fluxes, GAS LIT would give percentages that are in agreement

with the NRN results (see chap. 15.2).

We see that in this type of shield the accuracy of the neutron flux

predictions after « 1 metre penetration is much more important than in

the previous case. This is even more so because a relatively greater

part of the total dose comes from the fast neutron flux. The photons pro-

duced now penetrate a smaller length of material.

- 62 -

The resu l t s obtained here with thin, heavy layers a re qual i ta-

tively applicable to r eac to r shields of higher density, and it can be

es t ima ted that with p > 4 g cm the accuracy of the deep neutron p e -

netra t ion predict ions is of rapidly increas ing impor tance .

IV. Exper iments in the use of nuclear emulsions for fast neutron

detection

Some tes t s have been made concerning the possibi l i ty of using

nuclear emulsions for relat ive fast flux m e a s u r e m e n t s . The films

used were ordinary packs for health physics monitor ing, and the r e a d -

ing was per formed manually, counting the number of t r acks per a r e a

(normally 7 m m ) per fi lm,

The conclusions a r e that the emulsion method is not r ecommend-

able in this .type of exper iments with measu remen t s in a large number

of spat ial points because :

1) The gamma sensit ivity of^the films l imits the i r use to a dose

range where the number of usable t r a c k s , and therefore s t a t i s -

t i c s , is low. The maximum allowable gamma exposure was

found to be @ 2 r ,

2) The reading of films manually is very t ime consuming and the

method is thus not suitable for a large number of detecting

points .

3) The spat ial range that can be m e a s u r e d in a single run is very

smal l compared with the ranges of other detecting methods .

Limited by the facts mentioned in 1), it was found to be equal

to the length requi red for an attenuation with one power of ten,

or approx. 20 c m .

The resu l t s obtained in config. 3 a re presen ted in fig. 37. By

compar ing with the line drawn according to the known relat ive at tenua-

tion, we see that this method could have given the attenuation through

1 . 7 m of concrete within a factor of ten. With a large number of m a n -

hours the s ta t i s t ica l accuracy could, of cou r se , be improved.

Table 1. Data for the foil detectors

Foil

Au

Cu

Mn

In

Thickness(mg/cm )

18. 3

73

125 (90%)

7. 0

1

1

1

1

55)g /

. 005

.019

xd) =

0

(barn)

98 .8 +

4..3 +

13. 3 +

155 +

0. 0010

0

0

0

1

i

. 3

. 2

. 2

0

0. (

ares(barn)

1490 +

2.9 +

7. 7 +

2530 +

)005

40 5

0. 1

0. 5

250

6)a)a )

b)

0.

0

0

0

E

G

61

85

94

380

e)L,

b)

+ 0.

+ 0.

+ 0.

+ 0.

* 0.

03

02

04

013

105

1.

1.

1.

1.

t

008

028

024

040

>)

++

+

+

0. 020

0.

0.

0.

0.

eV

002

005

007

009

ECd(0. 5(eV)

0.

0.

0.

0.

19)

mm Cd)

61

55

55

72

0

0

0

0

Ecd-(eV)

. 44 +

.49 +

. 50 +

. 52 +

0

0.

0.

0 .

0.

04

03

03

03

57)

a) Private communication from Dahlberg (I960);, slightly changed in final report by Dahlberg et al '

b) Experimentally determined

c) Calculated from cross-section curves, F and recent values of E_ ,. Actually, 0.47 eV has mainly been used19)

d) Experimentally determined, de Juren and Paschall ' give 0. 0006e) Determined by Johansson et al

points.

58) in one position of calibration; then rather arbitrarily applied for all

Table 2. Composition and properties of magnetite concrete

Mix design:

Cement (LH)

Magnetite (from Grängesberg Mine}:

Sand, density

3-8 mm "

8-30 mm "

30-60 mm "

Water

Plastiment

Theoretical density

Water-cement ratio

Workability

4. 76

4.46

4.69

Slump

330 kg m~3

580 "

1070 "

875 "

875 "

148 "

1.65 "

3880 kg m"3

0.46

3 cm

Physical properties

a) 25 x 25 x 25 cm cubes

Compressive strengthH II

Specific heat

Thermal diffusivity

Thermal expansion coeff.

Density (stored in water)

28 d

150 d

(30°-90D)

(20°-80°)

(20°-70°)

(70-130°C)

28 d

b) 101 mm diamond drilled core

490 kg cm"2

710 "

0. 18 cal g"1 °C"1

3. 7 » 10"3 m2 h"1

9. 2 • 10 -6

10. 1 • 10-6

3. 83 g cm -3

Density (from small particles after crushing) 3.9 g cm -3

Weight lost by heating up to 900 C 3.3 - 3.4 per cent

c) Most probable values, used for the calculations

Density

Water content

3. 74 g cm

133 kg m"3

Table 3. Composition and properties of ordinary concrete

Cement (L.H) - slowly hardening

Sand 0 - 8 mm

Gravel 8 - 3 2 mm

Water

Theoretical density

Water-cement ratio 0. 50

Physical properties

a) 25 x 25 x 25 cm cubes

Compressive strength 28 d

II 90 d

Densi ty 28 d

" 90 d

b) 20 x 20 x 20 cm cubes

Compressive strength 28 d

330

915

990

165

2400

k gn

i i

kg

m

m

- 3

- 3

. i

402 kg

599 "

2.43 g2.45 "

471 kg

599 "2.43 g

c m

c m

c m

c m

- 3

- 2

- 3Density 28 d

'" 90 d 2. 41 "

c) Most probable values used for the calculations

Density

Water content

sio2

Fe2°3CaO

MgO

Ti03

Rest

Ballast analysis

68

14

4.

2.

2.

3.

2.

1.

.

4

3

5

3

6

Z

0 -

- 4

- 3

- 2

- 1

69

15

. 6

. 7

. 7

. 3

(Gravel)

. 0 per

-1 1i t

it

i t

i t

II

n

centn

it

II

n

it

t i

II

2

1

. 4 3

65

g cm"

kg m"

Table 4. Compositions of the real and calculation concretes,weight per cent

\ Con-\sCrete

Ele- \ .ment >s.

H

O

Na

Mg

Al

Si

P

S

K

Ca

Mn

F e

L a

Magnetite

Real

0. 40

34. 0

(0.009)X

1. 2

0 , 8

3. 6

0. 7

(0. 05)

< 0. 1

6.1

(0. 009)X

53. 2X

0. 022X

0» 3. 14- g cm"

Calc.

NRN

0.40

34. 0

-

-

0. 8

4 . 8

-

-

-

6.8

-

53. 2

-

RASH

0.40

34. 0

-

1.2

0. 8

3 . 6

0. 7

-

-

6.1

-

53. 2

-

Ordinary-

Real

0. 77

49. 0

1.7X

1. 5

6.5

27. 2

-

(0.08).

2 . 5

7 . 8

0. 03

3. 0x

-

p« 2. 43- 3

g cm"

Calc.

NRN

0. 77

49. 0

-

-

9 . 7

29. 8

-

-

-

7 . 8

-

3 . 0

-

RASH

0. 77

49. 0

1.7

1.5

6.5

27.2

-

0. 08

2. 5

7. 8

0. 03

3 . 0

-

XDetermine the activation of the concrete

Table 5. Shield configurations studiedConfiguration 1 « H~0, > 200 cm

Concrete

^ s . Config. No.Layer (cm) ""-v

Water 10

" 15" 2011 50Aluminium 1.2" 2Air 26Plexiglas 1

Air 2. 4" '• 4

" 8Lead 5

Borated plastic 0. 6Concrete 60" • . 9 0

" 168» 208Lead 5

Borated plastic 0. 6Air 0. 4

6

Concrete 108

Magnetite

2

X

X

X

3

X

X

X

X

X

X

X

X

X

X

4

!X .

X

X

X

X

X

X

X

5

X

X

X

X

X

X

X

X

X

X

6

X

. X

X

X

X

X

X

X

X

X

X

X

Ordinary

7

X

X

X

X

X

X

x)

8

X

X

X

X

X

X

magne-tite)

Table 6. Macroscopic Removal Cross Sections for the Concretes

[lO~3 cm"1]

Concrete

Magnetite

Ordinary

P

[g cm" J

3. 74

3. 65

3. 52.43

••Water

[kg m"-J

133a>146

13314666

I65a>

Neutron Energy (MeV)

0. 5

288293281

286

232

291

1. 5

183186

179182151

182

2. 5

11812011511798

116

3. 5

141143

138140134

143

4 . 5

127128124125

110

107

5 . 5

118120

116117

101

95

6. 5

104105101102

91

80

7. 5

101102100101

89

78

8. 5

99100

97

9887

77

9 . 5

9192

8990

80

71

10. 5

92

93909081

73

11. 5

9596939484

78

12. 5

9798959585

81

13. 5

9798959586

83

14. 5

9595929383

81

15. 5

9192

909081

79

16. 5

9192

899081

79

17. 5

90

9188

8980

79

a) Most probable value at the time of the experiment.

Table 7. R2-0 Core parameters for RASH calculation

^ £ j ^ 61. 7 x 60. 0 x 32. 4 cm

formalj_zing_ 'J?ower: 100 kW

H20 58.4, : Al 41.4, U 0.2

Removal cross-sections:

Neutron Energy (MeV)

Neutron Energy (MeV)Er (cm-1)

0-1.387

9-10.0763

1-2.225

10-11. 0753

2-3

. 166

11-12. 0747

3-4

. 153

•12.-13.0742

4-5

. 127

13-14. 0738

5-6

.110

14-15.0718

6-7. 0974

15-16. 0680

7-8

. 0909

16-17

. 0669

8-9.0844

17-18. 0661

Relative Source Strengths:

1

2

3

4

5

6

7

8

Sx

1. 000.931.710

.489

Sy

1. 000. 89 6. 715

.. 570

Sz

1. 000.976.945

.901

.846

.776

. 718

. 765

Table 8. Energy Groups for RASH calculation

Group No,

1

2

3

4

5

6(Thermal)

Upper

2

0 . 3

0. 030. 01100

0. 105

En. Limit

MeV1!

It

It

eVi i

Table 9. RASH Multi-Group Parameters for Various Concretes

Concrete

p(g cm" )

Water(kg xxi )

Energy-Group

1

2

3

4

5

6

Magnetite

3. 74

D

1.35

i: 07

1.04

0. 75

0. 66

0.54

133 a

103-K2

27

55

165

61, 5

48. 3

100

)

103-*2

0

0

0

2

14.4

-

3. 50

50 b>

D

1. 57

1. 30

1. 30

0.89

0.775

0 . 4

103-K2

12. 5

21

56

21. 8

17. 5

146

, n 3 210 • a

0 . 8

1

1

2. 6

10. 7

-

Ordinary

2.43

165 a>

D

1. 64

1. 27

1. 26

1.08

1. 10

0. 69

3 ?10 • K

22.8

54.8

163

49.6

32.9

18. 6

103-«2

0

0. 01

0.01

0, 07

1. 86

a)

b)

Most probable value at the time of experiments.

Used, in R-3 calculations

D

K2

(cm)

(cm )

Table 10. Data for the gamma calculations

E » Macroscopic neutron capture cross-section (cm )

Y * (MeV/capture)

""• JL 1

- 1 ,y a Macroscopic gamma ray linear absorption coefficient {cm )

A) 2 • Y (10 MeV cm ) for thermal (th) and epithermal {epi) neutron fluxes.

Y ^-Energy (MeV)

Flux

Core

H2°Al

Plastic

Magnetite c oner.

Ordinary concr.

P b

Boron plastic

0(0-

th

18. 1

-

IV 65

-

2. 13

0. 56

-

754

71)

epi

-

-

0.40

-

0. 34

0. 09

-

107

2

C 1 -th

48.3

4.96.51

5. 79

10.1

3.49

-

4. 65

3)

epi

-

1.31

1.59

1.31

1. 62

0.56

-

0. 60

4(3 -

th

21. 1

• -

3.47

0. 06

5. 74

2.46

-

1.05

epi

-

-

8. 59

' • -

0.92

0. 39

-

0.15

6{ 5 -

th

1.4

-

1.57

-

8. 79

1.55

0. 25

0. 3.8

7}ep i

-

-

3.89

-

1.41

0. 25

0. 03

0. 06

8(>

th

1. 1

-

2.13

-

17. 7

0.93

4.46

0. 13

7)epi

-

-

5. 18

-

2.8.4

0. 15

0. 52

0. 02

iY -Energy (MeV)

Core

H2O

Al

Plastic

Magnetite concr.

Ordinary concr.

P b

Boron plastic

0. 7

15. 7

9.66

22.7

9. 14

31. 8

18.3

164.6

11.5

2

7

4

1

4

1

1

. 95

.93

1. 7

. 66

6 .3

0 .9

51.8

5 88

j ~

4

5.

3 .

8.

3 .

12

7.47

4.

62

39

37

17

. 1

73

. 6

90

6

4.

2.

7.

2.

10

6.

49

3.

74

75

13

52

. 7

54

. 4

19

8

4 .

2 .

6.

2,

.10

5.

52

2.

29

4

51

16

. 0

91

. 1

77

Table 11. Relative gamma sources for GASLIT

Region

All layers between thecore and concrete

Concrete

Width ordiam. of thediscs (cm)

36

60

No.ofdiscs

3

2

Relative sources

0.94 0. 61 0. 22

0.94 0.50

Table 12. Taylor build-up factors used in GASLIT

EnergyMeV

0. 7

2

4

6

8

Magnetite Concrete

A l

12.8

19.2

37.9

35. 0

30.0

0. 107

0.044

0. 014

0. 012

0. 012

0

0

0

0

0

Ordinary Concrete

A l

11. 5

6.3

3.9

3. 1

2. 7

" a i

0. 101

0. 069

0. 059

0. 059

0. 056

°2

0. 018

0.058

0. 079

0.083

0. 086

Table 14. Fission source density for NIOBE calculation .

Core diam. * 60 cmLayerNo.

1

2

3

4

5

6

7

8

9

10

Sourcer1A10 -3 -1]{10 n cm s J

8. 65

8.49

8.30

8. 05

7. 70

.7. 35

6.48

6.3 6

6. 10

6. 66

Table 13. R2-0 Core Parameters for NRN calculation

I. Data for fission source

A) Z * 0. 0438 cm" 2

B) Thermal flux

II. Data for gamma calculation

x [cm]

-30.85

- 1 4

- 4

0

4

14

30. 85

Sx [cm" s l]

7. 0, 11

1.07,12

1. 13, 12

1. 13,1-2

1. 07, 12

7. 0, 11

Y [cm]

-30

- 1 4

- 4

0

4

14

30

Sy

. 644

.924

1.0

1.0

.9.24

. 644

z [cm]

0

1

2

5

6.5

8

11

18

22

26

28. 5

31

32.4

Sz

.860

. 787

.768

.810

.855

.922

.990

.925

. 810

. 715

. 678

. 730

E [MeV]

.10865

. 4321.. 510 . 80.60. 50 . 40. 30. 20. 150.10. 080.060. 050. 040. 030. 020. 0150.01

X [cm]

24. 823.4,21.119. 717.815. 612. 711.88.857.946.906.255.714.98-3.893.063.152. 601.811.320.8260.4000. 2270... 09100.0277

°c + 0por

tot

0.9980.9980.9980.9980.9980.9980,9950.9950.9910.9 760.9 660.9620.9430.9150. 8250. 7060.8110. 7030. 5160.3850. 2490. 1240. 07320. 02970. 009 22

0 P0 + 0c p

0. 3300. 2570. 1600. 1360. 09480.05110. 01510. 003510

Table 15. Neutron fluxes in configuration 1 *

1

1

1

1

1

1

1

1

1

1.

2.

5

7.

10

12

20

30

50

70

90

00

10

20

30

40

50

60

70

80

Z

0

5

5

. 5

EXP

1.345,12

1 .43^0.03, 11 . 1 lto.24, 1

7.33to.16,1

4.60*0.10,1

2.40t0.60,1

6.44, 10

9 .5 l to .O2 ,9

3.48to.O8,8

1.88to.O5,7

1 .4 t o . 1 ,6

1,27to.O7,5

1.33"£o. 15,4

1.35to.2O,3

5.1 t o . 5 , 2

2.7 t o . 5 , 2

1.2 t o . 3 , 2

2

2

1

1

1

r -2 - ih Lcm s

RASH B 3

9.00,11

1.05, 12

8.03, 11

5.01,11

3.07,11

1.85, 10

4. 19, 10

6.84,9

1 .56,8

5.79,6

4.94,5

1.64,5

5.51,4

1.85,4

6.26,3

JNRN

7.20, 1

8.35, 1

7.20, 1

5.08, 1

3.33, 1

2.09, 1

4.44, 1

5.88,9

1 .74, 8

1.02,7

9,01,5

2.87,5

9.50,4

3.25,4

1. 15,4

1.56,3

5.94,2

2.30,2

9.06, 1

1

1

1

1

1

1

0

5

EXP

5. 26 t o . 60, 1

4.48to.58, 1

2.5oto.4O, 1

1.48to.27, 1

8.5 t 1.8,9

4.9 t o . 9 , 9

1.11 t o . 3 0 , 9

1. 9Oto.O8, 8

5.4 t 1.2,6

3.4 to .8 ,5

3.4 t l . 3 , 4

te

0

0

0

0

RASH B 3

3.45, 10

2.50,10

1 .21,10

6.00,9

3. 16,9

1.90,9

4.42,8

7.51,7

1,65,6

6.67,4

6.22,3

2.09,3

6.99,2

2.34,2

7.94,1

2.84,0

'JNRN

2.45, 10

1.90,10

1.13, 10

6.36,9

3.60,9

2.04,9

3.89,8

5.34,7

,1.82,6

1.17,5

1.07,4

3.44, 3

1.15,3

3.94,2

1 .40,2

1.92,1

P(n, p)

EXP

3.88to

2.65to.

2.40t0

3.42to.

1.22to

1.7 to.

5.7 t 2 .

02,5

02,4

07, 3

31,2

03, 2

2 ,1

1,0

kV]NRN

2.45,8

1 .85,8

1. 13,8

7.06,7

4.40,7

2.74,7

7.24,6

1.30,6

6.98,4

5.42, 3

5.75,2

1.92,2

6.59,1

2.38, .1

8.81,0

3.29,0

.1 .28,0

# 2 - 0 .

RASH

1.85,1

1 .59, 1

1 .03, 1

6.40, 1

3.97, 1

2.50,1

6.48,9

1.10,9

2,36,7

1 .03,6

1 .03,5

3. 45,4

1 . 16,4

3.90,3

1.32,3

9.71,1

3

B

1

1

1

0

0

0

MeV) cm s

3 NRN

1.85,11

1.32, 1 1

7.10, 10

3.95, 10

2.23, 10

1,27, 10

2.59,9

3.73,8

1 . 33,7

8.73,5

8.01,4

2.58,4

8.62, 3

2.97,3

1.06,2

3.87,2

1.45,2

Table 16, Thermal and epithermal fluxes, configuration 2.

Sign

F

F

F

01

02

03

04

05

F

f

Z

0

10

20

22

35

87

127

167

207

231

EXP

i . ioto.1 .82"to.1.64±0.

1.62"to.

02 ,

08 ,

14,

12,

9

6

4

2

r -2 -n[cm sRASH B 3

5.50,11

3.16,11

1.46, 10

1.37,10

7,95,8

1.05,6

7.68, 3

5.27, 1

6.45, -1

1 ,02 , -2

NRN

5.50,11

3.01,11

1.61,10

7.29,8

3.12,6

2 .98 ,4

3.50,2

5.30,0

9 .83 , - 2

3.

5.

4.

4 .

EXP

05±0.85.to.

13to.4 +, .

15,8

27,5

25,3

U

0 . err

RASH B 3

3.82, 10

3.32,9

5.52,8

5.32,8

1 .58 ,8

2. 32,5

1.41, 3

1.20,1

1 .28, -1

2 . 8 0 , - 3

NRN

2.75,10

3.13 ,9

4 .57 ,8

1 .74, 8

7.31,5

6 .91 ,3

8. 34,1

1.29,0

3 .08 , -2

NIOBE

2.

2..

1 .

1 .

6.

5.

5.

5.

6.

8.

74,

5 1 ,

4 1 ,

36,

00 ,

65,

74,

95,

15,

86 ,

10

9

8

8

7

5

3

1

-1

_3

Table 17. Fast fluxes and gamma exposure ra tes , config. 2.

Sign.

F

F

F

01

0 2

0 3

0 4

0 5

F .

Z

0

10

20

22

35

87

127

167

207

231

EXP

1.6Oto1 . 0 9 + O .

8,75to.6.4 to

01

06

70

6,

,6

, 3

,0

-2

(n,p) 1?

' NRN

2.99,8

3.64,7

6.52,6

9.81,5

1.66,3

1.96, 1

3.03, -1

5.45, -3

4 .61 , -4

r-'.-TNIOBE

2.05,8

7.8,5

1 .52,3

1 . 45, 1

1.56,-1

1.71,-3

9.74, -6

0(2-0. 3MeV) | c m ~ 2 s ]

RASH B 3

2.08,11

4.32, 10

7.28,9

5.87,9

8.59,8

7.55,5

4.88,3

4.82, 1

5.23, -1

2.33, -2

NRN

2.38, 11

2.00, 10

3.14,9

8.92,8

2. 14, 6

2.05,4

2.67, 2

4.35,0

2.30, -1

1

I

!

FILMS .

.1 t o , } , 2

.osto.10,0

.7 t o .3 , -2

E

ION CHAMB.

1

1

1

1

6

ioto.30tQ.

0 to..2 to

Scint. •

12

05

05

1,

5,

, 5

,2

, 0

-2

-4

r [R/h|

IND.DET.

1

!

1

6

1

.O4to

.35to.

.0 to.5 t 2 ..0 to

05

13

3,

5,

3,

,2

,0

-2

-4_5

GAS LIT

1.62,6

1 .70,5

1. 31,2

1.08,0

1.21,-2

1.62,-4

1.40,-5

SALOMON

2.3to.2,3.3to.3,1.1 to .1 ,1.9-0.2,

3.2to.5,5.4to.5,4.oto.7,(3.3to.7

5

4

2

0

-2

-4

-5

,-5)

Table 18. Thermal and epithermal fluxes, configurations.

Signo

F

F

F

F

F

F

T 2

F

T 3

T 4

T 5

F

Z

0

10

15

17

43

44

52

82

1 12

120

162

202

226

0 1EXP

3. I5 to .

2. 1 9"to.

T . 1 4 ^ 0 .

1.83to.3.20t0.5.36to.1.86^0.

1.3 to .

05, 10

08, 10

01 , 10

06,8

16,6

14,5

01,4

2 , 2

' -2 - l lcm s JRASH B 3

5.50,11

2.84, 1 1

2. 17, 10

1.97, 10

1.97,10

8.22, 9

8.22,9

9.05,7

1.62,6

1.35,5

3.98, 3

3.19,1

4 .89 , -1

NRN

5.50,11

2.92,11

8.15,10

7.72,10

7.72,10

3.95,10

3.95, 10

2.25, 8

5.02,6

6.57,5

1.60,4

1.43,2

2.51,0

EXP

*.34to.7. 13^0.

6.29^0,5.53to1.7lto5.45to4.6lto

02 ,

12,

40,

16,

08 ,

19,

3 1 ,

98

8

7

6

5

3

JÖ . c m " i

RASH

3.82,

.3.05,

4.77,

3.74,

3.74,

3.04,

3.04,

2.11,

4 .61 ,

•7 . 10,

8.72,

7. 12,

1.36,

B 3

10

9

8

8

8

8

8

7

5

4

2

0

-1

• iNR]S

2.73,

3.50,

1 .22,

1.17,

1.17,

9.17,

9. 17,

5.82,

1 .67,

5 . 2 1 ,

3.65,

3.40,

7.65,

[

10

9

9

9

9

8

8

7

6

5

3

1

-1

NIOBE

7.

1 .

3.

7.

6.

6.

8.

90,8

01,9

80, 7

77,5

45,3

20, 1

89, -1

Table 19. Fast fluxes and gamma exposure rates, config. 3

Sign

F

F

F

F

F

F

T2

F '

T 3

T 4

T 5

F

Z

0

10

15

1 7

43

44

52

82

112

120

162

202

226

EXP

1.39*0.02,7

6 . 4 1 * 0 . 5 8 , 6

5 . 6 9 * 0 . 2 3 , 6

4 . 9 3 * 0 . 0 2 , 61 .69*0.02,-5

3 .48*0 . 12,3

1.23*0 .04 ,3

3 .57 *0 .82 ,0

NRN

1.52,7

1.20,7

1.03,7

8 .09 ,6

7. 8-4, 6

1 . 35,5

3.49, 3

1.01,3

7 .57 ,0

1. 18, -1

1 . 02 , -2

NIOBE

6.88, 6

4. 37,6

5 .38 ,6

4 . 9 9 , 6

1 .62 ,5

4 . 9 5 , 3

2.37, 3

1.55,1

1 .43 , -1

7 . 8 1 , - 3

0(2-0. 3MeV)jcm"2s"1|

RASH B 3

2.08,11

3.94, 10

1.20,10

5.55,9

5.55,9

4.64, 9

4.64,9

8.23,7

1 .77,6

7. 38,5

2.92,3

2.73,1

1 .02,0

NRN

2.38 , 1 1

2. 15, 10

8. 15,9

6 .99 ,9

. 6.99,9

5 .60 ,9

5 .60 ,9

2 .00 ,8

5 .62 ,6

2 . 0 9 , 6

9.20,3

1 .04, 2

5.44,0

FILMS

2.2*0.

1.1*0.

9.1*0.

7.0*0.

1.2*0.

3.7*0.

2.7*0.

5.5*0.

4.4*0.

6,6

1,6

4 , 5

5,5

2,4

3 , 2

2 , 1

6,-1

3,-3

DrION CHAMB.

5

1

3

9

8.

9

.2 to

.28*0

6

* 1

5

*

to., -1

to.

. 7 ,5

. 5 0 , 4

1 J

2 , - 3

2 , - 4

1

2

7

1

1

[k/h]IND.DET.

.6*0 .4 ,

.8*0 .4 ,

.9*0 .7 ,

.0*0 .3 ,

. 1 * 0 . 1 ,

4

1

-1

- 2

- 3

GAS LIT

1.91

7.5,

6.09

5.05

7.55

1.62

1. 32

• 1 . 74

2. 10

1 .43

,6

5

,5

,5

,3

, 2

, 1

, -1

, - 3

, - 4

3.

6.

2 .

2 .

3.

4 .

3.

(3

NRN

6*0.

8*0.

1*0.

7*0.

6*0.

3*0.

0*0.

4 * 0

4,

7,

2 ,

3,

4 ,

4 ,

3,

5

3

2

1

-1

- 3

_4

.4,-4;

t

Table 20. Thermal and. epithermal fluxes, configuration 4

Sign

' F

F

F

F

F

F

T2

T3

T 4

T5

F

z

0

15

17

43

44

52

82

112

122

162

202

226

tn.

EXP

3. is to.05,10

2.19*0.08,10

1 . 14 to ,O l , 10

1 .85-0.02,8

3.72*0.25,6

3.08*0.29,6

3.44*0. 10,4

2.86*0.27,2

r -2 -n[cm s>- A

RASH B 3

5 . 5 0 , 1 1

2 . 1 7 , 1 0

I . 97, 10

1.97,10

8 . 2 1 , 9

8. 21 ,9

9. 10,7

2 . 1 1 , 6

? . 2 5 , 6

7 . 2 4 , 3

6 . 0 2 , 1

9.40, -1

NRN

5 . 5 0 , U

8. 14, 10

7 . 7 1 , 10

7.71,10

3.94, 10

3.94, 10

2.26 ,8

7.37,6

4. 34,6

3 .43 ,4

3.63,2

6 .47 ,0

' -2 - ] ]cm s 1

epi _EXP

1.34*0.02,9

7. 13*0. 12,8

6.29^0.40,8

5.44*0.07,7

1.73*0.21,6

] . 19*0.04,6

7.5 t o . 5 , 3

j

RASH B 3

3.82, 10

4.77,8

3.73,8

3.73,8

3.04, 8

3.04,8

2. 1 1,7

4.65 ,5

2.74,5

1.58,3

1.35, 1

2.62, -1

NRN

2 . 7 3 , 10

1.22 ,9

1. 17,9

1 .17 ,9

9. 17,8

9. 17,8

5 . 8 4 , 7

1 .75 ,6

1 . 0 2 s 6

8 . 0 2 , 3

8 . 8 2 , 1

1 .99 ,0

Ai r space ** 6 cm

Table 21 , .Fast fluxes and gamma exposure rates, config. 4

F

F

F

F

F

F

T2

D-E*

• T3

T 4

T5

F

z

0

15

17

43

44

52

82

112

122

162

202

226

P (n,p) Lg

EXP

1 . 39to.O2,7

6 . 4 l t o . 5 8 , 6

5 .69 to .23 ,6

4 .93 to .O2,6

1.66+-0.O1,5

3.3oto .O6,3

2.39^0.06,3

1 . 6 8 t o . 1 1 , 1

- 1 - T ' js JNRN

2.99 ,8

1 .53 ,7

1.20,7

1.03,7

8.09,6

7.84,6

1 . 33,5

3.04, 3

1.75,3

1.86,1

3. 15, -1

2.63, -2

0(2-0. 3MeV) [cm""2s"1|

RASH B 3

2.08, 1 1

1 .20 , 10

5.55 ,9

5.55,9

4 .64 ,9

4.64,9

8 .20,7

1.43,6

8. 34,5

5.42, 3

5.27, 1

1.94,0

NRN

2. 38, 1 1

8.15,9

6.98 ,9

6 .98 ,9

5.59,9

5 .59 ,9

1.98,8

4 .67 ,6

2.70,6

2 .21 ,4

2 .75 ,2

1 .43 , 1

2.

1 .

9.

7,1 .

2.

1 .

1.

i

FILMS

2to.6,6

l t o .1 ,6

i t o .4 ,5

Oto.5,5

2+-0.2.4

5 t o . 2 , 2

80 t0 .15 ,2

6 t o . 2 , 0

8+-0.8,-2

ION CHAMB.

5

1

2

2.

2

2+0

28^i

3to.oto3±0.

7,

).<

4,

6,

2,

5

)5 ,4

2

0

-2

D r [R/h]

IND.DET.

1.4to.2, -3

GAS L I T

1.91,6

7,5,5

6.09,5

5.05,5

9.63,3

4.7,2

1.50,2

K l 1,0

1 . 35,-2

K02, -3

9.

2 .

6.

4.

5.

5.

4 .

(4-

NRN

2+-0.

9+-0.

5+-0.

ito.4+-0.

oto.oto.

9

2

7

5

5

5

6

6

5

, 4

, 2

, 2

,0

, - 2

, - 3

, - 3 )

XAir space ft 6 cm

Table 22. Thermal and epithermal fluxes, configuration 5

Sign

F

F

F

F

F

F

T2

F

T 3

T 4

T5

F

Z

0

10

12

38

39

47

77

107

115

157

197

221

EXP

1.35to.O5,11

7.23^0.18,10

2.78to.O2,10

3.97t0.04,8

6.12^0,03,6

9.20^0,60,5

3,92^0.01,4

2.90-0. 10,2

" -2 -1]cm B J

RASH B ,

5.50,11

5.65,10

5.07,10

5.07,10

2.09, 10

2.09,10

2. 12, 8

3. 19,6

2.90,5

7.00s 3

5.48, 1

8.45, -1

NRN

5.50,11

1.72,11

1 .64 , 11

.1 .64 ,11

8.67, 10

8.67, 10

5.82, 8

1 . 18,7

1 .50 ,6

3 .39 ,4

2 .73 ,2

4. 36,0

0 . [cm'Vi^epi L j

EXP

4.8 t o . 6 , 9

2.6 l to .21 ,9

1 .5 l to .10 ,9

1.24^0.05,8

3 .39-0 .07 ,6

1.17to.O2,6

9.7Oto.5O,3

RASH B 3 ;

3.82, 10

1.34,9

1.00,9

1 .00 ,9

8.01,8

8.01,8

4 .98 ,7

8.84,5

1 .45,5

1 .56S3

1.25,1

2.3 0, -1

NRN

2.73, 10

3.70,9

3.55,9

3.55,9

2 .71 ,9

2 .71 ,9

1.49,8

3.85,6

1.16,6

7 .61 ,3

6.51 ,2

1.32,0

Table 23. Fast fluxes and gamma exposure rates, ccmfig. 5

Si P"n

F

F

F

F

F

F

T2

F

! T3

T 4

T 5

F

z

0

10

12

38

39

• 4 7

77

107

1 15

!57

197

221

(n, p)-1

a

EXP

2. 94-to. 02,

9.97*0.18,

3.34*0.02,

6. 76-0.64,

2 .40-0 . 01 ,

1.6 to .1 ,1

7

6

5

2

3

-11s i

NRN

2 .99 ; 8

3.83,7

2.98,7

2 .57 ,7

1.99,7

K 93, 7

2.90,5

6,83,3

1 .90 , 3

1 . 40, 1

2.08, -1

] . 70 , -2

0(2-0, 3MeV) |cm"2s~]

RASH B ,

2.08, 1 1

3.08,10

1.37, 10

1.37,10

1 . 14, 10

1,14,10

1 . 77,8

3. 30,6

1.31,6

5.23, 3

4.89, 1

1.77,0

NRN

2.38,1 1

2.41 , 10

2,04, 10

2.04, 10

1.60,10

1 .60, 10

4.86 ,8

1 . 24, 7

4.44 ,6

1 . 8 2 , 4

1.92,2

9.21,0

2.

9._

1 .

4 .

4 ,

9,

1 .

FILMS

8

2

2

9

8

3

5

to. 2,

to 5to, 2,t 0 . 3 ,

t 0 . 4 ,

to.9,

to ,3 ,

6

5

4

2

1

-1

-2

ION CHAMB.

2.1 t o . 8,0

1.2 t o . 1 , -2

Dr tk / h ]IND.DET.

9.3to.4, -11 .5*0 .4 , -2

2. 3*0.3, -3

GAS LIT

3

8.

]

3.

2

2

3.

2.

. 07

91 ,

36,

06,

30,

5 1 ,

20,

29,

,6

5

4

2

1

-1

-3

-4

NRN

2.3*0.

4.5to.

6.5*0.

1.2*0.

1.2*0.

1.45*0

i . i to .( 7 . 0 * 1 .

2,

5,

6,

1 ,

1 ,

. 1

1 ,

0 ,

6

4

3

2

0

5, -2

-3

-4)

Table 24, Thermal and epithermal fluxes, configuration 6

Sign

F

F

F

F

F

F

F

T2

F

T3

T 4

T5

F

Z

0

10

12

38

39

41 . 4

47

77

107

1 15

157

197

221

KEXP

1.35to.O5,11

7.23*0. 18, 10

3.28*0.04, 10

5.56 t i . lO ,8

2. 72*0. 13, 8

3.8oto.O8,6

4 .54 to .25 ,5

2.2Oto.O5,4

1.29*0.10,2

' -2 -1]cm s

RASH B 3 '

5.50,11

5.71,10

5. 14, 10

5. 14, 10

2. 19, 10

2. 19, 10

1 .68 ,8

1 ,33 ,8

1.75,6

1.55,5

3.84, 3

3.05,1

4.69, -1

NRN

5.50,11

1 .71 , 1 1

1.62,11

1.62,11

8.38,10

8.38,10

5. 31,8

2.91 ,8

4 .92 ,6

5.83,5

1 . 2 6 , 4 •

1.00,2

1 .61 ,0

0 . [ernes'1!epi I. J

EXP

4.8 to .6 ,9

2 .61*0 .21 ,9

1.93*0.25,9

6 .61*0 .46 ,8

8 .21*0 .47 ,7

1.89*0.08,6

6.09*0.06,5

4 .73*0 .48 , 3

RASH B 3

3.82, 10

1.33,9

9.81,8

9.81,8

7.46,8

7.46,8

1.49,8

3.07, 7

4.81,5

7 .70 ,4

8.50,2

6. 94,0

1 .28, -1

NRN

3.73, 10

3.78,9

3.62,9

3.62,9

2 .57 ,9

2.57,9

9.55,8

7.22, 7

1.55,6

4.53,5

2.81,3

2.38,1

4.87,. -1

Table 25. Fast fluxes and gamma exposure rates, config. 6

Sign

F

F

F

F

F

F

F

T 2

F

T 3

T 4

T5

F

Z

0

10

12

38

39

41 . 4

47

77

107

1 15

157

197

221

1 .

5,

?.

3.

1 .

1 .

P ( n , P)

EXP

39to.95to.87t0.

97-0.

2Oto.

38to.

06,

18,

02 ,

1 1 ,

0 1 ,

23,

7

6

5

3

3

1

-i -nJ

NRN

2.99-, 8

3.98,7

3.18,7

2.77, 7

2.24, 7

2.22,7

6. 9 6 , 6

1 ,04,5

2. 48,3

6.87,2

5.19,0

7-98,~2

6.46, -3

0(2-0.

RASH

2.08,

3. 27,

1 .63,

1 .63,

1.45,

1 . 45,

7.56,

9.70,

1.73,

6.79,

2.85,

2.68,

9.89,

3MeV)[cm"VJ|

B 3

1 1

10

10

10

10

10

9

7

6

5

3

1

-1

NRN

2.38, 1 1

2.55, 10

2.21,10

2 . 2 1 , 10

1,32, 10

1.82,10

9.91,9

2.00, 8

4.63,6

1 ,65,6

6.62, 3

7.06,1

3.41,0

1

4

4

1

2

5

F

.2

. 5

. 5

. 7

. 2

. 4

ILMS

to.+0,

to.to.to.to.

1 ,

5,

6,

2,

2,

2 ,

64

3

2

1

-1

°y MION CHAMB.

2.7 to .3 ,1

8 ±4, -1

IND.DET.

1.6 to .4 ,1

5.8 to . 6, -1

4 t l , - 3

1.1 t o . 3 , - 3

GAS L IT

3.09,6

1 .07 ,6

1.10,5

2.85,3

7.79,1

6. 12,0

1 .07 , -1

1 .46 , -3

1 , 0 6 , - 4

NRN

9.010.9, 4

3. ?to.4, 3

1 . s t o . 1 , 2

9 .o to .9 ,O

2.0 t0 .2 , -1

3 . 3 t o . 3 , - 3

3.0t0,4, -4

(2.<>to.4t -4)

Table 26. Thermal and epithermal fluxes, configuration 7

Sign

F

F

F

T l

F

F

T2

T3

T 4

T5

F

Z

0

10

12

27

39

43

77

117.6

157

197

210

EXP

5.30t0.03

1.82to.O2

2.91-0 .03

4.83-0 .05

8.ioto.30

2.0 to.2,

, 1 0

,9

, 7

, 5

, 3

3

L c m s JRASH B 3

5.50,11

7.-30, 10

6.68, 10

6,68, 10

4.09, 10

4.09,10

1 .27 ,9

1 .77 ,7

2.90,5

3.71,3

9.56,2

NRN .

5.50, 1 1

2. 13, 11

2,04, 11

2.04, 1 1

1 .28, 1 1

1.28, 1 1

3.00,9

4.27,7

6.55,5

1.08,4

2 .24 ,3

2.

7.

1 .

1 .

3.

0 •epi

EXP

39t0.06

l6to.8O

O2to.O3

79^0.09

9 to.4,

r -2 -iiicm s |

,9

, 7

,6

, 4

2

RASH B 3

3.82, 10

V.61,9

1.21,9

1.21,9

8.97,8

8.97,8

3.87,7

4 .56 ,5

7.66,3

1 . 34, 2

4.53, 1

NRN

2.73, 10

3.58,9

3.42,9

3.42,9

2.47 59

2.47 ,9

1.03,8

1 .20 ,6

1.77,4

3.32 ,2

1.08,2

Table 27, Fast fluxes and gamma exposure rates, config. 7

Sign

F

F

F

Tl

F

F

T2

T3

T 4

T5

F

Z

0

10

12

27

39

43

77

117.6

157

197

210

i

1 .

3.

4 .

9.

•p

( .

EXP

00±0.

12±0.

10±0.

01

01

18

41

)[g

,7

,5

, 3

,1

- 1 -11s

NRN

2.99 ,8

3.92,7

2 .97 ,7

2.46,7

1 .98 ,7

1 .77 ,7

3.28,5

3.69, 3

7.36,1

1.86,0

4.74, -1

0(2-0. 3MeV)|cm'"V1]

RASH B 3

2.08,11

1.70,10

8 .18 ,9

8 .18 ,9

6 .78 ,9

6 .78 ,9

1 . 16,8

1 .48, 6

2 .57 ,4

3. 31,3

1.93,2

NRN

2.38, 11

2,39, 10

2.01,10

2,01,10

1.54, 10

1 .54 , 10

3.58,8

3.74,6

5 .83 ,4

1. 19,3

3.78,2

2 .

8

3.

1 .

6

FILMS

7 to.2,4±2,2

0 to .6 ,1

9 ±0.2,0

±1,-1

I O N

1 , 3

3 .2

CHAMB.

to. 1,6

to.2,41 . 00±0.03, 3

3.6Oto.O3,1

1.9

6.4

to. 1,0to. 4, -1

IND.DET.

3.2 t o . 5 , 1

1.8 t o . 3,0

GAS L I T

2 .86 ,6

1.60,6

9.87,5

3 .02 ,4

7. 36,2

2.78, 1

1 .35 ,0

5.68, -1

NRN

2.7±0.3,5

1.9±0.2,4

8. l t o . 8 , 2

6.2±0.6,1

4. Oto.4,0

1.7±0.2,0

(2.4to.3,O)

Table 28. Thermal and epi thermal fluxes, configuration 8

Sign

F

F

F

F

F

F

T 2

T3

T 4

T5

F

Z

0

50

52

78

79

83 '

1 17

157.6

197

237

250

A,EXP

7. 15*0.05,7

5 .23*0.05 ,7

3 .89 -0 .07 ,6

1.30*0.10,5

2 .80*0 .10 ,3

r ~z - i iJem s jRASH B

5.50,1 i

2 .43 ,7

2 .32 ,7

2. 32,7

1 . 60 ,7

1 . 60 ,7

1 . 44,6

5 .16 ,4

\.60,3

4 .49 , 1

1.01,1

NRN

5,50.. 1 1

1 . 4 1 , 8

1 . 36,8

1.36,8

8. 94 ;7

8.94 ,7

4. 245 6

1 .80 ,5

3.79, 3

1 . 05 ,2

2.40, 1

e pi L

EXP

2.80*0 .20 ,6

2 .09*0 .11 ,6

2.OOto.10,5

4 .70*0 .50 ,3

2 . 5 t l . 0 , 2

-2 -1•n s

RASH B 3

3.82, 10

5.45 , 5

4 .86 ,5

4 .86 ,5

4 .26 ,5

4 .26 , 5

6 .27 ,4

1.82,3

5 .43 , 1

1.55,0

5.74, -1

NRN |

2. 73, 10

2 ,18 ,6

2. 13,6

2, 13,6

1.79,6

1 .79 ,6

1 .87 ,5

7.40, 3

1 .35 ,2

3.88,0

1 . 40, 0

Table 29. Fast fluxes and gamma exposure rates, config. 8

Sign Z(n,p)

EXP NRN

-2 -1

RASH B. NRN

D

FILMS ION CHAMB. IND. DET. GAS LIT NRN

F

F

F

F

F

F

T2

T3

T4

T5

F

0

50

52

78

79

83

1 17

157.6

197

237

250

7.26^0.12,3

4. ioto. 18,4

1.70t0.07,3

9.92to.47, 1

2.99,8

6.98,4

5.73,4

4.79,4

3.99,4

3.91,4

1 . 44, 3

3. 15, 1

9.28,-1

2.90,-2

9.40, -3

2.08,U

6.48,6

4.73,6

4.73,6

4. 34,6

4.34,6

2.93,5

7.65,3

2.23,2

6.46,0

2.55,0

2.38, 11

1.68,7

1.52,7

1.52,7

1.29,7

1.29,7

8,07,5

3.06,5

5. 17, 2

1.51,1

5.20,0

7. 3 to.7,4

5.3 to. 4, 4

2.0 to. 3, 3

1.0 to.2,2

3. 7 to. 3,0

3.4 to. 3, -1

2 .5

9.0

5 . 5

3 .6

1.0

to.to.t o .

to.to.

1,

5,

2,

2 ,

2,

3

1

0

-1

-1

3.6 to.6,0

2.2 to. 7, -1

1.76,5

9 .41 ,43.28,3

1.67,2

3.82,0

1.97, -1

8. 38 , -2

(

3. 8-0 . 4

3.1 to.31.8to,21.1 to.1

9.0t0.94.5to.55.6to.6

, 4

, 3

, 2

, 1

, - 1

-1

Fig. i. R2-0 reactor with shielding facilities.

oooooooooo

D

ooXXXXXXoo

c

oXXXXXXXXo

B

oXXXXXXXXo

A

oXXXXXXXXo

8

10

Axis of measurement

XX

Fuel element

Control rod element

Dummy element

Fig. 2. R2-0 core loading.

02

01

0203CH05

S3

fS£

/

Pool

M

RCD

= 0 O Oj ] =

— o o o o 6\2 -

~ o ö ö 5 bJ3

o o o o oJ5

NI1 1 1 1 1

S5

/

1

I

1

— 1 1

1

1

0 5m

Fig. 3. The R2-0 shielding facilities. Plan view.

o

I Water

[Ordinary concrete

i Magnetite concrete50 100

Lead (5cm) borated Lucite

200 (cm) 250

t

5 ;

10f

LJin:il t8»—»

Trm

5,0

Fig. 4. Configurations for the bulk shielding study.

/ B:0f with P (10-10* cps)/ C;0f with film (DY-CL02-2r)

D:0th with Mn (Dmin « 1cps)

/ T.3

^?57T7VVV

T5C* ffB-plastjcVW[Concre

i r-10 0 50 100 150 (cm) > 200

Yig. 5. Usable ranges vs. exposure for neutron detectors in config, 3.

Exposure(kWh)

,2-10

-10 !

-10c

-10',-1

-10'.-2

-10-3

T1

unsensitive comp.(50-500r)»sensitive comp.(03-5r)

:Gamma pens (0.02-0.2r):Gamma pens(60-600r): Landsverk ionchamber (0.002-1000 r)

T.5

Reoctor Hp j - A l -Air

-10 0 50 100 150 (cm) 200

Fig. 6. Usable ranges vs. exposure for gamma detectors in config. 3.

10

5

2

1

0.5

- f

_ Removal_ Removal

-

Ill

I

—

sourcesource

50

(p=3.74,133 kg water

——

100

m"3)

__——-—_ _ — — ' • — •

Magnetite

_ —

concrete

150i

p=3.74, w=H6

• M M

200i

(cm) from the cone

•Ml!

—

J-JJ

JL

250

Fig. 7. Removal source in config. 3. as a function of the density and

water content of the concrete.

^Centre for R # « 80 o» i"Centre for ft's •

Fig. 8. Determination of the effective core radius for spherical

geometry from isoflux lines.

Fig, 9. Relative thermal fluxes in configurations 3 and 2 as a

function of the core radius.

118R

En (MeV)

4- 2

-4-0

—— = Fixed energyboundary.

= Boundary offree choice.

R=Removal groups.\ D= Diffusion groups.

u

D

"RASH B NRNFig. 10. Principles for neutron slowing-down in RASH/B and NRN methods.

•*- =NRN• — =N!OBE

tr

y

f

10°

0.90.8

r\~ 310~J 10~2 10"1 10°—*E(MeV)

Fig. l i . Neutron spectra in config. 2 at z = 35 cm by NRN and NIOBE.

Neutron fluxes;»= measured values

•—=:. RASH calculation

~~= NIOBE calculationA - P(n, p) reaction rate

Gamma exposure rates (D. ):

.=: NRN calculation, ^-plane.•"- geometry

- measured with films

" G~M detectors

i o n chambers

Materials:

r- 1

Air

Water

XXXXl Magnetite concrete

Ordinary concrete

Al (2cm); Pb (5 cm) + borated lucite

Fig. 12, Explanation of the signs.

0epi(NRNH

N.

-. A(P)(NRNM

fi

2

1

0.5

0.2

0.1

5

2

1

0.5

0.5

0.2

0 50 100 150 —»cm 200

Fig. 13. Neutron fluxes in configuration i (water).

ffepi (NRN)*1

* ——

2

1

0.5

0.2

0.1

5

2

1

0.5

0.2

0.1

0 50 100 150 »»cm 200

Fig. 14. Thermal and eplthermal fluxes in configuration Z.

A(p)(NRNM

2

1

0.5

0.2

0.1

0.1

150 —>cm 200

Fig. 15. P(n, p) reaction and, gamma exposure rates,

configuration 2.

l _

2

1

0.5

0.2

0.1

5

2

1

0.5

0.2

0.1

0 50 100 150 —Km 200

Fig. 16. Thermal and epitherrnal fluxes, configuration 3.

0

D-y(GASUT)»1

0.5

0.2

0.1

50 100 150 200

Fig. 17. P(n, p) reaction and gamma exposure rates,

configuration 3.

-S5

2

1

0.5

0.2

0.1

I TO 50 100 150-—»cm 200

Fig, 18. Thermal and epithermal fluxes, configuration 4.

A(p)(NRN) = 1

0.5

0.2

0.1

5

2

1

0.5

0.2

0.1

Fig. 19. P(n> p) reaction and gamma exposure rates,

configuration 4.

r* y i

0th(NRN}=1

\ I Efepi(NRN)=1A1 -s-—"-"-\I \

LJL -Li i

—

—

i^~ "." _——|>WO0O(>00<X)O0^TSA^AAAAAAA A A A A A

— nr

2

1

0.5

0.2

0,1

5

2

1

0.5

0.2

0.1

0 50 100 150 —»cm 200Fig. 20. Thermal and. epithermal fluxes, configuration 5.

-I A;p)(NRN)-1

0.3-2 MeVJ

£"" — — ~— 5

2

0.5

0.2

10

0.5

0.2

0.1

0 50 100 150 - * c m 200Fig. 21. P(n, p) reaction and gamma exposure rates,

configuration 5.

0 50 100 150 —-> cm 200Fig. 22. Thermal and eplthermal fluxes, configuration 6.

0 50 100 150 ~> cm 200

Fig. 23. P(n, p) reaction and gamma exposure rates,

configuration 6,

I—il

0th(NRN)=1

2

1

0.5

0.2

0.1

5

2

1

0.5

0.2

0.1

0 50 100 150 —* cm 200

Fig, 24, Thermal and epithermal fluxes, configuration 7.

A(P) (NRN)=1

mni

2

1

0.5

0.2

0.1

5

0.5

0.2

0.1

0 50 100 150 - * c m 200

Fig. 25. P(n, p) reaction arid gamma exposure rates,

configuration 7.

v—v

Z \

\

2

1

0,5

0,2

0,1

MTTTT

0,2

0.1

0 50 100 150 200 -—> cm 250

Fig. 26. Thermal and epithermal fluxes, configuration. 8.

0 50 100 150 200 —> cm 250

Fig. 27. P(n, p) reaction and, gamma esposure rates,

configuration 8,

Fig. 28. Definitions of the coordinates for a detector

in a channel.

T—T 1 1 1 T 1 T

0 = open channel1 » channel filled

N

o tt-

5 rneasu rements I \

Results compared tocalculations at Z = centerr"

_^o' I ° o^-Mn- falls.

Hkx

Jep\

\

-U-—L, _L L

10s

101

80 85 , Z(cm)

Fig, 29. Flux distributions in an open vs. filled channel

in magnetite concrete.

115

T—r

i^uCu

i

fMn/

i i

T—i—r

open chonn sL

calculated (RASH)

120i L

/(ncm'VS

•' I

125 2 (cm)

Fig. 30. Thermal flux distribution in channel T 3,

configuration 3,

101

10"1

ion

10,-3

10"

A t

= Observed values

0 20 30 40 50 60 70> Z (cm)

Fig. 31. Observed and predicted heating rates in

configuration 2. ' • '

+ => Fresh concrete (11th.Nov.-61), uncorrectedFresh concrete, corrected for the amplifiardr i f t observed, (-0.5±0.1 °C/h)

o = Dried out concrete (22nd.Jan, 1st. Feb.-62),uncorrected.

0.1

Z(cm)

Fig. 32. Observed and predicted heating rates in

configuration 7,

Fig. 33. Gamma exposure rate originating per 10cm shield

thickness for a dose point on the outside of config.2.

!77t

/ /

EZZ3 RASH-GASUT

[ I I I ] NRN

I T• !

— j — —

_ _ _ s

— 11tr

Ii1t

per centof Dy (2*221)per 10 cm shield

*

i ~~\11f111f

15

-10

r~-f

0 50 100 150 — * Z ( c m ) 200

Fig. 34. Gamma exposure rate originating per 10cm shield

thickness for a dose point on the outside of config. 5.

15

3 RASH-GASLIT

I] NRN

per cent !of D*(Z«221)per 10 cm shield)

I 10

50 100 150 —-Z(cm) 200

Fig . 35. Gamma exposure r a t e or ig inat ing pe r iOcm shield

th i ckness for a dose point on the outs ide of config. 6.

50 100 150 ~ * Z ( c m ) 20C

Fig. 36. Gamma exposure rate originating per 10cm shield

thickness for a dose point on the outside of config. 7.

150

10"

200 —(cm)

Fig. 37. Relat ive fast flux in configuration 3 by nuclear

emulsion method.

LIST OF PUBLISHED AE-REPORTS

1—80. (See the back cover earlier reports.)

81. The resonance integral of niobium. By E. Hellstrand and G. Lundgren.1962. 14 p. Sw. cr. 6:—.

82. Some chemical group separations of radioactive trace elements. By K.Samsahl. 1962. 18 p. Sw. cr. 6r—.

83. Void measurement by the (y, n) reactions. By S. Z. Rouhani. 1962. 17 p.Sw. cr. 6,:—.

84. Investigation of the pulse height distribution of boron trifluoride pro-portional counters. By I. D. Andersson and S. Malmskog. 1962. 16 p.Sw. cr. 6,:—.

85. An experimental study of pressure gradients for flow of boiling waterin vertical round ducts. (Part 3). By K. M. Becker, G. Hernborg and M.Bode. 1962. 29 p. Sw. cr. 6:—.

86. An experimental study of pressure gradients for flow of boiling waterin vertical round ducts. (Part 4). By K. M. Becker, G. Hernborg and M.Bode. 1962. 19 p. Sw. cr 6:—.

87. Measurements of burnout conditions for flow of boiling water in verticalround ducts. By K. M. Becker. 1962. 38 p. Sw. cr. 6:—.

88. Cross sections for neutron inelastic scattering and (n, 2n) processes. ByM. Leimdörfer, E. Bock and L. Arkeryd. 1962. 225 p. Sw. cr. 10:—.

89. On the solution of the neutron transport equation. By S. Depken. 1962.43 p. Sw. cr. 6:—.

90. Swedish studies on irradiation effects in structural materials. By M.Grounes and H. P. Myers. 1962. 11 p. Sw. cr. 6:—.

91. The energy variation of the sensitivity of a polyethylene moderated BFjproportional counter. By R. Fräki, M. Leimdörfer and S. Malmskog. 1962.12. 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. 1962. 18 p. Sw. cr. 6:—.

95. The paramagnetism of Mn dissolved in n and fi brasses. By H. P. Myersand R. Westin. 1962. 13 p. Sw. cr. 6 : - . H

96. Isomorphic substitutions of calcium by strontium in calcium hydroxy-apatite. By H. Christensen, 1962. 9 p. Sw. cr. 6:—.

97. A fast time-lo-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. 6r—.

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. 6:—.

101. Solid angle compulations 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)m?reaction. By J. Koniin. 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-! 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. Biörn-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. 8r—.

112. Determination of the absolute disintegration rate of Cs'37-sources by thetracer method. S. Hellström and D. Brune. 1963. 17 p. Sw. cr. 8r—.

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 r - .

115. Cross section measurements of the ^Nifn, p)HCo and 2>Si(n,a i»]MMg reac-tions in the energy range 12 to 3.8 MeV. By J. Koniin and A. Lauber1963. 30 p. Sw. cr. 8 r - .

116. Calculations of total and differential solid angles for a proton recoilsolid state 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 CaSO^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 Hult-gren. 1963. 20 p. Sw. cr. 8:—.

123. The neutron spectrum in a uranium tube. 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 speclrometry. 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. Hoimqvist 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 zircaloy-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. ö . Andersson and J. Braun. 1964. 14 p.Sw. cr. 8:—.

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 UO2 by fission fragments. By G. Nilsson.1964. 38 p. Sw. cr. 8:—.

137. Personnel neutron monitoring at AB Atomenergi. By S. Hagsgård andC-O. Widell. 1964. 11 p. Sw. cr. 8 : - .

138. Radiation induced precipitation in iron. By B. Solly. 1964. 8 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. 8:—.

141. Heat transfer and pressure drop with rough surfaces, a literature survey.By A. Bhatlachayya. 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. er. 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's 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 Yb ' " andHf'«. 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. Sw. cr. 8:—.

155. Test of neutron spectrum calculations with the help of foil measurmenfsin a DjO and in an H2O-moderated reactor and in reactor shields ofconcrete and iron. By R. Nilsson and E. Aalto. 1964. 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. 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. Sw. cr. 8:—.

Förteckning över publicerade AES-rapporter

1. Analys medelst gamma-spektrometri. Av D. Brune. 1961. 10 s. Kr 6:—.2. Bestrålningsförändringar och neutronatmosfär 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 reaktorområdef. Av Erik Jonson. 1963. 64 s.

Kr. 8:—.

Additional copies available at the library of AB Atomenergi, Studsvik,Nyköping, Sweden. Transparent microcards of the reports are obtainablethrough the International Documentation Center, Tumba, Sweden.

EOS-tryckerierna, Stockholm 1964