A Guide to Radiation and

A Guide to Radiation and Radioactivity Levels Near High

Energy Particle Accelerators

A. H. Sullivan

Nuclear Technology Publishing Ashford, Kent, TN23 IJW

England .

r\/ 9~~(a2") S'lL

--

A Guide to Radiation and Radioactivity Levels Near High

Energy Particle Accelerators

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without the permission in writing of the

publishers.

British Library Cataloguing in Publication Dates A catalogue record for this book is available at the British Library

COPYRIGHT © 1992 Nuclear Technology Publishing ISBN 1 870965 183 (hardback)

11

I , ~ I

..

"A little inaccuracy sometimes saves tons of explanation"

H.H. Munro in Short Stories of Saki

iii

ACKNOWLEDGEMENTS

The author would like to thank the Director General of CERN for pennission to publish this work in book fonn. Many colleagues have made useful comments on the text at various stages, which have been appreciated. I would like especially to thank Ralph Thomas (LLNL, Livennore), Keran O'Brien (North Arizona University) and Ian Thorson (TRIUMF, Vancouver) for taking the trouble of going through the text and making suggestions for improvements. Thanks are also due to Luc Danloy (CERN) for asking many questions which have helped in improving the presentation.

Typesetting by Lin-Art, Ashford, Kent. Printed by Geerings of Ashford, Ashford, Kent. Published by Nuclear Technology Publishing, Ashford, Kent. ISBN 870965 183

iv

THE AUTHOR

Born in April 1933, Dr Sullivan obtained an Honours BSc Degree in Physics and then a PhD from London University. He has w0.rked on radiation problems with the UK Atomic Energy Authonty and on the Nuclear Power Programme with the Electricity Generating Board before coming to CERN in 1962 where he is currently a Senior Physicist in the Radiation Protection Group. He has been an author of many papers concerning radiation from accelerators, instrumentation and radiobiology using high energy radiation. Over the past 15 years he has been responsible for radiation safety at the CERN-PS (proton synchrotron) complex where a number of high intensity target areas, both for protons and electrons have been successfully (and safely) put into operation.

v

vi

Contents Preface

Chapter 1

1.1

High energy particle interactions

Properties of high energy particles 1.1.1 High energy particle types 1.1.2 Energy and momentum 1.1.3 Ionisation by high energy

charged particles 1.1A Charged particle range 1.1.5 Nuclear interactions 1.1.6 Units and conversion factors 1.1.7 The significance of radiation levels

Contents

3 4 6 9

10

1.2 Secondary radiation from high energy interactions

1.3

1.2.1 Radiation fields 11 1.2.2 Multiplicity and energy of secondaries

in an interaction 13 1.2.3 The number and energy of secondaries

in a cascade 17 1.2A The number of high energy particle

interactions 20 1.2.5 Secondary particle fluence build-up

in an absorber 20

The dose due to high energy particle interactions 1.3.1 Dose ina charged particle beam 1.3.2 Absorbed dose near a target in a

proton beam 1.3.3 Radiation damage to accelerator

materials 1.3A Conversion of hadron fluence to dose

22

23

25

equivalent 26 1.3.5 Dose equivalent in a beam 28 1.3.6 Dose equivalent near a target 29 1.3.7 Dose equivalent rate near a beam

line 30 1.3.8 Dose near targets of different

materials References

Vll

31 33

Contents Contents

Chapter 2 Shielding for high energy particle accelerators 3.1.4 Radiation near a target in an electron beam 76

2.1 Shielding for high energy protons 2.1.1 Radiation attenuation in a shield 35 3.2 Shielding for high energy electrons

2.1.2 Source terms for shielding 3.2.1 Source terms for shielding

calculations 35 calculations 77

2.1.3 Dose build-up in an absorber 38 3.2.2 Muons from electron beams 79

2.1.4 Beam line shields 39 3.2.3 Secondary particle attenuation 81

2.1.5 Dose equivalent outside beam dumps 43 3.3 Low energy electrons

2.2 Shielding for protons below 1 Ge V 3.3.1 X ray production 83

2.2.1 The secondary radiation distribution 45 3.3.2 X ray attenuation 85

2.2.2 Source terms for shielding 3.4 Synchrotron radiation calculations 49 3.4.1 The production of synchrotron

2.2.3 Secondary particle attenuation 52 radiation 86

2.3 Shielding for muons 3.4.2 Synchrotron radiation energy 86

2.3.1 Muon production 54 3.4.3 The synchrotron energy spectrum 88

2.3.2 Muon attenuation 54 3.4.4 Synchrotron radiation levels 89

2.3.3 Ranging out the muons 56 3.4.5 Dose rate outside the vacuum

2.3.4 Angular distribution of muons 57 chamber 90

2.3.5 Muon beam strength 59 References 91

2.3.6 Isofluence contours 60

2.4 Radiation transmission through holes and Chapter 4 Radioactivity induced in high energy chicanes in a shield 2.4.1 Radiation at the entrance to a hole

particle accelerators

in a shield 61 4.1 Properties of induced radioactivity

2.4.2 Radiation scatter down holes 4.1.1 High energy particle activation 93 in a shield 63 4.1.2 The activity produced in an

2.4.3 Transmission down multi-legged interaction 94 chicanes 67 4.1.3 Relation between activity and

2.5 Skyshine gamma ray dose rate 96

2.5.1 Neutron dose rate at a distance 71 4.1.4 Shielding for induced activity

References 73 gamma dose 100

4.1.5 Dose from beta activity 101 4.1.6 Ratio between beta and gamma

dose 103

Chapter 3 Shielding for high energy electron machines 4.2 Radioactivity in targets and dumps

3.1 Electron interactions 4.2.1 Radioactivity induced by high energy

3.1.1 Critical energy 75 particle interactions 103

3.1.2 Radiation length 75 4.2.2 Radioactivity in iron and copper

3.1.3 Nuclear interactions by electrons 76 targets 104

viii ix

Contents

4.3

4.4

4.5

I

4.2.3 Dose rate from targets and beam dumps 105

4.2.4 Effective half-life 107 4.2.5 Activation of heavy element targets 110 4.2.6 Comparison of calculated dose rates

with measurements 112 4.2.7 Beta dose from thin targets 113

Activation by secondary hadrons 4.3.1 Activating particles 114 4.3.2 High energy particle activation 116 4.3.3 Activation by thermal neutrons 119 4.3.4 The activation of aluminium 124 4.3.5 The activation of concrete 125 4.3.6 Earth activation ' 128

Accelerator activation 4.4.1 Total activity in an accelerator 132 4.4.2 Induced activity dose rate

near a beam line 134 4.4.3 Activation in high energy

electron accelerators 135

Activation of air and water 4.5.1 Radioactivity production in air

and water 137

4.5.2 Air and water activation in electron machines 138

4.5.3 Dose rates from activated air and water 141

4.5.4 Passage of radioactive air through a ventilation system 142

4.5.5 Activity concentration and dose rate from a release of radioactive air 145

4.5.6 Activation of cooling water 148

References 150

x

Preface An appreciation of the magnitude of radiation and radioactivity

levels that can be expected when subatomic particles are accelerated to high energies is an essential requirement for the safe and efficient operation of a particle accelerator. A realistic assessment of all aspects of the radiation problems that can arise in accelerator installations involving different types of particles over a wide range of energies is necessarily an inexact exercise on account of the diversity and complexity of the situations that may occur. Even if all the parameters affecting beam losses in an accelerator were known, the variability inherent in accelerator layout and operation together with the complicated physics of high energy particle interactions and the subsequent production of secondary radiation and radioactivity make it extremely difficult to quantify radiation and radioactivity levels in an absolute way.

An estimate of likely radiation and radioactivity levels is needed at the design stage of an accelerator for deciding the radiation safety features to be incorporated in the infrastructure of the machine and for predicting where radiation damage possibilities will have to be taken into account. Both these aspects can have a significant influence on the machine layout and cost. Failure to make a reasonable assessment at the right time may have far reaching consequences for future costs.

When assessing the radiation safety features of a proposed new installation it is also prudent to take into account possible future developments even if the parameters are only vaguely specified. In such cases it will be necessary to make quantitative radiation assessments to identify situations where only minor modifications of the infrastructure could prove highly cost effective for the future. Even after a machine has been in operation and its characteristics are well understood, reliable assessments of the additional radiation risks to be associated with machine improvements or unusual modes of operation are often required - usually at short notice - to ensure that adequate although not excessive precautions can be incorporated.

Given this inherent uncertainty in real-life accelerator situations, any prediction of the radiation or radioactivity levels that are likely to arise in any given part of an accelerator installation will tend to be subjective and an overall appraisal

xi

may in reality depend more on judgement guided by experience than on the exact result of detailed computations. Consequently the methods used to assess radiation levels under idealised conditions need only lead to adequate guideline values rather than give a detailed scientific description of the situation being studied. Precision is of secondary importance.

The purpose of this guide is to bring together basic data and methods that have been found useful in assessing radiation situations around accelerators and provide a practical means of arriving at the radiation and induced radioactivity levels that could occur under a wide variety of circumstances. An attempt is made to present the information in a direct and unambiguous way with sufficient confidence that the necessity for large safety factors is avoided. However, care must always be exercised when extrapolating from generalisations to defined situations and in instances where all the necessary parameters are not specified or otherwise under control, the results obtained must be considered as nominal or reference values, which will merely indicate the conditions under which a problem worthy of further study could arise. In many cases assumptions and simplifications have been made and reliance placed on extrapolating from experimental data into regions where the basic physics is too complicated to make meaningful absolute calculations. Wherever possible such extrapolations have been tied to real or otherwise acceptable data originating from independent sources. No wild discrepancies have been found and in cases where suitable data for checking results are lacking this usually implies that the problem being analysed has not been considered to be of critical importance in the past.

The guide covers all aspects of radiation situations that have been found by experience to warrant consideration for the safe operation of high energy particle accelerators. It is intended as a practical guide for accelerator physicists, engineers and technicians rather than as a scholarly review for the expert. The approximate nature of the methods used will be more than compensated by the ease and rapidity with which even complicated radiation situations can be reasonably quantitatively assessed. In particular, it is hoped that this guide will provide reference values that will lead to an overall consistency in assessments of all aspects of radiation safety associated with the

xii

I !

J 1

I (

II

l

operation of an accelerator. Although every effort has been made to ensure the reliability of

data and methods presented, the possibility of an oversight or misunderstanding cannot be completely dismissed. Unless otherwi~e stated, there are no built-in safety factors either in the logic or III the data presented. It is therefore recommended that the user takes his own precautions and where results obtained using this guide are of critical importance they should always be checked against independent calculations based on alternative methods that may be found in the literature.

xiii

xiv

CHAPTER 1

High Energy Particle Interactions

1.1. Properties of high energy particles

1.1.1. High energy particle types High energy particles divide into two basic classes,

hadrons and leptons, depending on their ability to interact with nuclei in the material through which they pass. When a high energy hadron interacts with a nucleus, many secondary particles are emitted which could themselves have a high enough energy to produce further secondaries when they interact, thus creating a nuclear particle cascade. In addition to the neutrons, protons and other nuclear fragments that may be emitted in a hadron interaction, unstable secondary particles can also be created which may have a sufficiently long lifetime that a proportion of them have time to interact before they decay or, if they do decay, form particles that have to be taken into consideration as a component of the secondary radiation field from the interaction. Leptons on the other hand only rarely interact with nuclei but, if they are charged, will contribute to the radiation field by way of the ionisation they produce in the material through which they . pass.

The secondary particles emitted in high energy particle interactions with sufficient abundance and mean lifetime that they need to be taken into account in shielding calculations are listed, with their appropriate properties(1), in Table 1.1.

The particle mass and lifetime given in Table 1.1 are those when the particle is at rest. At high energies both mass and lifetime increase due to relativistic effects. For a particle with a rest mass of M Me V accelerated to an energy of E Me V its mass and lifetime will be increased by a factor (1 + ElM) due to these effects.

1.1.2. Energy and momentum The degree of acceleration of a charged particle is often

expressed as its momentum, whereas calculations of radiation

1

Radiation and Radioactivity Levels near High Energy Particle Accelerators

10~L-~~~di~l---~~~~~--~~~~1~03~~~~~·1~04 10 102

Momentum (MeV/c)

Figure 1.1. Relation between energy and momentum for different types of high energy particles.

levels and the dose rates generated by particle interactions generally require a knowledge of energy depo~ition inv~lving the interacting particle kinetic energy. At very hIgh energIes, when the particle kinetic energy is many times its rest ~ass energy, momentum and kinetic energy become equal numencally when expressed in appropriate units, whereas there are important

Table 1.1. High energy particles of interest for shielding calculations_. _"

Particle Charge Symbol Mass Mean life Principal (MeV) at rest decay

(s) products ._--_.

Hadrons Proton + p 938 stable Neutron 0 n 940 900 p,e

+ 2.6x 1 0-8 + Pion ± 7r 140 )r

Pion 0 1[;0 135 8.4xlO-17 gamma rays

Leptons + 106 2.2xlO-6 + Muon ± )r e-

Electron e 0.511 stable Positron + e+ 0.511 stable

2


differences at lower energies. The kinetic energy, E Me V, of a particle of rest mass M Me V (given in Table 1.1) and momentum P MeV/c, can be obtained from the relation

E = -J(P2+M2) - M (1.1)

This relation between energy and momentum is plotted III

Figure 1.1 for commonly encountered high energy particles.

1.1.3. Ionisation by high energy charged particles High energy charged particles lose energy by ionisation

in the material through which they pass. This rate of energy loss, or stopping power, can be calculated and depends primarily on the particle charge and velocity and the electron density of material through which it passes(2-4). Stopping power is plotted in Figure 1.2 as a function of energy for protons and muons traversing water and iron. The stopping power for pions will be similar to that of muons. As can be seen in this figure, the

of' E ()

4

" 3 Ol

:> Q)

6 =ci 2 1i:J "0

Protons

\ '.

\

\ \

" Muons

\

,Iron ___ _

--._------..-... ......

Energy (GeV)

-- -

Figure 1.2. The stopping power of protons and muons in water (solid curves) and iron (dashed curves) as a function of particle energy.

3


stopping power passes through a broad minimum where the rate of energy loss is in the region of 2 MeV.g-1.cm-2. Charged particles in this energy range are commonly referred to as minimum ionising particles. A more precise estimate of the minimum ionising energy loss rate, S, taking into account the atomic weight A and number Z of the material being traversed is approximated by

S = 3.76 ZIA M V -I -2 e .g .cm (1.2)

The energy lost by charged particles is mainly deposited along the track of the particle but at very high energies appreciable energy can be transferred to electrons (commonly referred to as delta rays) which may then deposit energy away from the primary track, effectively reducing the rate of energy deposition close to the charged particle track.

1.1.4. Charged particle range The range of a charged particle is obtained by summing

the energy loss rate up to the point where the energy loss equals the particle energy. Charged particle range in iron (assumed density 7.4 g.cm-3) is plotted in Figure 1.3 for high energy protons(2), muons(3) and electrons(5). Muons, being leptons, only

102w-~~-rrn~--~-r"~~---r-r~~~---r-rrT~~

~ c e :s 10-1

Q) OJ c &. 10-2

10-3

.~.,

Proton

1 Energy (GeV)

10

Figure 1.3. Range--energy curves for high energy electrons, protons, and muons in iron of density 7.4 g.cm-3

•

4


very rarely undergo nuclear interactions and will have a high probability of surviving to the end of their range. Charged pions would have essentially the same range curve as muons if they can survive from having a nuclear interaction before reaching the end of their range. The shape of the range curve for protons shown in Figure 1.3 indicates an empirical relation for the range of a proton of energy E GeV, below about 0.8 GeV, in metres of iron, of

R = 0.7 EI.6 (1.3)

Above 2 Ge V a proton will have a range about 10% greater than that of a muon of the same energy if it is able to avoid having a nuclear interaction. The range of high energy electrons is also shown in the figure. In this case the range at high energies is limited by the emission of bremsstrahlung (X rays) which is described in Chapter 3.

As was shown in Figure 1.2, minimum ionising charged particles lose energy at a practically constant rate of about 2 Mev'g- l .cm-2

and hence the range of these particles can be expected to approximate to E/2 g.cm-2, when E is their energy in MeV. A more precise estimation of the range in metres of high energy muons (and pions) can be made from

R=KE (1.4)

where R is the range in metres of a particle of energy E Ge V and K is the mean linear range per Ge V of particle energy in the material being traversed and is given in Table 1.2 for common

Table 1.2. Mean range of charged particles per GeV of particle energy between 2 and 100 GeV and the linear range relative to that in iron for

different materials.

Material Densiti: K Relative (g.cm- ) (m.GeV-1

) range

Water 1.0 4.0 5.7 Earth 1.8 2.5 3.6 Concrete 2.35 1.8 2.6 Aluminium 2.7 1.8 2.6 Baryte 3.2 1.7 2.4 Iron 7.4 0.70 1.0 Copper 8.9 0.60 0.86 Lead 11.3 0.55 0.79 Uranium 19.0 0.32 0.46 Tungsten 19.3 0.30 0.43

5


accelerator shielding or target materials. The quasi-linear relation between range and energy holds up to about 100 Ge V for muons; at higher energies relativistic processes become important, the energy loss rate increases and the approximate linear relation breaks down.

The values for K given in Table 1.2 will give the range of muons to an accuracy of better than 10% over the energy range 1 to 100 Ge V if material density is correctly assessed. In cases where a more precise particle range is required reference needs to be made to detailed particle range tables(2. 5).

1.1.5. Nuclear interactions When a high energy hadron strikes a nucleus in the

material through which it is passing it has a high chance of making an inelastic interaction where a range of secondary particles are emitted in a so called spallation reaction. The nuclear cross section for such a reaction approaches the geometric cross section of the nucleus at high particle energies. A review of nuclear interaction cross sections(l) suggests an empirical dependence of the interaction cross section, ° in cm2, on the atomic mass of the target nucleus A of

0= 42 AO.7 x 10-27 (1.5)

which is a good approximation for the cross section for an inelastic collision by a hadron of energy greater than about 120 MeV. This cross section is plotted in units of barns (l bam = 10-24 cm2

) as a function of atomic weight of the target nucleus in Figure 1.4. Effective high energy particle nuclear interaction cross sections for common target materials determined from a review of available data are also indicated on the figure.

For shielding applications, the probability for an interaction by a high energy hadron in a given material is best expressed as the interaction mean free path (mfp) or nuclear interaction length of the material. This mean free path, Ie, in g.cm-2

, is related to the nuclear interaction cross section, 0, by

A Ie = ~.-N0 (l.6)

6


where N is Avogadros number with a value of 6.02 x 10" atoms per mole, A is the atomic weight of the material and 0 is the nuclear interaction cross section in cm

2

• Combining Equations 1.5 with 1.6 leads to the relation for the interaction mean free path of

Ie = 40 A 0.3 g.cm-2 (1.7)

For radiation shielding purposes it is assumed that at high energies the particle fluence incident on a shield will be attenuated basically by inelastic nuclear interactions and hence particle interaction and attenuation mean free paths will be the same. However, it should be noted that as further generations of secondary high energy hadrons may be produced in the nuclear interactions in a shield, the apparent or experimentally determined high energy hadron attenuation mean free paths will tend to appear longer than those calculated using Equation 1.7 and could also appear to vary with absorber depth and incident particle energy. Apparent attenuation mean free paths up to 30% greater than the expected value have been noted(6--8).

Effective interaction/attenuation mean free paths(l) for calculating the attenuation of high energy hadrons incident on various target

c ~ 1.0 t--c: o t5 Q) (/)

(/) (/)

& 0.1 ~ ::-........... .

_ ..... -... -."

Be .. ,/ _,.,-·,.~C

.•... ~

-

-

0.01 '":1;--------......... ----:-:1 0:---"'O'----;""O"...l-'-U-I.1..l..~0-...... --~ ............. 1...:..JOOO

Atomic weight

Figure 1.4. The nuclear inelastic interaction cross section as a function of atomic weight of the target nucleus in units of barns where 1 bam = 10-24 cm2

.

7


Table 1.3. High energy particle interaction cross sections and attenuation mean free paths in various target and shielding materials.

Inelastic Nominal Attenuation Tenth Material cross section densit¥ mfp value

(bam) (g.cm- ) (g.cm-2

)

(cm) (cm)

Beryllium 0.20 1.8 75 42 96 Graphite 0.23 2.0 86 43 100 Water 1.0 85 85 195 Concrete 2.35 100 43 99 Earth 1.8 100 56 128 Aluminium 0.42 2.7 106 39 90 Baryte 3.2 112 35 80 Iron 0.70 7.4 132 17.8 41 Copper 0.78 8.9 135 15.2 35 Tungsten 1.61 19.3 185 9.6 22 Platinum 1.78 21.4 190 8.9 20 Lead 1.77 11.3 194 17.0 39 Uranium 1.98 19.0 199 10.5 24

Table 1.4. SI units, conversion factors and assumed quality factors.

(a) Beam power 1 kW = 6.24 X 1012 GeV.s-1

1 ampere = 6.24 x 1018 singly charged particles.s-1

(b) Absorbed dose 1 gray (Gy) = 1 J.kg-1

1 Gy = 100 rad 1 Gy = 6.24 X 106 GeV.g-1 = 6.24 x 109 GeV.kg-1

I Gy.h-1 = 1.73 X 106 MeV.g-1.s-1 = 2.8 x 10-7 W.g-1

(c) Dose equivalent sievert (Sv)= Gy x Quality factor (Q)

1 Sv = 100 rem

(d) Assumed quality factors

(e) Radioactivity

Q = 1 for X and gamma rays Q = 5 for charged hadrons Q = 1 for charged leptons Q = 3 to 6 for secondaries from high energy particle interactions.

1 bequerel (Bq) = 1 disintegration per second I curie (Ci) = 37 GBq

(f) Cross section I bam = 10-24 cm2

8


and shielding materials are listed in Table 1.3. In practical shielding applications it is usually the volume of the shield that is important, where a major uncertainty will be the real density of the material being used. Relatively low densities have been assumed to determine the linear mean free paths in Table 1.3 and where shield thickness is critical, these mean free paths should be adjusted on the basis of density measurements. Also given in Table 1.3 is the corresponding shield thickness estimated as necessary to attenuate high energy particle radiation levels by a factor of 10.

1.1.6. Units and conversion factors The basic radiation quantity required from shielding

calculations is the dose equivalent outside the shield, which in the International System of Units (SI units) is determined in sieverts (Sv). The Sv is expressed as energy absorbed in tissue in gray (Gy), multiplied by modifying factors. These modifying factors weight the absorbed dose in an attempt to make dose equivalent proportional to risk for all types of ionising radiation. As far as high energy particle radiation is concerned, the only modifying factor of significance is the radiation quality factor (Q)(9) which is a function of the ionisation density or linear energy transfer (LET) along the tracks of charged particles. The Sv replaces the rem and the Gy the rad as units of dose equivalent and absorbed dose respectively. Estimated quality factors together with definitions and conversion factors of use for calculating radiation levels are listed in Table 104.

Where possible radiation and radioactivity levels have been expressed in the recommended SI units with prefixes as given in Table 1.5 to denote multiples.

Table 1.5. Prefixes used with SI units.

Prefix

Tera Giga Mega kilo milli micro nano pico femto

Symbol

T G M k m

~ n p f

9

Value

10 12

109

106

103

10-3

10-0 10-9

10-12

10-15


1.1.7. The significance of radiation levels Radiation and radioactivity levels that can be estimated

using the data presented in this guide need to be judged against reference levels in order to assess the overall health risk they represent. Reference levels relating to radiation safety are set by national laws, usually based on internationally accepted recommendations, from which local rules are derived. Although compliance with local laws and regulations has overriding importance when assessing any situation, guidelines as to the possible consequences of exposure to radiation could be of use for judging the relative importance of different aspects of radiation safety and hence determining the most cost effective way of minimising the overall radiation risk. A possible set of guidelines against which the significance of exposure to radiation near an accelerator may be judged is given in Table 1.6. It should be noted that the dose levels considered in this table are those to a person rather than that existing near a machine. The high dose effects are primarily based on those observed after exposure to gamma ray s(l 0) and would be for an exposure lasting a relatively short time, whereas for the low dose categories the possibility of the radiation originating from multiple sources has to be taken into account. The annual occupational dose limit of 50 mSv.y-l was considered an upper limit for the exposure of radiation workers as recommended by the International Commission on Radiological Protection (ICRP) and is based on a mortality risk factor due to radiation induced cancers of 10-2 per Sv(ll). In practice the use of this upper dose limit will imply an average dose to radiation workers of 10% or less of the limit, making the mean annual

Table 1.6. Possible guidelines to the significance of exposure to radiation.

Exposure

3.5 Sv > 1 Sv

> 50 mSv 50 mSv.y-1

15 - 50 mSv.y-1 5 - 15 mSv.y-! < 5 mSv.y-1

1 mSv.y-1 10 fl.SV.y-1

----- .. ---

Significance

50% chance of survival Serious to lethal Requiring medical checks Occupational dose limit Strict dose control necessary Professional exposure Minimum control necessary Natural background Insignificant

10


radiation mortality risk from radiation induced cancers 5 x 10-5 or 50 cases per million workers. This additional professional risk to the radiation worker is thought to be well within the range of risk in an industry that is considered to be safe. However, long-term studies of radiation effects (principally on atomic bomb survivors) are indicating that the frequency of radiation induced cancer increases with age and hence the cancer risk is in fact greater than had been assumed. Consequently there is a possibility that the occupational dose limit for radiation workers may be reduced to 20 mSv.y-l(l2) in the near future. The natural background level given in the table is an approximate average and will vary with location and height above sea level. An annual dose of 10 j.1Sv is a small dose when compared to the natural variations in ambient radiation levels and hence could be considered as an insignificant annual dose. As can be seen, judgement will be necessary when applying these guidelines to decide the relevance of radiation levels around an accelerator.

1.2 Secondary radiation from high energy interactions

1.2.1. Radiation fields Analysis of the measured distributions of secondary particle

fluence around targets irradiated with high energy protons has shown that for incident protons in the energy range 1 to 1000 Ge V the fluence of secondary hadrons of energy greater than 40 Me V at 1 m and different angles from a proton interaction in a thin iron or copper target approximates to(l3)

5000 (1.8) hadrons.m-2

<pee) = (e + 35/oJEi

where e is the emission angle in degrees and E the interacting proton energy in Ge V. This expression has been found reasonably to fit experimental data over a wide energy and angular range(l4,15) and can be expected to give a useful approximation of secondary radiation distributions suitable for estimations of dose rates, source terms for shielding calculations, and of particle fluences for induced radioactivity calculations. The angular distributions

11


of secondaries from interactions by protons of various energies, as predicted by Equation 1.8, are plotted in Figure 1.5 which shows how the secondary radiation is predominantly forward directed and how this predominance increases with increasing

proton energy. The hadron fluence at 1 m from a target and for different emission

angles is plotted as a function of proton energy in Figure 1.6 where it can be noted that the zero degree fluence increases linearly with the interacting proton energy whereas that perpendicular to an interaction is only slightly energy dependent. The fluence at 1 m from an interaction and at 90 deg to the beam direction is of particular interest and for incident protons of energy E Ge V will be given by

0.62 <p (90) = (i~ 0.4/~E)2 (1.9) hadrons.m-2

The above expression leads to an average value of 0.5 ± 0.17 hadrons.m -2 per interaction at 1 m perpendicular to the beam

~100

"'E ui c e -g :S E

Figure 1.5. The angular distribution of secondary hadrons, plotted as particles per m2 at 1 m per interaction by protons in the energy range 1 to 1000 GeV.

12


direction over the entire interacting proton energy range from 1 to 1000 Gev.

1.2.2. Multiplicity and energy of secondaries in an interaction The secondary particle fluence from an interaction can be

integrated over emission angle to obtain the number of secondaries emitted into a cone of given half angle. The results of such an integration are plotted as a function of the cone half angle in Figure 1.7 which shows the number of secondary hadrons emitted into an increasing cone angle for interacting proton energies of from 1 to 1000 Ge V. The integral has been normalised and plotted as the fraction of the total secondaries emitted into a given angle in Figure 1.8, from which an indication of the proportion of particles emitted in any given direction can be obtained.

The total number of secondary hadrons per interaction, Q, or particle multiplicity can be obtained from the above integration

<f' ~ (f) o deg c e

1:l CIl E E 10

Cii 10 (])

u c (]) :J

u:::

10-1

90

H!Q 10-2

1 10 102 103

Proton energy (GeV)

Figure 1.6. Secondary hadron fluence per proton interaction at different angles as a function of incident proton energy.

13


rJJ Q)

.~ 10 "0 C o <.> Q) rJJ

'0 iii .0 E :J Z

20 40 60 80 100 120 140 160 180 Angle (deg)

Figure 1.7. Total number of hadrons per interaction emitted into a cone of given half angle relative to the incident proton direction for protons of energy from I to 1000 Ge V.

1.0

1000 0.8 /

rJ)

~11 Q)

/10 "fa -g 0.6 0

/ () Q) rJ)

0 C gO.4 1 GeV () <1l u::

20 40 60 80 100 120 140 160 180 Angle (deg)

Figure 1.8. The fraction of secondary hadrons that are emitted into a forward cone of given half angle for different energy incident protons.

14


and is plotted in Figure 1.9 as a function of interacting proton energy. A best fit simple expression for this multiplicity is found to be

secondaries per interaction (1.10)

where E is the primary proton energy in the range 1 to 1000 Ge V. The above multiplicity has been found to compare reasonably with that determined from detailed Monte Carlo calculations(l6).

The secondary hadrons will have an energy spectrum which will contain a large fraction of the kinetic energy of the interacting proton. Some energy will have gone into the production of unstable secondary particles and some lost as kinetic energy of particles of energy below that necessary to cause further spallation interactions. Energy will also be lost by elastic interactions and by ionisation by charged particles, particularly that of leptons that cause no further nuclear interactions and escape from the vicinity of the hadron cascade.

40 0 en Q)

.~

"0 c 30 0 <.> Q) .< rJJ

'0 iii

,.e

E 20 :J z

10

Interacting proton energy (GeV)

Figure 1.9. Total number of secondary hadrons emitted in an interaction as a function of incident proton energy (dashed line). Solid line is multiplicity given

by Equation 1.1 O.

15


The precise amount of energy dissipated per hadron interaction is difficult to estimate and will depend on the interacting particle type and energy as well as the target nucleus. As a first approximation it is assumed that some 80% of the energy of an interacting hadron is retained as the effective kinetic energy of secondary hadrons of energy above 120 Me V, independent of the primary energy provided this is greater than 1 Ge V. This assumption is expected to overestimate the energy loss per interaction at very high energies but will not affect the energy of the secondaries by more than 20%. Hence the assumption is not over-critical for the analysis of the hadron cascade.

U sing the above assumptions, the average energy of secondary hadrons from an interaction by a proton of E Ge V will be given by

Esec = 0.8 E/Q GeV (1.11)

where Q is the multiplicity given by Equation 1.10. This secondary particle average energy is plotted against

primary energy in Figure 1.10 and reasonably fits a relation

:;-Q)

S2->-2' Q) c Q)

i::' rn "0 c o <) Q)

(f)

10-1L-__ ~~~~~~ ____ ~~~~~~~ __ ~~~~~~ 1 10 102 103

Primary energy (GeV)

Figure 1.10. The average energy of secondary hadrons as a function of interacting proton energy.

16


E = 0.12 E 0.76 = (0.06 E)0.76 GeV sec (1.12)

For simplicity it is assumed that the secondary particle energy does not vary with emission angle, which will result in an underestimation of energy in the forward direction and an overestimation for secondaries emitted at large angles.

Equally, for interactions by hadrons of less than 1 Ge V, 80% of the incident energy is assumed to go into the kinetic energy of the secondaries. However, in this case charged secondaries from the interactions will lose a considerable part of their energy by ionisation while passing through an absorber which may reduce their energy to below that necessary to cause further spallation interactions. This effect will depend on the proportion and energy of the protons, neutrons and pions making up the hadron field and will be difficult to estimate precisely. Detailed calculations suggest that a 1 Ge V proton will initiate a cascade (in iron) that results in, on average, 3.5 spallation interactions(l7), two of which could be by hadrons of energy greater than 100 MeV(l8).

1.2.3. The number and energy of secondaries in a cascade U sing the above estimations for the multiplicity and

energy of secondaries produced in an interaction, the number of collisions necessary to reduce the average secondary hadron energy to E Ge V in a cascade initiated by a proton of energy Eo Ge V can be estimated. Using Equation 1.12, the effective energy of the secondary hadrons after one interaction, E

1, will be

E - (aE)p 1 - ° (1.13)

where, from Equation 1.12, a = 0.06 and 13 = 0.76. Replacing Eo in Equation 1.13 with E1 will give the average

energy of the second generation of hadrons E2 which becomes

(1.14)

after q interactions the average energy of the hadrons in the cascade will be

where

p = 13+132+133+ ... 13q = 13 (1 - u)/(1 -13) 17

(LISa)

(l.lSb)


and

(1.I5c)

q is the average number of collisions or the number of generations of secondary particles necessary before the secondary hadron energy reduces from the primary energy Eo Ge V to an average value E Ge V. The above relations can be transposed to estimate this number of collisions which will be given by

q = 3.65 In WnEo + 8.91)/(lnE + 8.91») (1.16)

The resuiting effective number of collisions required to reduce the average secondary hadron energy to 1 Ge V is plotted in Figure 1.11 as a function of the energy of the proton that initiates the cascade.

If, as has been assumed, 80% of the interacting particle energy goes into the kinetic energy of secondaries, then the average number of secondaries of mean energy E Ge V that will exist in a cascade will be

N(E) = EJE (0.8)Q ( 1.17)

where q is the average number of collisions required to reduce the

3

(/)

c 2 0 Ow

0 0

'0 Qi .D E ~

z

10 Proton energy initiating cascade (GeV)

Figure 1.11. The number of collisions required to reduce the average energy of secondary hadrons to 1 Ge V as a function of the energy of the proton initiating

the cascade.

18


energy to E from the primary energy Eo. The resulting average number of secondaries of mean energy

1 Ge V in a cascade initiated by primary protons of different energies is shown in Figure 1.12 as a function of the initiating proton energy. Inspection of these curves shows that the number of hadrons in the cascade when the mean energy has reduced to E Ge V from an initial energy Eo Ge V can be adequately represented by

N(E) = (EJE)o.92 (1.18)

The above relation is assumed valid down to an average secondary energy E of I Ge V. Below this energy ionisation losses by charged secondaries become important as was explained in Section 1.2.2. In this energy region it is assumed that each hadron of I Ge V produces two secondaries capable of interacting at an energy greater than 120 Me V.

The effective number of hadrons, N sec' with an average energy of 120 Me V produced in a cascade initiated by a proton of energy Eo Ge V therefore becomes

(/) Q)

.~ 102 -0 C o o Q) (/)

'0 Qi .D E 10 ~

z

N = 2 E 0.92 sec 0 (1.19)

10 102

Proton energy initiating cascade (GeV)

Figure 1.12. The average number of secondary hadrons of 1 GeV in a cascade as a function of the energy of the proton that initiates the cascade.

19


In the case of the secondary radiation incident on a shield as a result of a primary hadron striking a target, these hadrons will have an average energy given by Equation 1.12, and the total number of hadrons of energy greater than 120 MeV that can be produced in the shield per incident secondary hadron from the target, Nt' obtained by combining Equations 1.12 and 1.19, becomes

N = 0 24E 0.7 t • ° 0.20)

1.2.4. The number of high energy particle interactions Inelastic nuclear interactions also occur at energies below

120 MeV and the total number of inelastic or spallation interactions is a quantity of interest from the point of view of estimating any induced radioactivity that may be produced. The secondary multiplication of high energy particles in a cascade is such that the majority of the interactions will be by hadrons in the energy region below I Ge V. Using Equation 1.18 and noting that there are an average of 3.5 interactions in a cascade originating from a proton of 1 GeV(I7), the total number of spallation interactions or 'stars' in a cascade initiated by a proton of energy Eo GeV becomes

N = 3.5 E 0.92 sec ° (1.21)

The expected number of spallation interactions or stars in a cascade per Ge V of primary energy is plotted as a function of the initiating proton energy in Figure 1.13.

1.2.5. Secondary particle fluence build-up in an absorber Having determined the average number and energy of

secondary hadrons that result from an interaction, an estimate can be made of the equilibrium fluence in an absorber when particle production and attenuation just balance. The fluence of first generation secondary hadrons <PI' at an angle e degrees and a radius R metres from the site of the interaction, and behind a shield with a high energy particle collision mean free path of A and thickness t (in same units as A) has a value (in hadrons per m2

) of

<P = <pee) e-tf)..

I R2 (1.22)

20

5


where <pee) is the hadron fluence at 1 m and angle e that originates from the incident proton interaction as given by Equation 1.8.

On passage of these first generation secondaries through a shield, a cascade of secondary hadrons may be created causing a build-up of the fluence with depth that continues until secondary particle equilibrium is reached. Suppose that at a point in the shield where equilibrium is established there is a fluence of <PI first generation hadrons (given by Equation 1.22) with <P2 high energy cascade particles in equilibrium. The rate of attenuation of the cascade particles will be <PiA where A is the attenuation mean free path for hadrons above 120 MeV in the shield and the rate of production will be (from Equation 1.20) 0.24Eoo.7 x 4>/A. Equating these two quantities, the fluence of secondary hadrons will be

<P2 = 0.24Eoo.7 <PI hadrons.m-2 (1.23)

and the total hadron fluence inside the shield after equilibrium is reached will be given by

4

~3 (')

Q; 0. 00

!§2 (f)

<P = <PI + <P2 = <PI (1 + 0.24Eoo.7 ) hadrons.m-2 (1.24)

Primary proton energy (GeV)

Figure 1.13. The expected number of spallation interactions (stars) per GeV of primary proton energy as a function of the primary proton energy.

21


This equilibrium fluence is plotted in Figure 1.14 as a function of incident proton energy for various directions from the target.

1.3. The dose due to high energy particle interactions

1.3.1. Dose in a charged particle beam The dose to a thin object placed in a charged particle

beam will depend primarily on the rate of energy loss of the particles and their distribution across the beam. As was shown in Figure 1.2, protons of energy greater than about 600 Me V and muons and pions above about 100 Me V deposit energy at a rate of about 2 MeVg-I .cm-2 in practically all target materials. This so called minimum ionising energy loss rate can be converted to absorbed dose using data given in Table 1.4, making the dose per unit fluence of high energy charged particles, CD'

CD = 32 fGy.particle.m-2 (1.25)

For purposes of calculating dose in a charged particle beam it is conventional to express the particle fluence rate or particle flux

10 deg··/

---~-~

.-----------


Figure 1.14. Effective equilibrium fluence of hadrons of average energy 120 MeV as function of interacting proton energy corrected to 1 m and zero absorber depth

for the radiation emitted at 10, 30, and 90 deg from a target.

22

- :


as particles per cm2 per second. In which case the appropriate factor to convert flux into absorbed dose rate becomes

(1.26)

The dose rate in a beam of a given intensity will depend on the beam size and the distribution of the particles across the beam profile.

Charged particles in a beam interact with each other to form naturally a profile with a gaussian intensity distribution. For a beam of strength minimum ionising particles per second, the particle flux exp(-r/a)2 <p= (1.27)

where a is the radius of the beam that contains 63% of the particles, and is also referred to as the standard deviation of the normal distribution of the particles across the beam. Beam diameters may be variously quoted as being 2 standard deviations (2a), a diameter that contains 63% of the particles or as (4a) containing 98% of the beam. A diameter of (1.66a) will contain 50% of the particles in the beam.

The dose rate due to direct ionisation in a beam of 1012 charged particles per second is shown in Figure 1.15 as a function of distance from the beam axis for beams of different diameters (the diameter is assumed to be that containing 98% of the particles).

In an irradiation of an object in a high energy proton beam, the dose due to particle interactions as well as direct ionisation needs also to be considered. This component will depend on target thickness and composition as well as on the size of the beam itself. However, the contribution of nuclear interactions and the resulting secondaries to the dose in the beam will be small and is unlikely to enhance the dose due to the passage of the charged particles by more than a factor of 2 under normal circumstances.

1.3.2. Absorbed dose near a target in a proton beam The absorbed dose to a sample placed near a target in a

high energy particle beam will depend on many factors such as its size and composition as well as the uniformity of the radiation

23


field. The dose to the sample per interaction in a target will also depend to some extent on the spectrum of secondary particles, which in tum depends on the energy of the interacting proton, the nature of the target and the angle of emission. Given that a proportion of the secondaries will be charged particles in the minimum ionising energy range (see Section 1.1.3), as a first approximation, an overall secondary particle fluence to absorbed dose conversion factor of 3.2 x 10-14 Gy.m2 is assumed for high energy hadrons independent of incident proton energy above 1 Ge V. The secondary particle fluence at 1 m per primary proton interaction in a target, ~ hadrons per m2

, is given by Equation I. 2. 'E ~ and the absorbed dose at 1 m per primary interaction in the

target will be

D = 32 ~ fGy per proton (1.28)

The corresponding absorbed dose rate in an object at I m from 1010 protons of energy greater than 1 Ge V interacting in the target

~5 ,. .c :>, e:l .S; 4 2 ~ Q) (f)

o ~3 Ol o

....J

2

1 o 2 4 6 8 10 12 14 16 18 20

Distance from beam axis (cm)

Figure 1.15. The absorbed dose rate as a function of distance from the beam line in a beam of 1012 minimum ionising particles per second for beams of different diameters. The numbers on the curves indicate the beam diameter in cm that

contains 98% of the particles.

24


per second is shown in Figure 1.16 as a function of angle to the beam direction.

1.3.3. Radiation damage to accelerator materials The properties of materials exposed in a particle beam or

near a target may be degraded due to the effect of the radiation. The extent of this degradation will depend to a first approximation on the dose received but will also be influenced by factors such as dose rate, temperature and whether or not the material is exposed to air. The absorbed dose level at which a change in material properties may start to be observed will depend on the application of the material and the level of stress involved. The ability of radiation to cause damage depends on the type of interaction the radiation can have and therefore the degree of damage may be different for the same absorbed dose from different radiations. Hence there is considerable uncertainty as to the quantity of high energy particle radiation that will cause a particular material to fail. As a rough guide, dose levels at which properties start to be significantly modified after exposure to

100 ~~~~~-r-T~~--~r-~~~~~~~--

::- 10 I .c :>. Q. Q)

Ii! Q) (f)

o -0 -0 Q) .0 o (f) .0 «

30 60 90 Angle (deg)

120 150 180

Figure 1.16. The absorbed dose rate as a function of emission angle to a sample placed at 1 m from a target, per 1010 interactions per second in the target by

protons of different energies.

25


gamma rays are listed in Table 1.7 for some common materials. In some applications materials could continue to perform satisfactorily at dose levels 10 times or more than those given but it may also happen that deleterious effects will be noticed at lower doses. Hence in cases where the possibility of radiation damage is of critical importance, more detailed information relating directly to the effects of high energy particle radiation on materials must be consulted(l9).

In addition to modification of the physical properties of materials, high energy particle radiation encountered by spacecraft has been found to have a non-destructive transient effect on sensitive electronic junctions in integrated circuits and microelectronics(20). The importance of these so called 'single event upsets' is very device dependent and the probability of occurrence will be a function of the radiation type as well as the dose. If it is supposed that these sensitive electronic junctions are of the order of 10 !lm diameter and that a single high energy particle interaction within a junction will cause an effect, then it is estimated that of the order of one anomalous event can be expected per 106 junctions for a dose as low as 20 !lGy.

1.3.4. Conversion of hadron fluence to dose equivalent The dose equivalent will be the maximum absorbed dose

in a 30 cm tissue sphere(2!) multiplied by a quality factor (Q). For the radiation field near a target in a proton beam, where the dose is resulting from the passage of minimum ionising particles

Table 1.7. Radiation levels at which damage to various materials may start ___________ to become significant.

Material ------

Electronic components Teflon (PTFE) Nylon Plastic scintillator Mylar Rubbers-butyl

-silicone Organic cables Oil-mineral

-silicone Polythene Polyeurathane Epoxy resins Paint-epoxy resin

-celluose ester Magnet coil insulation Glass filled polyester

Dose Gy

26


as well as from hadron interactions, a quality factor of 3 is assumed. Using the absorbed dose to fluence conversion factor given by Equation 1.25, the effective fluence to dose equivalent conversion coefficient for high energy hadrons becomes 100 fSv per hadron.m-2. However, a review of computed values of this parameter indicates that it has a slight dependence on particle energy(22) and for particles of energy above about 500 Me V some allowance should be made for particle multiplication or dose build-up in the body. The data on the dose equivalent rate as a function of hadron energy at a depth of 1 cm in tissue-equivalent material can be fitted to an energy dependent fluence to dose conversion of

CH = 40(1 + E-6) fSv per hadron.m-2 0.29)

where E is the hadron energy in Ge V. For neutrons with energy in the 1 to 50 Me V range the conversion

factor approaches a constant value of

CH = 40 fSv per neutron.m-2 (1.30)

At neutron energies between 1 MeV and 10 keV the conversion(23) approximates to 40 E·8 fSv per neutron.m-2 when E is in MeV and below 10 keV the factor is constant at 1 fSv per neutron.m-2.

The resulting fluence to dose equivalent conversion factors are plotted in Figure 1.17 as a function of the incident particle energy

103~~~~mr~~~~~~mrTn~~mm-r~

Eo c 2 ~ 10 .t::

Q; "> '2.

10-3 103 105

Hadron energy (MeV)

Figure 1.17. Fluence to dose equivalent conversion factors for low energy neutrons and high energy hadrons.

27


for low energy neutrons and high energy hadrons over the energy range from I ke V to 100 Ge V.

1.3.5. Dose equivalent in a beam An estimate of the likely dose equivalent to a person

exposed in a proton beam is of interest for assessing the possible consequences of an accidental exposure. Absorbed dose to thin objects placed directly in a proton beam can be determined from Equation 1.26 which indicates that a pulse of 1012 protons, uniformly distributed over an area of 1 cm2

, will give an absorbed dose of 320 Gy to the part of the body traversed by the beam. The biological effect of such a pulse will depend on whether or not it passed through a vital organ. However, in order to be able to assess the possible biological consequences resulting from a beam exposure it is necessary to define an 'effective whole-body dose equivalent' that could be reasonably compared with the dose equivalent reference levels given in Table 1.6. For this purpose it is proposed to use the average dose equivalent from the secondary

12~--~~~~~~--~--T-~~~~ __ ~~~~~~

11

Q) (f)

"3 0. 10 (j; 0. (f)

C o (5

S 9 Ol o

..J

8

~ Possibly lethal --__ ~v

________ Requiring medical supervis~

~ Requires investigation ~

1 mSv

No serious consequences

10 102

Proton energy (GeV)

Figure 1.18. Beam pulse strengths estimated to give the indicated effective whole- body dose equivalent levels as a function of the proton beam energy.

28


radiation over a 30 cm diameter tissue sphere centred on the point of interaction in the body. The results of calculations of such a quantity are shown in Figure 1.18 which gives the intensity of proton pulses necessary to produce different effective dose equivalent levels as a function of the beam energy together with an indication of the possible consequences of exposure to a single pulse.

1.3.6. Dose equivalent near a target For secondaries from an interaction by a proton of energy

Eo Ge V, (greater than 1 Ge V) the average hadron energy will be given by Equation 1.12 and the fluence by Equation 1.8. The fluence is then converted to dose equivalent using Equation 1.29. Hence the dose equivalent at 1 m and an angle a degrees per interaction in a target becomes

R(a) = 2xlO-1O (1 + 0.28 Eo°.45) Sv per proton (a + 35/...JEo)2

(1.31)

The corresponding dose rate at 1 m from a target in which there are 1012 interactions per second is plotted as a function of the interacting proton energy in Figure 1.19. However, in addition to

/.-/........ 10 ...-----------~., ------.....---

.... ---. ..-----... / ~-.----

~----~------ 30_-----/~......--- ..-------------~ 90 ______

------- ----------------------~----- -------_------------------180---

10L---~~~~~U---~~~~wu~--~--~~~uu

1 10 102 103

Proton energy (GeV)

Figure 1.19. The dose equivalent rate at various angles and at 1 m from a target in which there are 1012 interactions per second as a function of the interacting

proton energy.

29


the high energy secondaries emitted in an interaction, low energy neutrons and gamma rays are also emitted in an evaporation process following a spallation interaction. This radiation is emitted isotropically and at low incident proton energies will make a significant contribution to the dose equivalent near a target at large emission angles. Assuming there are 2.5 neutrons emitted in the Me V range per high energy interaction then an additional dose equivalent of 6 fSv per incident proton independent of emission angle and incident proton energy needs to be added to the high energy dose equivalent given above. This component is expected to about double the dose equivalent III the backwards direction from I Ge V proton interactions.

The classification of target areas, from the radiation security point of view, will depend on the possible dose level near the target. The beam strength necessary to give rise to different dose rate levels at 1 m and 90 deg when it interacts in a target is shown as a function of the incident proton beam energy in Figure 1.20.

1.3.7. Dose equivalent rate near a beam line On account of the angular distribution of secondaries

from an interaction, the maximum dose equivalent near a beam

11 ~

" I Lethal

' §

'",10 f~ 1 SV.h-1

ui ~ c --------§ 9

----

0. r- Strictly controlled ""1

c L: 8r- § 0, c 2 7r lmSv.h-1

"1 Ui --E ---<1l

6r Controlled

--= Ql

e =-OJ 5 r 1011SV.h-1 ~ 0

....J Open I , i

4 , ,

1 10 102 103

Proton beam energy (GeV)

Figure 1.20 .. The beam strength such that if the beam interacts in a target it will produce the mdlcated dose rate levels at I m perpendicular to the beam direction

as a function of the beam energy.

30

,

j


line will depend on the position of the beam loss as well as distance from the beam line. The maximum dose equivalent per proton interaction at 1 m from a beam line will come from secondaries emitted at an angle e deg where

57.3 tane - e = 35/..JEo (1.32)

This critical emission angle is plotted in Figure 1.21 as a function of the interacting proton energy. The resulting dose equivalent at 1 m from the beam line due to radiation emitted at the critical angle, as well as the dose rate at 1 m perpendicular to the point of loss, is shown in Figure 1.22 as a function of proton energy for a beam loss equivalent to 106 interactions per second. As can be seen the dose at 1 m from a beam line due to a loss making an optimum angle will exceed that from the same loss but perpendicular to the interaction by a factor of 2 at the highest proton energy considered.

1.3.8. Dose near targets of different materials The above dose estimates are essentially those of high

energy secondary hadrons from protons interacting in iron or

60 "-. I T

-.",

"', - "'-. -,

"'\ ,

- 50 " OJ. - "

-Ql ~ 2-Ql

~ 0,.

I- -C <1l

<ii ()

~" "" (5 40 - -",

'. "",,-

- "' .. ,-"-.

30 I 1 10 100

Proton energy (GeV)

Figure 1.21. The emission angle at which the dose equivalent will be maximum at I m from a beam line.

31


103~ __ ~--~I~i~i~iTT I I

c fa 102 I-> ·S 0-Q)

Q) (/)

o o

I I 10

Proton beam energy (GeV)

'-

-

Fi§ure 1.22. Dose equivalent rate at 1 m from a beam line for a beam loss of 10 protons per second at the optimum point for maximum dose rate and at

90 deg from point of loss.

copper targets. Measurements of high energy particle fluence around targets of different materials(24,25) indicate that the yield varies with target material. Approximate relative secondary particle yields that can be used to estimate the local high energy hadron flue nee and dose rates are summarised in Table 1.8.

The dose transmitted through a thick shield will be much less dependent on target material than the dose near the target as the effective secondary particle energy will have an inverse relation

Table 1.8 Relative high energy secondary particle yields from high energy particle interactions in different target materials.

Target material

Cu Fe Be AI Pb U

32

Relative yield

1.0 1.0 0.4 0.6 1.5 1.7


to the yield. Source terms for shielding calculations therefore tend towards being independent of the material in which the primary interaction takes place.

References 1. Review of Particle Properties. Phys. Lett. B, 204, 1 (1988). 2. Serre, C. Evaluation de la Perte d' Energy Unitaire et du Parcours de

Particles Chargees Traversant un Absorbant Quelconque. CERN Yellow Report 67-5 (Geneva: CERN) (1967).

3. Richard-Serre, C. Evaluation de la Perte d' Energy et du Parcours pour des Muons de 2 a 600 GeV dans un Absorbant Quelconque. CERN Yellow Report 71-18 (Geneva: CERN) (1971).

4. National Academy of Science, National Research Council. Studies in the Penetration of Charged Particles in Matter. Nucl. Sci. Series, Report No 39, publication 1133 (Washington, DC: NRC) (1964).

5. Berger, M. J. and Seltzer, M. S. Tables of Energy Losses and Ranges of Electrons and Positrons. NASA, SP-3012 (Washington: NASA) (1964).

6. Hoefert, M. Shielding Material Equivalence in LEP Experimental Areas. LEP Note 507, (Geneva: CERN) (1984).

7. Ban, S., Hirayama, H., Kondo, K., Miura, S., Hozumi, K., Tanio, M., Yamamoto, A., Hirabayasha, H., and Katoh, K. Measurement of Transverse Attenuation Lengths for Paraffin, Heavy Concrete and Iron around an External Target for 12 GeV Protons. Nucl. Instrum. Methods 174, 271 (1980).

8. Thomas, R. H. and Stevenson, G. R. Radiation Safety Aspects of the Operation of Proton Accelerators. Ch 4, Radiation Shielding, 223. IAEA Technical Report Series No. 282, Vienna (1988).

9. International Commission on Radiation Units and Measurements. The Quality Factor in Radiation Protection, ICRU Report 40 (Bethesda, MD: ICRU Publications) (1986).

10. UNSCEAR. Report of UN Scientific Committee on the Effects of Atomic Radiation (New York: United Nations) (1988).

11. ICRP. Recommendations of the International Commission on Radiological Protection. Publication 26, (Ann. ICRP 1(3) (Oxford: Pergamon) (1977).

12. ICRP. The 1990-1991 Recommendations of the International Commission on RadiOlogical Protection. Publication 60, Ann. ICRP 21(1-3) (Oxford: Pergamon) (1991).

13. Sullivan, A. H. The Intensity Distribution of Secondary Particles Produced in High Energy Proton Interactions. Radial. Prot. Dosim. 27(3), 189-192 (1989).

14. Levine, G. S., Squire, P. M., Stapleton, G. B., Goebel. K. and Ranft. J. The Distribution of Dose and Induced Activity around External Proton Beam Targets. In: Proc. Int. Congr. on Protection against Accelerator and Space Radiation, CERN 71-16, VoLl, p. 798 (1971).

15. Stevenson, G. R., Fasso, A., Sandberg, G., Regelbrugge, A., Boniface, A., Muller, A. and Nielson, M. Measurements of the Hadron Yield from Copper Targets in 200 GeVlc and 400 GeVlc Extracted Proton Beams - An Atlas of Results Obtained. TIS report TIS-RP/112 (Geneva: CERN) (1983).

33


16. Ranft, J. Hadron Production in Hadron-Nucleus and Nucleus-Nucleus Collisions in a Dual Monte Carlo Multichain Fragmentation Model. Phys. Rev. 37(7), 1842 (1988).

17. Thomas, R. H. and Stevenson, G. R. Radioactivity Produced in the Accelerator and its Surroundings. Ch 6.3, Radiation Safety Aspects of the Operation of Proton Accelerators. STI/DOC/1O/283 (Vienna: IAEA) (1988).

18. O'Brien, K. Star Production by High Energy Hadrons. Nuc!. lnstrum. Methods 101, 551(1972).

19. Beynel, P., Meyer, P., Schonbacher, H. and Tavelet, M. Compilation of Radiation Damage Test Data. Published as CERN Yellow Reports. Part 1, Cable Insulation, 79-04 and 89-12. Part 2, Thermo-Setting Resines, 79-08. Part 3, Accelerator Materials, 82-10. CERN, Geneva (1979-89).

20. McNulty, P. J. Charged Particles Cause Micro-Electronics Malfunction in Space. Physics Today 9, 36 (1983).

21. International Commission on Radiation Units and Measurements. Determination of Dose Equivalents Resulting from External Radiation Sources. ICRU Report 39, (Bethesda, MD: ICRU Publications) (1985).

22. Thomas, R. H. and Stevenson, G. R. Radiation Safety Aspects of the Operation of Proton Accelerators. Ch 3, Radiation Measurements at Accelerators, 177. IAEA Technical Report Series No. 282, Vienna (1988).

23. Wade Patterson, H. and Thomas, R. H. Accelerator Health Physics, Ch 2, Radiation Fields; their Specification and Measurement, 70, Academic Press, New York (1973).

24. Charalambus, S., Goebel, K. and Nachtigall, D. Studies of the Shielding Required for the Secondary Radiation Produced by a Target in a High Energy Proton Beam. CERN Health Physics Report, DIIHP/97, CERN, Geneva (1967).

25. Tesch, K. A Simple Estimation of the Lateral Shielding for Proton Accelerators in the Energy Range 50 to 1000 MeV. Radial. Prot. Dosim. 11(3) 165- (1985).

34

CHAPTER 2

Shielding for High Energy Particles

2.1. Shielding for high energy protons

2.1.1. Radiation attenuation in a shield The detennination of the shield necessary around a high

energy particle accelerator usually requires the estimation of the dose equivalent to be expected outside a given shield for a known beam loss.

This dose equivalent, H, at a distance R metres from a high energy proton interaction and after the radiation has passed through a thickness t of shielding is represented by

H -t/A H-~ (2.1) - R2

where Ho is the so-called source tenn which is the effective equilibrium dose equivalent per interacting proton, nonnalised to 1 m from an interaction and to zero absorber depth and A is the hadron attenuation mean free path (mfp), in the same units as the shielding thickness t, as given for different shielding materials in Table 1.3.

The exponential tenn in Equation 2.1 expresses the transmission of the incident high energy hadrons through the shield and is plotted against shield thickness for various materials in Figure 2.1.

Although transmission has been plotted from zero shield thickness, exponential attenuation of the dose equivalent, as described by Equation 2.1, will only occur after secondary particle equilibrium has been established. For high energy radiation effective equilibrium will be reached after the radiation has traversed about 3 mean free paths through the shield when 95% of the incident hadrons will have interacted.

2.1.2. Source terms for shielding calculations The quantity to be used for Ho in Equation 2.1, for the

estimation of dose equivalent outside a shield for a given beam loss, will be the effective dose equivalent after secondary particle

35


equilibrium has been established. This quantity is estimated in a similar way to equilibrium particle fluence as given in Section 1.2.5. The equilibrium dose at a depth in an absorber will occur when the energy being liberated per unit mass in interactions by the residual incident hadrons equals the energy being absorbed. When this condition has been reached the energy deposited and hence the dose will be proportional to the fluence of the hadrons times their energy divided by their interaction mean free path in the shield. However, this full equilibrium will only occur inside a shield of large dimensions that is uniformly irradiated. At the outer surface of the shield the energy absorption per unit mass drops to about 50% of that liberated as the contribution from 'backscatter' is removed. The degree of equilibrium will also depend on local conditions. For the exposure of a person on the outside of a non-uniformly irradiated shield the dose will further reduce with distance from the shield. Differences between the absorption of secondary particles in tissue and in the shield material will also have to be taken into account. As an overall approximation it is assumed that the absorbed dose to a person near the shield will be 90% of that at the surface of a uniformly irradiated shield. Taking the secondary particle energy to be as

10-1

10-5 -

---.--r----

--.-....

-"'"

'; -. ..... '--. \,

\ \

"'. Earth

\.\ Iron', .

...

...• ,

\

'''',. '-..

Concrete "',

Baryte·· ... '-.. '

T

10---<; -.-:... .. I ~O----~----~----3~--~----~- ~6~--~7~---~8

Shield thickness (m)

Figure 2.1_ The transmission factor for dose from high energy hadrons in various materials as a function of shielding thickness.

36


given by Equation 1.12 and assuming a quality factor of 4, the dose equivalent source term Ho' for the secondary radiation produced when primary protons of energy Eo Ge V interact in a target and assuming an effective interaction mean free path in the shield of 100 g.cm-2 (see Table 1.3), becomes

Sv.m2per proton (2.2)

where <P is the first generation secondary hadron fluence (hadrons.m-2

) at 1 m from the primary proton interaction, which depends on emission angle and incident proton energy and is given by Equation 1.8. Substituting for this fluence in Equation 2.2, gives the source term for calculating the dose equivalent through a shield at an angle 0 deg from interactions by primary protons of energy Eo Ge V, of

1.8 x 10-10 E 0.76

H (0) - 0 Sv.m2 per proton (2.3) o - (0 + 35/--JEo)2

Ho(O) is plotted as a function of the interacting proton energy for various angles in Figure 2.2 where it can be noted that for

o deg

--_.-.. -... -_ .. ,- ---.--

o' .--------------------------.-

/_----/----- 30 ----------.

-~.

-: -.-:::-.::=---::---~--- .,'

10-2 .. ' I ....L..l-l....L I I I I I I I I I I I 1 10 102 103

Interacting proton energy (GeV) Figure 2.2. Effective dose equivalent source term in pSv at m per proton interaction that can be used to determine shield thickness in various directions to the incident proton beam and for thick shields. Dashed line is EO.s law given by

Equation 2.4 for radiation emitted at 90 deg.

37


radiation emitted at 90 deg, the dose equivalent source term can be approximated by

H o(90) = 1.7 x 10-14 Eoo.s Sv.m2 per proton (2.4)

This dose equivalent source term and its dependence on incident proton energy, when combined with the distance and attenuation terms given by Equation 2.1, results in dose rates that agree reasonably with those that have been determined experimentally outside thick lateral concrete shields for primary protons in an energy range from 5 to 450 Gey(l).

The hadron dose equivalent source terms for 0 deg emission are also indicated; however, it should be noted that for high incident proton energies (greater than about 8 GeY), the radiation field in the forward direction may be dominated by muons, for which the shielding has to be determined separately (see Section 2.3).

2.1.3. Dose build-up in an absorber At very high proton energies the shielding source term, or

the effective dose equivalent at 1 m from a target, that is to be used with the simple exponential attenuation to determine shielding thickness will be considerably higher than the actual dose equivalent near to the target. This is because particle multiplication or dose build-up occurs within the shield up to a depth where secondary particle equilibrium is reached. Comparison of the equilibrium dose equivalent or source term given by Equation 2.3 with the actual dose equivalent near the target (Equation 1.31), allows an estimate to be made of this dose equivalent build-up in the shield. An estimate of the dose variation with depth in the shield due to this build-up can also be made if it is assumed that particle multiplication continues until the average hadron energy has dropped to 120 MeV. The number of collisions and hence the average number of mean free paths the radiation has to traverse for this to occur can be estimated from Equations 1.12 and 1.16. If it is then assumed that the dose equivalent builds up exponentially with depth in the shield, then the resulting dose equivalent as a function of depth will be as shown in Figure 2.3 where it is compared with that calculated using the simple source and exponential absorption terms given by Equation 2.1 (dashed line). These calculations are for the dose equivalent rate due to secondary radiation at 90 deg from 1010

38


interactions per second by protons of the energy indicated. For convenience of presentation, the dose equivalent rate times the square of the distance in metres from the point of interaction has been plotted as this makes the shape of the curves presented independent of the target/shield geometry.

2.1.4. Beam line shields (a) Point losses

The dose equivalent at an angle e and a distance R metres from a proton interacting in a copper or iron target and behind a lateral shield of thickness t will be given by

H (e) H(e) =-°-2 - exp(-(t cosec eVA)

R Sv per proton (2.5)

where 'A is the attenuation mean free path of the radiation (in the same units as t). For the secondary radiation to be in equilibrium, the path length through the shield thickness should be greater than 3 mean free paths.

~ x ., .c :> (f)

10-1

F I~-

10-2 '-__ -'---_-L __ J ----'1 __ -'-_--'-. --'-_---I.I __ ._J_ o 2 3 4 5

Distance into shield (mfp)

Figure 2.3. Product of dose equivalent times distance squared from a target as a function of shield thickness for secondary radiation emitted at 90 deg from a medium atomic weight target struck by protons of energy given. The solid line is an estimate of actual dose build-up in the shield and the dashed lines are the effective equilibrium dose equivalent calculated using the simple source term

with exponential attenuation for 1010 interactions per second.

39


Ho(9) is the dose equivalent per interaction at 1 m given by Equation 2.3 and was plotted as a function of incident proton energy for selected-· emission angles in Figure 2.2. For practical purposes, this source term is plotted in Figure 2.4 as the equilibrium dose equivalent rate at 1 m from 1012 proton interactions per second in a target.

Dose estimations are often required for the determination of lateral shields where the effective emission angle can be taken to be 90 deg. However, the maximum dose outside a shield may occur at an angle slightly less than 90 deg owing to the angular distribution of the secondaries produced in the high energy particle interaction. Estimates of the angle at which this maximum dose is expected to occur are shown in Figure 2.5 as a function of shield thickness for different primary proton energies. The calculated maximum dose relative to that at 90 deg is shown in Figure 2.6 as a function of shield thickness where it can be seen that for shields of more than 3 radiation attenuation mean free paths thick the maximum dose will not exceed the perpendicular dose by more than 30% at any energy. Hence the effect can be considered as unimportant from the point of view of shield design.

., rf)

~ 105

.9 2 a. ~o 104

Q; Cl.

., 103

.c :> ~

102

10 1

.-.-.- .... -

I I I III

.-.---o deg _----------.

//-/1'0 .---------------.---~------ --.-

_/ , .. -/ ~----- .--.---.-----------~-------_ ..... -..... ------------- ---

__ -.---.-.. ------ 30·------- ~---.--

---------------

------------

90-----

10 Interacting proton energy (GeV)

Figure 2.4. Dose equivalent source term for the calculation of thick shields, applicable at the angle indicated, in Sv.h- I at 1 m for a primary proton beam loss of 1012 protons per second in a copper or iron target, as a function of beam energy.

40

g> 80 :g. Q) <n o

" E :::>

.~ 70

'" E '0 .!!! 0>

.:'i 60

E =1 GeV

2 3


--------

-~-., .... '

4 5 6 7 8 9 10

Shield thickness (mfp)

Figure 2.5. The angle to the beam direction at which the dose will be a maximum as a function of shield thickness in mean free paths for incident proton energies

frorn I to 1000 Ge V.

1.8

o 2 3 4 5 6 7 8 9 10 Shield thickness (mfp)

Figure 2.6. The ratio of the maximum dose on a shield compared to that calculated perpendicular to the point of loss, as a function of shield thickness and

for different beam energies.

41


(b) Unifonn beam losses along a beam line The dose outside a lateral shield of thickness t and at a distance

R metres perpendicular to the beam line along which there is a unifonn beam loss giving one interaction per metre of beam path will be given by the integral from 0 to 180 deg of

1 fl80 H = 2 Ho(e)exp(-(t cosec e)/A) sin2e de

R 0 (2.6)

where A is the mean free path of the radiation in the shield in the same units as the shield thickness t.

This integral for the dose outside a lateral shield has been plotted in Figure 2.7 relative to the dose that would occur at 90 deg from a point loss of intensity equal to the number of interactions occurring in a continuous loss along a distance of R metres of beam line. The calculations have been made for protons of 1,10 and 1000 Ge V and as can be seen no great error would result if

2.0

1.8

1.6

"' 1.4 "-

li... 1.2

~ 1.0 co u..

0.8

0.6

0.4

0.2

0 0 4 6 8 10 12 14 16 18 20

Shield thickness (mfp)

Figure 2.7. The factor by which to multiply the dose at a distance R from a point loss to obtain the dose to be expected from the same loss but spread uniformly along R metres of beam line. Curves are for protons of energies (a) 1 Ge V , (b) lOGe V

and (c) 1000 GeV. Dashed line is factor given by Equation 2.7.

42


the dose ratio was taken to be unity for all primary proton energies provided the shield is more than 3 mean free paths thick. Hence as a first approximation for shielding calculation purposes continuous and point losses may be considered equivalent. From the data given in Figure 2.7 it can be seen that some improvement in the equivalence could be made if the point loss dose is multiplied by a factor, F, given by

F = 1.5 exp(-O.06t/A) (2.7)

Hence the effective dose equivalent for a continuous beam loss of 1 proton per metre of beam path, outside a lateral shield of thickness t and at a perpendicular distance of R metres from the beam line, will be given by

F R H (90) H = 2

0 exp( -t/A) R

which can be represented by

H (cont) H = 0 exp( -t/0.94 A)

R

Sv. per proton (2.8)

(2.9)

Value for Ho(cont), the source tenn to be used in Equation 2.9 for calculating the lateral shield required for continuous losses along a beam line is plotted in Figure 2.8 as a function of the incident proton energy for the case of a continuous beam loss of 1010 protons.s-I.m-I and for a beam loss equivalent to 1 watt of beam power per metre.

2.1.5. Dose equivalent outside beam dumps The best approximation that has been found for estimating

the dose outside shielded targets or beam dumps is to assume that the entire beam is lost at 1 mean free path into the dump and then calculate the line of sight dose using the thin target angular distribution data, given in Figures 2.2 and 2.4, together with the attenuation mean free paths given in Table 1.3. This approximation is shown diagrammatically in Figure 2.9 where the dose at the point A will be given by

Ho(e) H(A) = 7 exp[-(x/A1 + XiA2)] Sv per proton (2.10)

43


Calculations of the dose equivalent along the outside of a beam dump consisting of a cylindrical iron core of 1 m diameter surrounded by 2 m of concrete, using Equation 2.10, is shown in Figure 2.10. It is estimated that this simplified approximation for the dose outside a dump or thick target is sufficient for all

----"..--'"

1-----------____ 1W per m

- .. _----------------------1~' ~ __ ~~~~~~I __ ~~~~~ul ____ ~~~~~

10 102 103


Figure 2.8. Source terms for calculating lateral shields (more than 3 mean free paths thick) expressed as dose at I m from uniform losses along a beam line of

1010 protons per metre per second and for losses equivalent to I watt per m.

A

Shield mfp A2

Beam

1,.,

Figure 2.9. Simplified geometry for the estimation of dose near a shielded target or beam dump.

44


configurations where the lateral shield thickness is more than three times the high energy radiation attenuation mean free path in the material of the dump.

2.2. Shielding for protons below 1 Ge V

2.2.1. The secondary radiation distribution At energies below about 1 Ge V, protons lose significant

amounts of their energy by ionisation before interacting with a target nucleus. Hadrons effectively interact with a nucleus in a two-stage process. In the first stage the hadron collides with individual nucleons in the nucleus giving rise to an intranuclear cascade. The resulting 'cascade' neutrons are the major component of the secondary radiation that has to be taken into account for shielding purposes. Any charged particles emitted in an interaction by a proton of energy less than 1 Ge V will have a high chance of losing all their energy by ionisation before they can interact further. The nucleus that is left after the initial interaction will be in an excited state and may

104~---r----r----r----r----.----r----r--__ r-__ -. __ ~

-----------------.. _--... , 10

.. " -'-'"

....•••....

.•..• "-

.............

Distance along dump (m)

Figure 2.10. The dose rate outside a I m diameter iron beam dump surrounded by 2 m of concrete exposed to a beam of 1012 protons per second of different

energies.

45


evaporate off neutrons (of energy below about 8 MeV) and gamma rays as it de-excites(2,3). As the incident proton energy decreases so the average energy of the cascade neutrons decreases and the relative importance of evaporation products increases. Also, a large proportion of the cascade neutrons will have an energy below 120 Me V and are absorbed more easily than are the secondaries produced by higher energy protons. Hence the neutron production, spectrum and angular distribution from interactions by protons of energy below 1 Ge V is more complicated than was found at higher energies. However, it has been shown that the secondary particle angular distribution determined for very high proton energies, as given by Equation 1.8, when suitably modified to take account of the energy loss of the incoming proton by ionisation, appears to give a reasonable approximation for the angular distribution of the neutrons emitted in interactions by protons of energy less than 1 Ge V(4). Supposing that on average protons of energy less than 1 Ge V incident on a thick target lose on average 20% of their energy by ionisation before interacting, then the total neutron emission per interaction, or multiplicity, for incident protons of different energies, obtained by integrating the angular distribution derived from that observed at high energies, will be as shown in Figure 2.11. This multiplicity, Q, for proton interactions of less than 1 Ge V, can be fitted to the relation

Q = 0.077 IfJ·63 neutrons per proton (2.11)

where E is the incident proton energy (less than 1 Ge V) in MeV. If E is expressed in Ge V, then this multiplicity becomes

Q -- 6 rtl.63 t (2 12) .t:- - neu rons per proton .

An indication of the average energy of the secondaries can likewise be determined and using Equation 1.11, which, with E in MeV becomes

E = 10 IfJ.37 sec MeV (2.13)

However, at low incident proton energies not all the protons will interact before coming to rest. The fraction that interacts will be approximated by

f= 1- e-R()... (2.14)

where R is the proton range m the target material (given by

46


Equation 1.4) and A the nuclear interaction mean free path in the same units as the range, which for protons of energy greater than about 120 MeV will have values as given in Table 1.3.

Examination of the values of the ratio of range to mean free path suggests that for protons of energy E, (less than 1 Ge V) this ratio can be approximated by

R/A=5.7x 10-5 EI.6 withE in MeV (2.15)

or

R/A= 3.6E1.6 withE in GeV (2.16)

-

-

o -

---

--

-

-

-

I III .l Lll1 I I I I I I I I 0.1~----~--~~~~~~~--~--~~~~~~ 10 102 103

Energy (MeV)

Figure 2.11. Number of cascade neutrons emitted per interaction as a function of the incident proton energy. (Interaction energy = 0.8 x incident energy). Dashed

line is empirical fit given by Equation 2.11.

47


The total neutron emission per proton incident on a thick copper or iron target will therefore be equal to fQ. This total neutron emission is plotted in Figure 2.12 as a function of the incident proton energy where it is compared with values taken from a review of experimental data(5). As can be seen the agreement appears reasonable over the entire energy range from 1 Ge V down to below 50 Me V.

Hence combining neutron yields as determined above with the angular distribution of secondaries as found for interactions at high proton energies but with corrections for the interaction probability and ionisation losses gives an estimate of the angular distribution of the fluence of secondaries from low energy protons

(/) Q)

.~

"0 C

8 Q) (/)

o Q; .0

E ::l

z 0.1

If 0/0 i

o !

/6 /

/

~// /

0.01 ...... --..I.-->--..J-..J-.L.....L-W~ __ ...J..._-'--L-L-L.LJ...u 10 102

Incident proton energy (MeV)

Figure 2.12. Number of neutrons emitted from a thick copper or iron target per incident proton, compared with experimental data, as a function of incident

proton energy.

48


incident on a target. This fluence, at I m and an angle 8 to the direction of an incident proton of energy E Ge V, will be given by

where

5000 (1 - e-m)

10(8) = (8 + 40/...)E)2

m = 3.6 E1.6

neutrons.m-2 (2.17)

(2.18)

This angular distribution is plotted in Figure 2.13 for incident protons in the 50 to 1 000 MeV range.

2.2.2. Source terms for shielding calculations The source term required is the dose equivalent that

can be used in a simple exponential attenuation equation, corrected to a distance of 1 m from the point of interaction, per proton incident on a thick target. Applying the fluence to dose

1 GeV

500 MeV

Cii Q) o

~-~ 10-2 100 MeV

50 MeV ___________

Figure 2.13. Angular distribution of neutron fluence per proton incident on a thick copper or iron target for various energy incident protons.

49


equivalent conversion factor for neutrons in the energy range of 0.5-100 MeV of 40 fSv per neutron.m-2 (see Section 1.3.4) to the expected fluence at 1 m and 90 deg as given by Equation 2.17, it has been shown(4) that the resulting dose equivalent corresponds well with experimentally determined values over an incident proton energy range from 50 to 800 Me V(6).

Hence the empirically derived relations appear to predict with reasonable accuracy radiation levels perpendicular to an interaction by incident protons of energy less than 1 Ge V as well as total neutron emission as was shown in Figure 2.12. Some confidence can therefore be placed in using the angular distribution, given by Equation 2.17, to estimate source terms for the determination of shielding at any angle from beam losses for protons in the 0.05 to 1 Ge V range.

Q; Q.

> C/)

.s

Q) o

..J

/ //

Odeg

90 deg

-18~--~~~~~~~~ ____ ~~~~~~~ 10 102


Figure 2.14. Effective source terms for shielding calculations expressed as dose equivalent at I m and 0 and 90 deg per proton incident on a thick target.

50


The derived dose equivalent per incident proton is plotted in Figure 2.14 for the secondaries emitted at 0 and 90 deg as a function of the incident proton energy. The source terms at 0 and 90 deg, expressed as Sv.h-1 for a beam of 1012 protons per second incident on a thick target are plotted in Figure 2.15. Although these data are for thick targets it should be noted that no correction has been included for the absorption of the secondaries in the target and the simplified geometry recommended for determining the self absorption in beam dumps as shown in

./ ./

//

90 deg

10-1

Figure 2.15. Source term for shielding calculations expressed as dose rate at 1 m and 0 and 90 deg for a beam of 1012 protons per second incident on a thick target.

51


Figure 2.9 should be used to correct for target thickness where appropriate.

The resulting source terms for radiation emitted at 0 and 90 deg as estimated for incident protons of 1 Ge V and shown in Figure 2.15 can be compared with those determined by extrapolating the high energy proton source terms down to 1 Ge V, as is shown in Figure 2.4. The agreement is very reasonable considering that the two sets of data are derived from different sets of assumptions.

The dose equivalent rate outside a lateral shield from a continuous loss of protons of energy less than 1 Ge V along a beam line can be estimated in the same way as for very high energy protons (see Equations 2.7 and 2.8) which at a distance R metres from the beam line approximates to

1.5 H (90) H = 0 exp(-t/0.94A)

R Sv.m-1 per proton (2.19)

where H o(90) is the source term for 90 deg emission as given in Figure 2.14.

2.2.3. Secondary particle attenuation For interactions by primary protons of energy less than

1 Ge V, the average secondary particle energy will be less than 120 MeV and, unlike very high energy particles, their attenuation mean free path in the shield will vary with energy. Experimentally determined values of the attenuation mean free paths of radiation in concrete exposed laterally to secondary radiation from proton interactions of different energies have been reviewed(5,6)and compared with calculated values(7,8). These mean free paths, expressed as a proportion of the limiting value at high energies, 1.0' are shown in Figure 2.16 as a function of the energy of the protons incident on a target and have been fitted to a relation

(2.20)

where a has a value of 3 when E is the incident proton energy in Gey.

There is much less information on which to base estimations of the secondary radiation attenuation mean free paths in the

52


forward direction from an interaction and reliance has to be placed on detailed computations(7). An approximation for these values is also found to fit Equation 2.20 reasonably but with a = 5 and this relation is also indicated in Figure 2.16. The experimentally determined mean free paths are for concrete and there do not appear to be consistent sets of data for attenuation lengths in other shielding materials. The data given in Figure 2.16 should therefore be treated with caution when used for estimating other than concrete shielding.

a. E Q)

> '@ Qi 0:

1.0

0.8

0.6

0.4

~ 0.2

o 10

- ~

V ,;'"

/

II 7

tJ

V [l'

,/ FO~1

f :/ ) r~ide

V V V

/ ~~

/ VV -::: ...

102


Figure 2.16. Secondary particle attenuation mean free paths as a function of primary proton energy, relative to limiting high energy mean free path as given in

Table 1.3. Points are experimental data for concrete(5l.

53


2.3. Shielding for muons

2.3.1. Muon production A proportion of the hadrons produced in a high energy

particle interaction will be pions which, being unstable, may have time to decay into a muon and a neutrino before they have a chance to interact (see Table 1.1). Unlike the parent pions, the resulting muons will only very rarely interact with nuclei and lose their energy by ionisation in the material through which they pass. Hence practically all muons will survive when traversing a shield until they reach the end of their range. Muon range in iron was shown in Figure 1.3 as a function of energy where it can be seen that very thick shields may be needed to remove the unwanted high energy muons that form part of the cascade in the forward direction from very high energy proton interactions. Muons therefore have to be given special attention when determining the shielding requirements in the forward direction from targets or beam dumps in high energy particle beams.

The lifetime of the pion increases with increasing energy as was shown in Section 1.1 and it can be shown that a pion of momentum P Me V Ie will have a mean flight path of 55 P metres. As was shown in Figure 1.1, at high energies pion momentum and energy become numerically equivalent so that the proportion of pions, f, that decay into a muon while traversing a distance q metres of path length will be approximated by

f = 1 - e-q/ss£ (2.21)

where E is the pion energy in Ge V. A muon produced in the decay of a pion of energy E will have

an energy in the range from 0.43E to E and is assumed to continue along the same path as the decaying pion.

2.3.2. Muon attenuation By empirical scaling of the expected pion spectrum

following a p:-oton interaction(9) and from this deducing the resulting muon spectrum following pion decay, it has been shown(lO) that the muon fluence outside a shield of thickness t metres in the forward direction and at a distance X metres ahead of a proton interaction approximates to

54


0.085 E q -(111£ -IS o = ? (e - e ) f1 X-

muons.m-2 (2.22)

where E is the interacting proton energy in Ge V, q is the average path length in metres that a pion produced in the interaction can travel before it in tum interacts and ex is an effective average energy loss rate for the muons. This loss rate is a function of the muon spectrum and includes losses due to muons reaching the end of their range as well as due to muons slowing down and is estimated to have values as given in Table 2.1 for common shielding materials. In the case of a beam stopper or dump where the proton beam is absorbed, it is assumed that the effective value for q, the average path length of secondary pions before interaction, is 1.8 times the hadron nuclear interaction mean free path(ll) as given in Table 1.3. It has been shown that the value for ext/E is 15 when t is the range of the highest energy muon in the spectrum(10) and the e-15 tenn in Equation 2.22 ensures that the fluence drops to zero at this depth in a shield.

With present-day beam intensities and energies it is not normally necessary to have shields approaching the range of the maximum energy muon in the spectrum and the e- 1S term can normally be neglected. Hence the fluence of muons in the forward direction from interactions by high energy protons will appear to be exponentially attenuated with depth provided the exponent does not exceed 14. This limiting shield thickness t is given by

t = 14 E/ex metres (2.23)

where E is the proton energy in Ge V and ex is given for different materials in Table 2.1.

Table 2.1 Effective muon energy loss rates (GeV.m-1) for the estimation of

muon shields.

Material

Iron Lead Concrete Baryte Earth Water

Densi!.i: ex (g.cm ) (GeV.m-l)

7.4 23 11.3 29 2.35 9.0 3.2 10.4 1.8 6.4 1~ ~O

55


The muon spectrum is such that the apparent attenuation mean free path of the muons, E/a, is in fact 1/15 of the range of the maximum energy muon in the spectrum. As this maximum muon energy will be about 93% of the energy of the interacting proton, the apparent attenuation mean free path of muons in a shield will be 1/16 of the range of a muon of energy equal to that of the interacting proton.

The muon fluence calculated using the above relation has been checked where possible against measured values outside beam dumps and target areas and a reasonably good correspondence has been found in the forward direction from targets and dumps for protons in the 10 to 26 GeV range(lO). The fluence calculated using the above relation has also been compared with those obtained from detailed Monte Carlo computations(12), where reasonable agreement is found for concrete and earth shields up to proton energies of a few hundred Ge V. For iron and heavier element shields, the formula is limited to proton energies of less than about 100 Ge V as at very high energies muons will be lost through photonuclear reactions and also will lose significant quantities of their energy by bremsstrahlung emission in addition to direct ionisation. These effects have not been taken into account in the formulation.

The expected fluence of muons on the beam axis and per incident proton into an iron beam dump is plotted in Figure 2.17 as a function of dump length for protons of various energies.

2.3.3. Ranging out the muons Ranging out the muons becomes necessary when the

required attenuation in the calculated exponential term in Equation 2.22 exceeds 14. If, for example, it is required that the flux of muons behind a beam dump be less than 104 m-2.s-1 (dose rate less than about 1 f..lSv.h-l) then ranging out muons becomes necessary for proton beam dumps for beams with a mean intensity greater than I protons per second, given by

1= 7.S X 1013 E/a2 proton.s-I (2.24)

where E is the proton energy in Ge V and a as given in Table 2.1. The required shield thickness or overall length of a beam dump, T, will then be

56


T= 1.8 A+ 16E/a metres (2.25)

where A is the proton interaction mean free path in metres taken from data in Table 1.3. These dump lengths, that will range out muons from high intensity proton beams, are shown in Figure 2.18.

2.3.4. Angular distribution of muons The angular fluence and energy distribution of the pions

from an interaction(9) and their subsequent decay into muons results in the muons forming a narrow beam in the forward direction from the interaction. An estimate of the width of this beam has also been made(lO) where it has been shown that if the muon fluence on the beam axis at a distance X metres down beam from a proton interaction of E Ge V after the muons have passed through a shield of thickness t metres is p(O), then the fluence at a radius r metres from the beam line will be given by

p(r) = p(O) exp[-O.13Eat (r/X)2] muons.m-2 (2.26)

where a is given in Table 2.1 for different shielding materials. This relation indicates that the muon fluence will have a

gaussian distribution across the beam with an expected width d,

N

'E ui c o ::::l

E £ (!) () c (!) ::::l

Ol o

....J

Metres of iron

Figure 2.17. Muon fluence on the beam line per proton into an iron beam dump as a function of the dump thickness for various incident proton energIes.

57


(full width at half maximum) of

d = 4.6 X/-V(Eat) metres (2.27)

This relation has been found to give a good approximation to muon beam sizes that have been measured outside beam dumps made of iron and concrete for protons in the 10 to 30 Ge V range(lO)

It is of interest to note that for a beam dump, where the distance from the point of interaction X and the linear shield thickness, t, will be practically equal, the muon beam width increases as the square root of depth into the dump and that for a given depth the muon beam will be narrower the higher the proton beam energy.

102

:[ a. E ::::l

U

'0 .<: 0, c (lJ

....J

10

1~ ____ ~~ __ ~~~~~ ____ ~ __ ~~~~~~ 1 10

Proton energy (GeV)

Figur.e 2.18. The length of a beam dump required to range out muons as a functIOn of the energy of the protons entering a dump made from different

materials.

58


2.3.5. Muon beam strength By integrating the muon fluence over the beam area, as

given by Equation 2.26, an estimate can be made of the total number of muons surviving at a depth in a dump per incident proton, or of the effective strength of the muon beam that exits from a dump. The resulting number of muons appearing in the forward direction from an interaction by a proton of energy E Ge V, surviving at a depth of t metres in a shield will be given by

I = 2q e-atlE

!1 at muons per proton (2.28)

where q is the pion decay path length in metres and a is the effective muon energy loss rate in the shield which was given for different shielding materials in Table 2.1.

The muon beam strength is probably a more appropriate parameter than the fluence for deciding the size of a beam dump, as it is independent of the divergence of the incident proton beam and will not be influenced by the presence of magnetic fields that could disperse the muons in an iron dump. The surviving muon beam strength per proton incident on an iron beam dump (where the mean pion flight path before interaction, q, is assumed to be 0.34 m) is shown in Figure 2.19 as a function of depth in the

c ~, .8 e ~,,~, ~ 0..

Q) 0.. if) 30 50 100 GeV c

~~ "'-0

:::::>

E-O> 0

....J

Metres of iron Figure 2.19. Intensity of surviving muon beam as a function of thickness of an

iron beam dump per incident proton of energy indicated.

59


dump for incident protons of different energies.

2.3.6. Isofluence contours The volume of a beam dump varies as the square of its

radius so that some consideration needs to be given to an estimate of the minimum lateral dimensions of a muon shield that would be consistent with the shielding requirements. The radius at which the muon fluence has a given value can be calculated as a function of depth into the shield using Equations 2.22 and 2.26. The radius r metres at a depth X metres in an iron shield, where the fluence will be lO-n muons.m-2 per incident proton of energy E Ge V, can be obtained from the approximate relation

r2 = X/E (0.77 n - 1.16 - 7.7 X/E + 0.33In(E/X2) m2 (2.29)

To be strictly correct, the shield thickness in the forward direction has to be increased by the average distance taken for the proton to interact and the pion to decay, which for iron is assumed to be 0.34 m.

2.or------.,---,.--,----r--.,---r--r---r---;--.---,----,

I c e ~·10-11 ~ 1.0 ~---~ -",

~ -~ (J)

OJ

'6 <Il a:

2

~~ 10-10 ."-.,.

~ ~ 10-9

~ ~ 10-8

\ /~ 10-7 ""\

10--6 \

4 6

10-5 \ \ .

\, 8 10 12 14 16 18 20 22 24

Depth in iron (m)

Figure 2.20. Isofluence contours of muons in iron per 30 Ge V incident proton. The numbers indicated on the curves are muons.m-2 per incident proton.

60


Isofluence contours of muons from 30 Ge V protons interacting in an iron dump are given in Figure 2.20 which shows the elliptical form that an optimised beam dump should have. However, the above generalisations may have little direct value as the design criteria for a beam dump will depend on the real conditions in a beam area where muons produced by the decay of pions originating from interactions in a target or beam element, which could have a considerable decay path, could be a more important consideration than those from protons lost in the dump itself. Even in such cases it should be possible to get a reasonable approximation for the ideal shape of a muon shield by combining Equations 2.22 and 2.26.

2.4. Radiation transmission through holes and chicanes in a shield

2.4.1. Radiation at the entrance to a hole in a shield All accelerator shields require holes or openings for

cables, ventilation ducts, personnel access, etc. and considerable care has to be taken to ensure that radiation escaping through these holes does not seriously undermine the overall efficiency of the shield.

If the radiation source is directly opposite the entrance to a hole then the radiation level at the exit from the hole or at the end wall of the first leg of a chicane can be calculated assuming the inverse square law of distance from the source into the hole. The source term to be used, or the effective dose equivalent at 90 deg and 1 m from a high energy proton interaction was estimated in Chapter 1 and was given by Equation 1.31. The resulting dose equivalent source term, Ro' expressed as Sv.h-1 at 1 m per 1010 protons interacting per second is plotted as a function of incident proton energy in Figure 2.21. With uniform losses along a beam line, the source strength could be considered as being equivalent to that of an axial point loss equal to that occurring along the length of beam path that has line of sight up to the exit from the hole or to the end wall of the first leg of a chicane.

Unless deliberately created, it is unlikely that the radiation source will be directly opposite a hole mouth and more usually the radiation will be obliquely incident as indicated diagram-

61


matically in Figure 2.22. For the purposes of estimating the radiation scattered down such a hole, it is assumed that all

,. ..c :> ~ <J.)

"§

10

~ 1-m > ·s 0-<J.)

<J.) (/J

o o . ..- ....

0.1 L-:---L-.l.-LLU.uL_-L-L.I....l...l..U...!.l--_.L-.L...I.....w..l..J...l.L----1---1-L....I...l..L.U.J 10-1 1.0 10 102

Proton energy (GeV)

Figure 2.21. Source term for dose equivalent rate at 1 m and 90 deg from 1010 proton interactions per second as a function of proton energy for use in

estimating transmission down holes whose axis is in line with a beam loss.

Cross section A

x Shield mfp A

Source

Fi.gure '2.'2'2. Diagram showing radiation incident at an angle e to a hole of length X and cross section area A in a shield where the radiation interaction mean free

path is A.

62


radiation traversing less than 1 mean free path of shield before striking the internal wall of the hole forms part of the radiation that is c6nsidered incident and may be eventually scattered down the hole.

Appropriate values for the effective dose equivalent at 1 m from a source consisting of 1010 proton interactions per second, calculated using Equation 1.31 are given in Figure 2.23 as a function of emission angle and for different proton energies. Similarly, approximate source terms for X rays from electron interactions may be estimated using Figure 3.1 (Chapter 3).

2.4.2. Radiation scatter down holes in a shield If the average diameter of a hole is small compared to the

thickness of shield it tranverses and to the distance from the radiation source, then for radiation incident at an angle e at a hole of cross sectional area A in a shield where the radiation attenuation

"", '"' ,E=1000GeV ., .

". 1 o~::::···--,--... --______ _ .'-"~ ..... -. ~--... ---------::'----

1 0 ____ ... _ __...,. ----______ ~ ___________ _

"-~1~~-==--==-----=---_====_ ~---.----------------------

10-1 ------0.1 - _____ ~ ---------------_.-

10~~~~--~~--~~~--~~~--~~~~~~--~~~ o ~ ~ W 90

Emission angle (deg)

Figure 2.23. Hadron dose equivalent source terms for hole transmission calculations as a function of emission angle. Dose rates are those at 1 m for an

interaction rate of 1010 protons of energy given per second.

63


mean free path is A, the effective area of wall inside the hole that is struck by radiation is approximately given by

Aeff = A tan(S) + IdA sineS) (2.30)

As the radiation is incident along the inside wall and a little way into the hole, the length along which radiation is scattered will be reduced and the effective hole length L is approximated by

L =X -Ae~A (2.31)

If Hm is the radiation level at the mouth of a hole, then the radiation level due to radiation scattered to a depth X into the hole is found to depend on:

(a) the amount of radiation entering the hole,- Aeff><Hm; (b) ratio of the effective hole cross section to wall area - -VAIL;

and (c) inverse square of distance the scattered radiation travels

into the hole = OIL)2.

Combining these parameters gives, for the expected radiation level at a depth X into a hole, where that at the hole mouth is Hm ,

K.A ff.-VA H=H. e n (2.32)

m L3

where K could be considered some scatter coefficient for the radiation and the wall material concerned.

Values for K have been estimated from data given in a review of radiation measurements in chicanes(6) where radiation is scattered round 90 deg bends. For neutrons or secondary radiation from high energy particle interactions, K is estimated to be in the range 0.2 to 0.6 -depending on the radiation source, the material of the wall and the radiation quantity being measured. The experimental data also indicates the possibility that the coefficient varies inversely with neutron energy and appears to have a limiting value, determined from data for thermal neutrons(13), of about 1.1. Measurements of scatter of X rays along chicanes suggest they are transmitted less easily than neutrons and a more appropriate scatter coefficient would be K = 0.1. In cases where the radiation is incident at the hole mouth at angles of less than 90 deg the scatter coefficient K can be expected to increase up to a maximum value of 1 for small angle scatter.

64


The relative transmission of neutrons and X rays along holes or ducting in a shield, calculated using Equation 2.32 is plotted in Figure 2.24 as per cent of the radiation level at the mouth as a function of the effective distance into the hole. The hole length is given in units of the square root of its cross sectional area as this quantity should lead to a universal transmission curve independent of the actual size of the hole. These calculations are compared with independently detennined transmission curves for neutrons (dashed line)(14) and as can be seen give a reasonable correspondence.

Using the above formulation the transmission of radiation down holes of different length-to-area ratios in a shield can be estimated. The results of such calculations are shown in Figure 2.25 for neutrons and in Figure 2.26 for X rays as a function of the angle at which the radiation is incident on the mouth of the hole.

There is found to be a slight dependence of transmission on hole size as well as the ratio X/-VA and the results given above are essentially for 30 cm diameter holes. The transmission down a 10 cm hole would be about a factor of 3 higher than for a 30 em hole with the same value for XtJA and for aIm diameter hole the trans-

c: o ·iii en ·E en c: jg (])

s c: (])

l: (])

a.

'\ \ \' , \\ ~ ..... ~eutrons

'- "-

\. ~', '~ ~'''-'' ~ ", X rays

0.1

0.010~-...I..--~--'---4.L--...I..--~6---''----~'';;::::''"'-----,'10

Distance from tunnel mouth, XtVA Figure 2.24. Calculated transmission of neutrons and X or gamma rays along ducting, plotted as percentage transmission as a function of distance from the mouth, in units of the square root of the cross sectional area of the tunnel. The dashed curve is a so-called universal transmission curve for neutrons that has

been determined independently(14).

65


--------' ........ ----.~ ---.--" ~-10----------------------

'j 1 0-3

,/_-----/.---------

f-10-4

----------~------

~---------_--50---------

_.,.,..-'

10~L--L--L--L~~-L~~~~--~~--~~--~~--~80 20 30

Angle between radiation direction and hole mouth (deg) Figure 2.25. Transmission factors of neutron dose equivalent down holes in a shield where radiation makes an oblique angle with mouth of hole for holes of different ratio of length to diameter. Data is for 30 cm diameter hole and small

correction necessary for other hole sizes (see text).

_-.. --/-.. -.. ---.. -.. 50-----------------------

-------...-------

10~~~~~~~~~~-L~~-L~~~~~~--~~--~ 40 50 60 70 80

Angle between radiation direction and hole mouth (deg)

Figure 2.26. Transmission factors of X ray dose down holes in a shield where radiation makes an oblique angle with mouth of hole for holes of different ratio of length to diameter. Data is for 30 cm diameter hole and small correction

necessary for other hole sizes (see text).

66


mission determined using the above curves should be divided by 2. The expected transmission of hadron radiation incident at a hole mouth with an angle of 45 deg is shown in Figure 2.27 as a function of hole diameter for holes through shields of different thicknesses.

2.4.3. Transmission down multi-legged chicanes The layout of a multi-legged chicane is shown diagram

matically in Figure 2.28. Transmission of radiation down the first leg will be the same as that calculated for a hole in the shield as given by Equation 2.32 and the data given in Figures 2.25 and 2.26. However, when dimensioning personnel access chicanes it is often necessary to assume the radiation source is directly opposite the chicane opening in which case the source term will be given in Figure 2.21. Attenuation of the radiation will follow the inverse square law of distance from the source until the radiation interacts in the end wall of the first leg from where it is scattered down subsequent legs of the chicane. It is assumed that

~.

8 m~

~_/----.. -------.~--------

100

Figure 2.27. Transmission of dose rate from hadrons incident at 45 deg to the hole mouth as a function of average hole diameter for holes through different

concrete shield thicknesses.

67


the chicanes are all of moderate dimensions where the effects of air scatter and absorption can be ignored. If H 0 is the radiation level at I m from the source in the direction of the chicane, then the level at the end of the first leg of the chicane of length X I whose mouth is at a distance R from the radiation source will be given by

HI = Ho/LI2 (2.33)

where

(2.34)

The length of a leg of a chicane would normally be measured from its mouth. However, the source of scattered radiation originates at the end wall of the previous leg so that the effective leg length is greater than that as measured from the mouth. For a leg of length Xn shown in Figure 2.28, the effective length is approximated by Ln where

Ln = Xn + ...JAn_I (2.35)

If Hn is the radiation level at the end of the nth leg of the chicane (after (n-I) bends), then the transmission along the nth leg will be similar as for a hole in a shield (see Equation 2.32) and be given by

L,

P /.

Protons E(GeV)

i

i-------,.-rI

Figure 2.28. Diagrammatic layout of a 3-legged chicane. Secondary radiation is assumed to be produced by high energy particle interactions at P, which then interact at the end wall of the fIrst leg before being scattered down successive

legs of the chicane.

68


KA( I) . ...JA H -H n- n n - (n-I)' L 3

(2.36) n

the radiation level at the exit of the chicane will therefore be

H =HI xr-I Al . ( ...JA2 . ...JA3 ... ...JAn )

n An L2 L3 Ln (2.37)

where HI is the radiation level at the end of the first leg. If the chicane has a constant cross sectional area of A m2

, then the dose equivalent transmission factor of a chicane with n legs, and in the case where the radiation source with a dose rate H 0 at I m is at a distance LI metres from the end wall of the first leg, the overall transmission becomes

(2.38)

where

T(n,A) = (KxA 3!2t-I (2.39)

0.1

2 3 4 5 Tunnel area, A (m2

)

Figure 2.29. Transmission factors for neutrons along a chicane with n legs (n = 2 to 4) as a function of cross sectional area of the tunnel.

69


Values for T(n,A), appropriate for determining dose equivalent transmission factors for chicanes in high energy particle shields, are given in Figure 2.29 as a function of the chicane cross sectional area and for chicanes with up to four legs. Note that T(n,A) = 1 for chicanes of cross sectional area of 1.6 m2

, independent of the number of legs in the chicane.

The above formulations enable a first estimate to be made of the transmission of radiation along holes, ducts and chicanes. There is very little reliable experimental data with which to check the duct or first chicane leg transmission when the radiation source is off axis and the data given should be considered as a guide only. The formulation for multi-legged chicanes appears to correspond reasonably well with measured data and an example of the fit for a four-legged chicane opposite a one interaction length target in a 400 GeV proton beam(l5) is shown in Figure 2.30. However, radiation transmission down multi-legged chicanes is a complex phenomenon

(/)

c o e a.

o

~ 10-1 -

CD a. >.

~10-2

.-.-&'-

First leg

-'--... Q

-------:;----______________ Second leg

o \ \C) "

\'"

'-~ Third leg

o~ \"

'",,-·' ..... -... _~.\.o

Fourth leg

-""\"

10~·L-~--~~ __ ~~~-L--~-J--~--L-~--~~~~ 8

Distance along chicane from source (m)

Figure 2.30. The calculated radiation level along the four legs of a chicane compared to measured data(l5) using a 400 GeV proton beam on a 1 interaction length target opposite the entrance to the chicane. Dose equivalent given in Figure 2.21 was converted to absorbed dose assuming a constant quality factor

of3.

70


and may also depend on parameters, such as the absorption properties of the tunnel walls, that have been ignored in the above analysis, although the formulation should reasonably apply to secondary particle transmission through the usual concrete walled chicanes with tunnel lengths of up to 10 times their width.

2.5 Skyshine

2.5.1. Neutron dose rate at a distance Radiation from an accelerator installation may extend out

to large distances from the source. As well as the radiation coming directly through the shield and in a straight line, radiation may also indirectly reach points at large distances by way of air scatter. This radiation is termed skyshine and is usually due to relatively high levels of neutrons escaping upwards through holes or thin parts of an accelerator shield in areas that are normally inaccessible during operation. These neutrons are then scattered in the air and a proportion--arrive back down at ground level.

Results of measurements of neutron skyshine have been reviewed and estimates of the magnitude of the effect made (16-19).

Practical measurements show that beyond about 100 m from the source the skyshine dose rate varies as the inverse square of distance from the source whereas at less than 100 m the local conditions are critical. A best estimate of the dose equivalent at a large distance R (m) per neutron per second emitted uniformly into a solid angle of 21t will be

10-11 e-Rf)...

R2 Sv.h-1 per neutron.s-1 H= (2.40)

where A, is the neutron attenuation mean free path in air which has been found to have an effective value of about 600 m (300 to 900 m depending on source energy).

Using the above data, and assuming the fluence to dose equivalent conversion factor of 40 fSv.m-2 per neutron (see Section 1.3.4) for the relatively high energy neutrons escaping from the installation, then a reasonable estimate of the effective dose equivalent due to sky shine at a distance R metres (greater than 100 m) from an accelerator installation becomes

H = 7 X 104 L(HaA) (e-R/6OO /R2)

71

(2.41)


where 2.EoA is the hadron dose equivalent rate in SV.h-1 times surface area (m2

) summed over the whole of the outside of the installation. The above relation indicates that the 'skyshine' dose is about 40% of what the dose would have been from direct radiation if the emission had been isotropic and the. source was directly visible.

Dose rates due to sky shine, at 100, 200, and 500 m from an installation are shown in Figure 2.31 as a function of total dose equivalent integrated over the whole surface of the installation which, for example, indicates that a local dose rate on a shield of 2.5 )lSv.h-1 averaged over 1000 m2 of shield surface, could give rise to a dose rate of only 15 nSv.h-1 at 100 m from the installation. Hence skyshine should not be an important problem in a shielded facility where free access is possible to all parts of the shield but could become the critical parameter in the design of inaccessible roof shielding or in cases where large quantities of radiation escape through holes in a shield.

,II i I r I j I ......... .,-

.....

...................... / .. , .. /

.... .,. .•........

..... ".

, .. "

................•...

.......

............

...... ,

10-1 ~-....L----'--I.......L-L..l...Ju..L;:----.JI.-...L......L.JI-.L..LU..L...._....L.--.J---L....J....u...uJ 10-3 10-2 10-1

Dose rate integrated over installation (Sv.h-1 x m2)

Figure 2.31. Expected dose rate due to neutron skyshine at different distances from an accelerator installation as a function of the integrated dose rate over the

surface of the installation (in Sv.h-1 x area in square metres).

72

Shieldingfor High Energy Particles

References 1. Thomas, R. H. and Thomas, S. V. Variance and Regression Analyses of

Moyer Model Parameter Data, a Sequel. Health Phys. 46, 954 (1984). 2. Metropolis, N., Bivins, R., Storn, M., Turkevich, A., Miller, J. M. and

Friedlander, G. Monte-Carlo Calculations on Intranuclear Cascades. Phys. Rev. 110, 185 (1958).

3. Skyrme, D. M. The Evaporation of Neutrons from Nuclei Bombarded with High Energy Protons. Nucl. Phys. 35, 177 (1962).

4. Sullivan, A. H. The Intensity Distribution of Secondary Particles Produced in High Energy Proton Interactions. Radiat. Prot. Dosim. 27(3), 189-192 (1989).

5. Tesch, K. A Simple Estimation of the Lateral Shielding for Proton Accelerators in the Energy Range 50-1000 MeV. Radiat. Prot. Dosim. 11(3), 165-172 (1985).

6. Thomas, R. H. and Stevenson, G. R. Radiation Safety Aspects of the Operation of Proton Accelerators. Ch 4, Radiation Shielding, 223. IAEA Technical Report Series No. 282, Vienna (1988).

7. Braid, T. H., Rapids, R. F., Siemssen, R. H., Tippie, J. W. and O'Brien, K. Calculation of Shielding for a 200 MeV Proton Accelerator and Comparison with Experimental Data. IEEE Trans. Nucl. Sci. NS-18, 821 (1971).

8. Alsmiller, R. G., Santoro, R. 1'. -and Barish, J. Calculations for Shielding Large Cyclotrons. Part. Accel. 7, 1 (1975).

9. Grote, H., Hagedorn, R. and Ranft, J. Atlas of Particle Production Spectra . (Geneva: CERN) (1970).

10. Sullivan, A. H. A Methodfor Estimating Muon Production and Penetration through a Shield. Nucl. lnstrum. Methods Phys. Res. 293,197 (1985).

11. Keefe, D. and Noble, C. M. Radiation Shielding for High Energy Muons. The Case of Cylindrical Symmetrical Shield and no Magnetic Field. UCRL 18117 (1968).

12. Stevenson, G. R. A User Guide to the MUSTOP Program. Radiation Protection Group Report, Tech. Memo. HS-RP!fMn9-37, (Geneva: CERN) (1979) .

13. National Council on Radiation Protection (NCRP), Radiation Protection Design Guidelines for 0.1-100 MeV Particle Accelerator Facilities. NCRP Report No. 51 (1977).

14. Goebel, K., Stevenson, G. R., Routti, J. T. and Vogt, H. G. Evaluating Dose Rates due to Neutron Leakage through the Access Tunnels of the SPS. Radiation Protection Group Report, LAB 11-RAfNoten5-1 0, (Geneva: CERN) (1975).

15. Cossairt, J. D., Couch, J. G., Elwyn, A. J. and Freeman, W. S. Radiation Measurements in a Labyrinth Penetration at a High Energy Proton Accelerator. Health Phys. 49, 907 (1985).

16. Wade Patterson, H. and Thomas, R. H. Accelerator Health Physics. 437 (New York: Academic Press) (1973) .

17. Stevenson, G. R. and Thomas, R. H. A Simple Procedure for the Estimation of Neutron Skyshine from Proton Accelerators. Health Phys. 46, 115 (1984).

18. Ladu, M., Pelliccioni, M., Pieci, P. and Verri, G. A Contribution to the Skyshine StUdy. NucL Instrum. Methods 62, 51 (1968).

19. Rindi, A. and Thomas, R. H. Skyshine - A Paper Tiger? Part. AeceL 7, 23 (1975).

73

74

CHAPTER 3

Shielding for High Energy Electron Machines

3.1. Electron interactions

3.1.1. Critical energy High energy electrons have a short range compared with

protons of the same energy (as was shown in Figure l.3) on account of energy losses due to bremsstrahlung (X ray) emission in addition to ionisation as they pass through material. For a target of atomic number Z, the electron energy at which the rate of energy loss by ionisation and bremsstrahlung become equal (called the critical energy)~) is approximated by(l)

Ec= 800/(Z + 1.2) MeV (3.1)

Values of this critical energy in some common target materials are given in Table 3.l.

3.l.2. Radiation length Radiation length is the distance an electron travels in a

given material before losing all but lie of its initial energy. This distance approaches a limiting value for high electron energies which gives the characteristic radiation length of the material concerned. The radiation lengths for some common target materials are given along with the critical energies in Table 3.1.

Table 3.1. Radiation length and critical energy for electron interactions and threshold energy for neutron production by gamma rays in common target

materials.

Target Critical Radiation length Neutron material energy threshold

(MeV) (g.cm-2) (cm) (MeV)

Air 102 36.6 30,000 10.5 Water 92 36.1 36.1 15.7 Iron 27 13.8 1.9 11.2 Tungsten 10.2 6.76 0.35 6.2 Gold 9.7 6.46 0.33 8.1 Lead 9.5 6.36 0.56 6.7

75


3.1.3. Nuclear interactions by electrons Electrons interact primarily by way of the bremsstrahlung

X ray photons they emit when slowing down in an absorber. At high energies these photons are commonly referred to as gamma rays. They may go on to produce high energy electron-positron pairs under the influence of the nuclear field and hence propagate an electromagnetic shower in the target or shield.

Above a threshold energy, given in Table 3.1 for various target materials, the high energy photons may undergo photonuclear interactions to produce neutrons in so-called giant resonance reactions. It should be noted that the threshold for photoneutron production is greater than 6 Me V in all materials except for beryllium (1.67 MeV) and deuterium (2.23 MeV). At higher photon energies neutron-proton pairs may be emitted from a nucleus and at very high energies photopions can be produced which, if their energy is high enough, can go on to initiate a hadron cascade. Above a few Ge V muon pairs may also be produced in photonuclear interactions by high energy gamma rays(2) which can become an important radiation component in the forward direction from a target or dump in a very high energy electron beam. Source terms and appropriate attenuation mean free paths for use in shielding calculations relating to these different radiation components can be determined separately.

3.1.4. Radiation near a target in an electron beam The radiation level near a target in an electron beam will

be entirely dominated by the bremsstrahlung X or gamma rays produced in the target. This local dose rate will be a function of emission angle and also be dependent on target thickness and the presence of surrounding material.

Analysis of dose .rate distributions(3) measured around targets bombarded with 33 Mev(4), 100 MeV(5) and 5 Gev(6) electrons suggest an approximate relation for the absorbed dose rate at 1 m from a target and at emission angles of greater than about 20 deg for a beam power loss of 1 kW in copper or iron targets of

D = 2700...JE 9-1.5 Gy.h-1.kW-1 (3.2)

where E is the electron energy in Me V and 9 the emission angle in degrees. The resulting dose rates at 1 m from targets in

76

Shielding/or High Energy Electron Machines

different energy electron beams are shown in Figure 3.1 as a function of emission angle.

The effect of adding material between an electron beam target and the point of measurement appears to cause a build-up of dose at small emission angles whereas perpendicular to the beam direction the radiation field appears to contain a soft component that is readily attenuated. This soft component appears to account for about 50% of the dose rate near a target in a 100 Me V electron beam but at 5 Ge V the dose rate appears to be reduced by nearly two orders of magnitude in the first 2 g.cm-2 of intervening material(6).

3.2. Shielding for high energy electrons

3.2.1. Source termsjor shielding calculations (a) Gamma rays

The source term for the gruwna dose rate due to bremsstrahlung

Figure 3.1. Dose rate at 1 m from a thick copper or iron target per kW of beam power loss as a function of emission angle for electron beams of different

energies.

77


production, at 1 m and per kW of beam power dissipated in a thick copper target(7) struck by electron beams of energy greater than lOMe V is taken to be

(i) In the forward direction

Ho = 3x105 E Sv.h-l.kW-1 at 1 m

where E is the electron energy in Ge V.

(ii) At 90 deg to the target

Sv.h-l.kW-1 at 1 m

(3.3)

(3.4)

The gamma dose rate at 90 deg from the target is considered to be independent of electron energy. The above data is for a thick target and it is suggested that the gamma dose levels from a target of 1 interaction length will be 1/3 of these values(7).

10-1

E

Cii

1 -": ., .r= :> Cf.)10-2

"

.-, , ",

", ",

/'

........ "

-------1------HE limits

_________ l.;_----------

... -

Electron energy (GeV)

Figure 3.2. Effective source terms for neutrons in the energy range 25-100 MeV and of energy greater than 100 MeV emitted at 90 deg from 1 kW electron power

dissipation in a thick copper target as a function of electron energy.

78

Shieldingjor High Energy Electron Machines

(b) Low energy neutrons Neutrons below 25 Me V, which includes the giant resonance

neutrons, are emitted isotropically with a yield for a thick copper target of 1012 neutrons S-I per kW of beam power dissipated(8). This neutron emission is considered to give an isotropic source term of 10 Sv.h-I at 1 m per kW of electron power dissipated independent of incident electron energy.

(c) High energy neutrons The source terms for the two neutron components, those in the

energy range 25-100 Me V and those of energy above 100 Me V, have been estimated for the radiation emitted at 90 deg to a thick copper target(3) from measured data(9) and are shown as a function of incident electron energy in Figure 3.2.

Relatively little information exists for the determination of source terms for high energy neutrons emitted in the forward direction from high energy electron interactions. Estimations of neutron production were made at the Stanford ··binear Accelerator(lO) and combining this data with a fluence to dose equivalent conversion of 100 fSv per hadron.m-2 (see Section 1.3.4) suggest a source term for neutrons of energy above 100 Me V, emitted at an angle e, from copper irradiated by electrons of energy above about 3 Ge V of

0.36 1 1 H = SV.h- .kW- at 1 m (3.5)

(1- 0.72 cosei

The resulting source terms for use in shielding calculations for the neutrons emitted at 0 and 90 deg are summarised in Table 3.2.

The data also suggests that the high energy neutron yield will be nearly a factor of two higher with an aluminium target and a factor of two lower for lead than the values that would be inferred from Equation 3.5. However, at high electron energies and for large shield thickness the dose rate in the forward direction due to muons could exceed that of the high energy neutrons(2).

3.2.2. Muonsfrom electron beams Computed muon spectra(2) suggest the muon dose rate on

the beam axis and behind an iron beam dump of thickness t metres could be approximated by

0.5 E e-lOtlE

H=----r (3.6)

79


where E is the electron energy in Ge V (greater than 3 Ge V) and t is the thickness of iron traversed in the range from O.IE to 0.65E metres of iron. This apparent representation of muon dose equivalent in the form of a source term with exponential absorption comes about because of the shape of the muon energy spectrum as was also the case for muons produced from pion decay following hadron interactions. The relation is only valid for shields of thickness up to the range of the maximum energy muon which occurs when the exponent has a magnitude of 6.5. The conversion of muon fluence to dose equivalent has been made using the relation given by Equation 1.25 and assuming a quality factor of 1.

The apparent muon attenuation mean free path in a given shielding material (O.IE metres for iron for muons originating from electrons of energy E GeV), will depend on the muon range in that material. Hence from a knowledge of the range of muons in different materials(ll), the apparent attenuation mean free path of muons in other shielding materials can be inferred by comparison with the data for iron. These mean free paths are indicated in Table 3.2. It can be noted that muons originating from high energy electrons appear to have a much longer attenuation mean free path than those resulting from proton interactions at the same energy and hence must have a harder muon energy spectrum. However the maximum energy muon will be approximately the same in the two cases and muons from electrons will be ranged out with about the same shield thickness as required for those from protons of the same energy. Hence reference can be made to Figure 2.18 for the shielding thickness

Table 3.2. Effective source terms of use for estimating high energy electron beam shielding in Sv.h-l at 1 m from an electron power dissipation of 1 kW in iron or copper by a beam of electrons of energy E GeV. High energy neutron data is for electrons of energy above about 3 GeV. Data for neutrons emitted at 90 deg by lower energy electrons can be obtained from

Secondary radiation

Gamma rays Neutrons < 25 Me V Neutrons 25-100 MeV Neutrons > 100 Me V Muons

Figure 3.2.

Sv.h-l.kW-1 at 1 m at 0 deg at 90 deg

3x105 E 50 10 10

1.2 4.6 0.36

0.5 E 0

80


required to range out muons from electron beams.

3.2.3. Secondary particle attenuation The estimated attenuation mean free paths in concrete

and iron for the different components of the secondary radiation formed when a high energy electron beam strikes a target are given in Table 3.3. The contribution of the different secondary radiation components to the dose rate at 90 deg to a target and their variation with depth in a concrete shield are shown for 500 MeV electrons in Figure 3.3 and for electrons above 10 GeV

Table 3.3 Attenuation mean free path of the secondary radiation emitted from a target in a beam of electrons of energy E GeV. (The assumed target

densities are given in Table 1.3.)

mfp (cm)

Radiation Concrete Iron Lead

Gamma rays 21 4.7 2.4 Neutrons < 25 MeV 18 16 Neutrons 25-100 MeV 28 Neutrons> 100 MeV 43 18 17 Muons 0.26E 0.1 E 0.077 E

E=500MeV

Metres of concrete

Figure 3.3. Variation of dose rate with depth in concrete of the various secondary radiation components emitted at 90 deg for a power dissipation of 1 kW in a

thick copper target by 500 Me V incident electrons.

81


in Figure 3.4 where it can be seen that for thin concrete shields the gamma rays are dominating whereas high energy neutrons

E

=10-1

co

"k1O-2

-'"

E>10 GeV

10~~--~--~--~~--~ __ -L __ ~ ____ ~~~ __ ~ __ ~ o 2 3 4 5

Metres of concrete

Figure 3.4. Variation of dose rate with depth in concrete of the various secondary radiation components emitted at 90 deg for a power dissipation of 1 kW in a

thick copper target by electrons of energy greater than 10 GeV.

~ .:.:; ., .r:. :> ~10.,,;l

~ <l> ~ 10-2

a

~ 10 GeV

Muons

Depth into iron dump (m)

Figure 3.5. Dose rate along the beam line in an iron dump due to the different secondary radiation components for 1 kW of electron beams of 3 and 10 GeV.

82


become the principal component for lateral concrete shields more than about 3 m thick. Low energy neutrons and neutrons between 25 and 100 Me V always contribute to the dose but never appear to be the dominating component. Note that iron is a poor absorber of low energy neutrons and where used for gamma or high energy neutron attenuation should always be followed by a layer of concrete to remove the excess low energy neutrons transmitted.

The apparent dose rate due to the different secondary radiation components in an iron shield in the forward direction from 1 kW beams of electrons of energies 3 and 10 GeV is shown in Figure 3.5. This figure indicates that for shield thickness above about 80 cm of iron the high energy neutron dose rate exceeds that of the X rays but that above about 3 Ge V the muon dose rate on the beam line will predominate.

Using the above data, a comparison can be made between the radiation levels near targets in beams of protons and electrons. At 1 m and 90 deg the calculated dose rate for a 1 kW loss of proton beam power at 10 GeV is 125 Sv.h- l (mainly high energy hadrons) which compares well with the 60 SV.h-1 (mainly X rays) estimated for the same power loss by electrons of the same energy.

3.3. Low energy electrons

3.3.1. X ray production Low energy X rays are included on account of the

necessity to deal with radiation from high voltage devices such as accelerating cavities and klystrons. The following data is approximate and is intended as a guide for anticipating problems and to assist in deciding on any remedial actions .

The dose rate from X rays emitted in the forward direction by slowing down electrons(12), extrapolated to apply to a copper target and per rnA of electrons of energy between about 0.5 and 5 MeV can be approximated by

Sv.h-l at 1 m per rnA. (3.7)

where E is in megavolts(13). Using the above relation, the dose from an exponential discharge of J joules of stored energy at E megavolts will result in a dose of

f.lSv at 1 m per discharge

83

(3.8)


The above relations give an upper limit of possible X ray levels from conventional equipment operating at a peak voltage of E MY. These levels are plotted in Figure 3.6 as the dose rate expected at I m per watt of power dissipated in X ray emission by electrons accelerated by different applied voltages. The curve has been extended down to low electron energies as a guide to possible radiation levels. However, it should be noted that radiation levels at 90 deg from an optimised target in an X ray set operating at below 500 kV appears to be up to an order of magnitude higher than those determined by extrapolating from X ray production at higher energies. Levels corresponding to the X ray set emission(l2) with 1 mm of iron filtration have been indicated in Figure 3.6 for comparison.

Account has also to be taken of self-shielding by the walls of the cavity, which can also be very energy dependent as well as the efficiency with which energy can be transferred by accelerating free electrons in an electric field. Measurements near high voltage accelerating cavities indicate that the X ray production efficiency may be low but depends strongly on operating conditions. An overall dependence of dose rate on up to the 9th power of voltage or

1~~·O~-~2--~~~~~~1~O~-1--~~~~"~1~--~~~~~~10

Accelerating voltage (MV)

Figure 3.6. Dose rate at 1 m from a power dissipation of 1 W in copper by electrons as a function of the peak accelerating voltage. The yield from an X ray

set with 1 rnrn of iron fIltration is shown for comparison.

84


power dissipation has been found. Special care is needed in cases where parasitic currents can be

accelerated along sections of an electron accelerator and in cases where magnetic and radiofrequency fields can combine to accelerate electrons by a cyclotron effect where X rays of energy orders of magnitude higher than any applied electric field can arise.

3.3.2. X ray attenuation The X rays are expected to cover a broad spectrum up to

the maximum accelerating voltage. This spectrum will depend on operating conditions and on the degree of filtration that has occurred. The thickness of lead, iron or concrete necessary to attenuate a narrow beam of monoenergetic X or gamma rays by a factor of 10 is shown in Figure 3.7 as a function of the X ray energy. For broad beams of X rays, the build-up of dose due to scattered radiation in the shield has also to be taken into account. This build-up will be a function ~:tthe X ray energy and beam size as well as depending on shielding material and thickness. As a precaution, for shields greater than 1 tenth value layer thick, a

Concrete

Iron

1000

Figure 3.7. Shielding thickness necessary to attenuate narrow beams of monoenergetic X or gamma rays by a factor of 10. Note that for shields greater than 1 tenth value layer dose build-up due to scattered radiation will have to be taken into account. This dose build-up could be a factor of 5 behind a tenth value layer

shield in the case of a broad X ray beam.

85


dose build-up of a factor of 5 should be included in a shielding estimation, implying that an extra shield equal to 0.7 of a tenth value layer should be added to the shield determined using the narrow beam data. Although the tenth value curves only allow crude shielding estimates to be made, they may be of use for determining an effective X ray energy after attenuation measurements have been carried out.

3.4. Synchrotron radiation

3.4.1. The production of synchrotron radiation Synchrotron radiation in the form of photons is emitted

by high energy electrons when following a curved trajectory(l4). These synchrotron photons will cover a very large energy range and may extend into the X ray region where they could constitute an unwanted source of radiation around a circular high energy electron machine(l5,16). Although this radiation occurs near to the machine, which is normally inaccessible during operation, the low energy X rays can cause high local dose rates with consequent radiation damage possibilities and may also provoke the formation of ozone and nitrous oxides in air.

The synchrotron radiation is emitted tangentially to the arc the electrons are following and with a small angular spread. This opening angle, expressed in milliradians, is approximately equal to the reciprocal of the electron energy in Ge V. The 'primary beam' of synchrotron radiation from electrons circulating in a machine will therefore form an intense narrow blade of radiation directed outwards from the machine.

The production, attenuation and scatter of the low energy synchrotron X rays is a multiparameter process depending very much on local conditions, and real estimations of the dose rates near a machine would need to take these variables fully into account. However, generalised estimates of the order of magnitude of synchrotron radiation levels and an analysis of the conditions under which they can be produced could be of use for identifying situations where radiation problems are likely to arise.

3.4.2. Synchrotron radiation energy The mean energy of the photons emitted as synchrotron

radiation is termed the critical energy (the photon energy above

86


and below which 50% of the synchrotron power is radiated) -not to be confused with the so called critical energy of electrons defined in Section 3.1.1. This critical energy is given by

E = 2.2 J3/R keY (3.9) c

where J is the electron energy in Ge V and R the radius of curvature of the arc the electrons are following in metres (this defmition of J and R is used throughout subsequent equations). The resulting critical energy is plotted in Figure 3.8 as a function of electron energy for electrons following arcs of curvature from 3 to 3000 m.

The total energy emitted by an electron per metre of path length, Q, is

Q=14J4/R2 keY (3.10)

A large fraction of this energy will normally be absorbed locally giving rise to local heating effects. The degree of heating can be estimated from a -calculation of the total synchrotron power dissipation per metre of path length. The results of such a

::;-Q)

~ 10-1

>. ~ Q) c Q)

~1O-2

><

10~O~-~1--~~~~~LU~--~~~~~~10L---~~~~~uU102


Figure 3.8. The critical or 'average' energy of synchrotron radiation as a function of electron energy for electrons circulating on arcs of different radii.

87


calculation is shown in Figure 3.9 for a 1 !lA electron beam circulating on arcs of different radii.

3.4.3. The synchrotron energy spectrum The energy spectrum of synchrotron radiation extends

from zero energy up to many times the critical energy and the power spectrum (photon fluence x energy) has a broad maximum at about a third of the critical energy. The theoretical spectrum has been empirically parameterised to obtain the power spectrum of synchrotron photons emitted by an electron traversing a metre of arc under conditions where the critical energy of the synchrotron radiation is E c ke V.

This spectrum, for an electron of energy J Ge V traversing an arc of radius R m, can be represented by

E dN/dE = 7.7 f/R [exp(--O.95E/Ec) -exp(-4.5E/E)] keY.keV-1 (3.11)

which appears reasonably valid over the energy range from 0.1 to lOEc·

10~~--~~~~~"--~~~~~~~--~--~~~~ 10-1 10 102


Figure 3.9. The synchrotron radiation energy disSipation per metre of path length as a function of electron energy for I JlA beams of electrons following different

curvatures.

88


As can be seen in the above equation, the form of the X ray spectrum depends only on the ratio of the X ray energy to the critical energy, E/Ec. By integrating the above equation an estimate can be made of the fraction of the synchrotron radiation energy that can be attributed to photons of energy greater than a given multiple of the critical energy. This 'universal' integral energy spectrum is plotted in Figure 3.10.

3.4.4. Synchrotron radiation levels The intense blade of synchrotron radiation, emitted in the

forward direction and tangential to the arc the electrons are following, will strike the machine vacuum chamber or some deliberately added shielding. Very low energy radiation will be absorbed but higher energy X rays will be scattered into the surroundings. These processes are highly dependent on photon energy and the thickness and composition of the vacuum window or shielding. If it is assumed that all photons of energy less than 50 ke V are absorbed and the rest scattered into the surroundings,

10~~0--~--~--~--~--~--~6~~--~8--~---1~0---L---J

Photon energy relative to critical energy, BEe

Figure 3.10. The universal integral energy spectrum of synchrotron radiation giving the fraction of the synchrotron energy that is emitted as photons of energy

above a given mUltiple of the critical energy.

89


then the resulting X ray power that escapes into the surroundings from 1 IlA beams of electrons of different energies following different curvatures will be as shown in Figure 3.11.

3.4.5. Dose rate outside the vacuum chamber The synchrotron radiation dose rate outside the machine

vacuum chamber will depend on the scattering and absorption that takes place. If it is assumed that the energy of all photons above 50 ke V is scattered uniformly away from the vacuum chamber then, as a guideline and assuming there is no further absorption of the X rays, the dose rate In Gy.h-1 to an object at

R 3 m

10~~----~--~-L~-L~~~ ____ ~~~~~~~~ 1 10 100


Figure 3.11. The synchrotron radiation power of photons of energy greater than 50 ke V from an electron beam of 1 J.lA circulating on arcs of different radii.

90


1 m from the beam line will be equal to about twice the X ray power dissipation in watts per metre by synchrotron radiation photons of energy greater than 50 ke V.

References 1. Berger, M. J . and Seltzer, S. M. Tables of Energy and Ranges of Electrons

and Positrons. NASA SP-3012 (Washington NASA) (1964). 2. Nelson, N. R. and Kase, K. R. Muon Shielding around High Energy Electron

Accelerators. Nuc. Instrum. Methods 120, 401 (1974). 3. Sullivan, A. H. Shielding of Electron Accelerators up to 600 MeV. Radiation

Protection Group Report, Int. Rep. HS-RPJIR/81-14 (CERN, Geneva) (1981). 4. Tomiasu, T. Angular Distribution of Emitted X Rays from Thick 270 0 Sector

Type Pb and Cu Targets Bombarded by 15-35 MeV Electrons. Nuc!. Instrum. Methods 173, 371 (1980).

5. Wyckoff, J. M., Pruitt, J. S. and Svenson, G. Dose Versus Angle and Depth Produced by 20 and 100 MeV Electrons Incident on Thick Targets. Proc. Conf. Protection against Accelerator and Space Radiation, CERN 71-16, 773 (1971).

6. Dinter, H. and Tesch, K. Dose and Shielding of Electron Photon Stray Radiation from a High Energy Electron Beam. Nuc!. Instrum. Methods 143, 349 (1977).

7. Swanson, W. P. Radiological Safety Aspects of the Operation of Electron Linear Accelerators. STI/DOC/IO/188, Ch.2.4.1 (Vienna: IAEA) (1979).

8. Swanson, W. P. Calculation of Neutron Yields Released by Electrons Incident on Selected Materials. Health Phys. 73, 353 (1978).

9. von Eyss, H. J. and Luhrs, G. Photoproduction of High Energy Neutrons in Thick Targets by Electrons in the Energy Range 150 to 270 MeV. Physik 262,393 (1973).

10. Jenkins, T. M. Neutron and Photon Measurements through Concrete from a 15 GeV Electron Beam on a Target - Comparison with Models and Calculation. Nuc!. Instrum. Methods 256, 159 (1979).

11. Richard-Serre, C. Evaluation de la Perte d' Energy et du Parcours pour des Muons de 2 a 600 GeV dans un Absorbant Quelconque. CERN Yellow Report 71-18 (CERN, Geneva) (1971).

12. National Council on Radiation Protection, Radiation Protection Design Guidelines for 0.1-100 MeV Particle Accelerator Facilities. NCRP Report No.51 (Washington, DC: NCRP Publications) (1977).

13 Sullivan, A. H. Radiation Protection Group Report. Tech. Memo TISRP/TM/88-1O (CERN, Geneva) (1988).

14. Winick, H. Properties of Synchrotron Radiation. In: Synchrotron Radiation Research, Eds H. Winick and S. Doniach , Ch. 2 (New York: Plenum Press) (1980).

15. Brianti, G. Synchrotron Radiation and its Effects in the SPS used as a LEP Injector. LEP Note 246 Rev. (CERN, Geneva) (1980).

16. Fasso, A., Goebel, K., Hoefert, M., Rau, G., Schonbacher, H., Stevenson, G. R., Sullivan, A. H., Swanson, W. P. and Tuyn, J. W. N. Radiation Problems in the Design of the Large Electron-Positron Collider (LEP). CERN Yellow Report 84-02, (CERN, Geneva) (1984).

91

92

CHAPTER 4

Radioactivity Induced in High Energy Particle Accelerators

4.1. Properties of induced radioactivity

4.1.1. High energy particle activation When a high energy hadron interacts with a nucleus,

neutrons, protons and other nuclear fragments may be emitted, converting the struck nucleus to that of a different isotope, most probably of a different element, which has a high chance of being radioactive. Some of the secondary particles emitted in an interaction may have sufficient energy to go on and cause further activation by spallation rea.~tions or end up being captured by nearby nuclei which may result in a radioactive isotope being produced. Hence, although the overall quantity of radioactivity induced in an accelerator will depend on the primary beam loss, the probability of producing a particular isotope will depend on the composition of the material struck, the spectrum of secondaries produced and the production cross section of the isotope concerned. The amount of a radioactive isotope present at any given time will also depend on the isotope half-life and the time that the accelerator has been in operation as well as the time that the activity has had to decay since operation stopped. Hence the complexity of the processes governing the amount of radioactivity in an accelerator at anyone time makes it very difficult to quantify the activity in any detail. All that can be attempted is to establish general guidelines governing the production of induced radioactivity and the systematics of its build-up and decay together with estimates of the dose rates that are likely to result near a high energy particle accelerator.

An important parameter concerning the production of radioactivity in a given material is the nuclear cross section for inelastic spallation interactions by high energy hadrons and the corresponding radiation mean free path in the target material. These spallation mean free paths, which are listed in Table 4.1 for common accelerator materials, are essentially j}e same as those

93


detennined for the estimation of the attenuation of high energy hadrons as was described in Section 1.1.5 of Chapter 1.

4.1.2. The activity produced in an interaction The isotope remaining after an interaction by a high

energy particle with a nucleus can have an atomic weight of anything up to that of the target nucleus (or even higher in the case of a capture reaction). The probability of producing a particular isotope in a given target material, or the isotope production cross section, depends on the energy (and charge) of the incident hadron. The relative importance of a particular isotope from the point of view of its contribution to the local dose rate depends on its half-life and the radiation emitted when it decays. The common isotopes found in an accelerator environment are listed in Table 4.2 together with their half-lives, decay mode and the level of gamma radiation they emit(l) expressed as the gamma dose rate at 1 m when the decay rate is 1 Bq or 1 disintegration per second. As can be seen the radioactive isotopes may decay by beta (B-) emission or, where proton rich isotopes are produced, by positron (B+) emission. In some cases the nucleus decays by capturing an orbiting electron (EC). The daughter nucleus resulting from a decay may de-excite by emitting gamma radiation as well as the characteristic X rays of the new atom. In the case of the positron emitters, the two 0.511 Me V gamma photons resulting from the eventual annihilation

Table 4.1. High energy particle inelastic interaction or spallation mean free paths in accelerator shielding and target materials.

Material .. , _ Nominal Spallation

mfp density (g.cm-3

) (g.cm-2) (cm)

Water 1.0 85 85 Concrete 2.35 100 43 Earth 1.8 100 56 Aluminium 2.7 106 39 Baryte 3.2 112 35 Iron 7.4 132 18 Copper 8.9 135 15 Tungsten 19.3 185 10 Lead 11.3 194 17 Uranium 18.8 199 11

94


of the positron with an electron has to be included as part of the average gamma radiation emitted in the decay of the isotope and makes a significant contribution to the gamma dose rate from activated accelerator components.

A large range of different isotopes will nonnally be present in radioactivity induced by high energy particle spallation reactions, each isotope with its characteristic half-life and radiation emission. Providing there are enough isotopes present, then the average properties of the isotopes concerned will be sufficient for determining the 'average' amounts of induced activity and resulting dose rates.

Examination of the isotope charts suggests that on average there are 1.5 gamma photons of mean energy 0.8 Me V emitted per decay of isotopes of half-life between 10 min and 2 y and of mass less than about 60 on the atomic weight scale. In addition, in about 25% of the decays the daughter nucleus is also likely to be radioactive, making the effective average photon emission per decay of an induced radioactl~e isotope in medium atomic number materials equivalent to 1.9 photons of mean energy 0.8 MeV.

Beta particles or positrons are emitted in about 75% of the decays with an 'average' maximum energy in the region of 1.8 MeV. Again, if 25% of the daughter isotopes are also radioactive and the average energy of a beta particle or positron is 30% of the

Table 4.2. Principal radioactive isotopes produced in accelerator structures by spallation reactions and their gamma dose rate constant (dose rate at 1 m

per disintegration per second).

Isotope Half-life Decay fSv.h-1.Bq-l mode at 1 m

7Be 53 d EC 7.8 llC 20 min 13+ 140 18F 1.8 h 13+ 132 22Na 2.6 y 13+ 298 24Na 15 h 13' 560 46SC 84d B' 283 48SC 1.8 d 13' 455 48V 16 d 13+ 397 51Cr 28 d EC 4.3 52Mn 5.7 d 13+ 326 54Mn 303 d EC 114 56CO 77d 13+ 350 6OCO 5.3 Y B' 340 65Zn 245 d EC 76

95


maximum, then the average beta or positron energy emitted per induced activity isotope decay will be 0.5 Me V.

4.1.3. Relation between activity and gamma ray dose rate (a) Dose rate at 1 metre

The gamma dose rate at 1 m from an isotope decaying at a rate of 1 disintegration per second is a useful parameter for converting radioactivity levels into dose rate and could be considered to define the radiological importance of the isotope concerned. This conversion factor is referred to as the isotope gamma dose rate constant or k factor. Values of this k factor for the main induced activity isotopes found around accelerators were given in Table 4.2(1).

The effective average value for the dose rate at 1 m from a mixture of spallation produced isotopes can be estimated. The absorbed dose to tissue in a fluence of 1 photon of energy E Me V per cm2 can be calculated using conversion factors given in Table 1.4 and will be given by

d = 1.6 X 10-10 J.Lr E Gy per photon.cm-2 (4.1)

where J.Lr is the mass energy absorption coefficient for gamma rays in tissue which has values 0.029 ± 0.004 cm2.g-1 over the gamma energy range 60 ke V to 2 Me V(2).

Converting absorbed dose to dose equivalent with a quality factor of 1, the dose rate at 1 m from an isotope emitting a single photon of energy E Me V per decay per second becomes

k = 4.6 X 10-12 J.LrE Sv.h-I.Bq-l at 1 m (4.2)

The value-for this k factor or gamma dose rate constant has been plotted in Figure 4.1 as a function of photon energy. For isotopes that emit several different energy photons per disintegration the k factor is the sum of the dose rate at 1 m from all the gamma rays per disintegration per second. From Figure 4.1 it can be seen that isotopes emitting a single gamma photon of 0.8 MeV per decay have a k value of 120 fSv.Bq-l.h-l at 1 m, hence for spallation produced isotopes in iron or copper, where, as was shown in Section 4.1.2, there will be effectively 1.9 photons emitted per decay, the appropriate average value for the k factor, ks' becomes

96


(4.3)

The above constants are for the dose rate at 1 m. The dose rate at other distances from a point source is assumed to follow the inverse square law and would be obtained by dividing the above constants by the square of the distance from the source measured in metres.

(b) Gamma dose rate near uniformly activated thick material The gamma ray energy deposition per unit mass, at the surface

of a semi-infinite slab of uniformly radioactive material, will be just 50% of the energy emitted. Hence the energy absorbed per gram of tissue, at the surface of a uniformly active slab containing 1 Bq.g-l of a gamma emitter of energy E MeV, will be 0.5 E (f.LrIJlp) where f.LrIJlp is the ratio of the mass energy absorption coefficients of the gamma rays in tissue and the material of the slab(3). This energy deposition is converted to dose rate using data in Table 1.4 which leads to

d = 2.9 X 10-7 E (f.LrIJlp) Sv.h-1 per Bq.g-l (4.4)

Values for d, the dose rate at the surface of a large activated

E

:!. 102 ., c-eo

1: :> g ....

j .lc

{OL_~2---~~~~~~10~-~1--~~~~~~--~--~~~~10

Gamma energy (MeV)

Figure 4.1. The gamma ray dose rate constant or k factor, the dose rate at 1 m from 1 disintegration per second emitting a single photon of a given energy .

97


volume of unit specific activity is plotted in Figure 4.2 as a function of gamma ray energy for activated iron, lead and water. From this figure it can be seen that the dose rate on the surface of a large iron slab in which there is uniformly distributed an isotope emitting a 0.8 Me V gamma photon per disintegration, will be 0.26 J.1Sv.h-

1 per Bq.g-I, making the appropriate value for the

gamma surface dose rate due to spallation products (with an average of 1.9 gammas per decay) of d

s where

ds = 0.5 J.1Sv.h-1 per Bq.g-I (4.5)

As can be seen in Figure 4.2, the dose rate on the surface of lead and other heavy materials will be less than that for iron by an amount depending on gamma energy and an overall reduction of the above dose rate by a factor of 2 can be assumed for the surface dose rate from lead. The activity to dose rate conversion factors apply to the surface dose rate on large uniformly activated volumes of material, which are rarely found in practice except perhaps for the case of radioactive liquids in an enclosed volume.

The ratio of dose rate on the surface of uniformly activated material with a specific activity of 1 Bq.g-I, to that at 1 m from

~1O-1 ,-'<' ,-0-~ 10-2 ,-.s::: ::>

(J)

3 10-3

Iron / /

-/

/Lead

/

1°10~~~~--~~-L~1~0~_1~-L~~-L~wU----L--L-L~~~ 10

Gamma energy (MeV)

Figure 4.2. The g~~a do~e ~ate at the surface of different materials per Bq.g-l of actIVIty emIttmg a single photon of given energy.

98


1 Bq is plotted as a function of the gamma ray energy in Figure 4.3 where it can be seen that the ratio is reasonably independent of the gamma energy for medium atomic number materials with gamma energies above about 200 ke V. Hence for isotopes that emit several photons of different gamma ray energies, as a first approximation, the surface dose can be considered proportional to the gamma dose constant (given for common accelerator produced isotopes in Table 4.2). The mean ratio of surface dose rate on uniformly activated medium atomic weight material to the dose rate at 1 m from 1 g of the material becomes

Dose ratio = 2.5 x 106 (4.6)

As shown in Figure 4.2 the surface dose rate for a given activity in lead will be about half that for iron. Hence the dose ratio given by Equation 4.6 can be expected to be about a factor of 2 lower for high atomic number materials.

---(c) Gamma dose rate near thin materials

The above relations are for the dose rates from materials that

1 O~O-2

Water / /

/

./ ,/ /

./

./ ./

10-1 10 Gamma energy (MeV)

Figure 4.3. The ratio of the dose rate at the surface of large volumes of different materials per Bq.g-l of activity to that at 1 m from an activity of 1 Bq with the

same gamma energy.

99

-Radiation and Radioactivity Levels near High Energy Particle Accelerators

are thick compared to their gamma mean free paths as given in Table 4.3. As a first approximation it is supposed that the dose rate builds up exponentially with material thickness where the dose rate D(X) from a plate of thickness X will be given by

D(X) = D (1 - e-x()..) ~SV.h-1 per Bq.g-l (4.7)

where D is the dose rate as given above for thick materials and A.. the gamma mean free path of the material expressed in the same units asX.

For plates of thickness less than about 10 g.cm-2 and taking an average gamma attenuation mean free path of 14 g.cm-2 as being applicable to all materials listed in Table 4.3, the gamma surface dose rate on a plate of thickness X g.cm-2 due to spallation produced isotopes will be

D(X) = 0.036 X ~SV.h-1 per Bq.g-l (4.8)

when X is the plate thickness in g.cm-2•

As can be seen the gamma surface dose decreases linearly with decreasing plate thickness below 10 g.cm-2 and for thin plates or foils the surface dose due to beta particles may exceed that due to the gammas. This additional hazard due to beta radiation from the spallation induced radioactivity has been determined separately in Section 4.1.5.

4.1.4. Shieldingfor induced activity gamma dose The gamma dose rate from induced radioactivity may

Table 4.3. Dose attenuation for 0.5 and 0.8 Me V gamma rays. Narrow beam attenuation mean free paths and the average shield thickness required to

obtain a factor of 10 dose attenuation.

Narrow beam Tenth value Shield mfp layer material (g.cm-2

) (cm)

0.5 MeV 0.8 MeV 0.5 MeV 0.8 MeV

Lead 6.2 11.3 1.4 2.6 Copper 12.0 15.1 4.0 5.0 Iron 11.9 14.9 4.8 5.9 Aluminium 11.8 14.2 14 16 Concrete 11.4 14.1 15 18 Earth 11.4 14.1 19 23 Water 10.3 12.7 35 40 Air 11.5 14.3 290m 340m

100


need to be reduced by adding shielding or an estimate may be required of the likely attenuation by surrounding material.

If the gamma dose rate determined before shielding is added is D , then the dose after the gamma rays have passed through a shield of thickness X of a material with a narrow beam gamma attenuation mean free path of A.., will be given by

D = Do B e-x().. (4.9)

where B is a dose build-up factor(4) that takes into account the contribution of scattered photons to the dose(S). This build-up factor depends on the gamma ray energy, the spatial distribution of the radiation field, the thickness of shield already traversed by the radiation and the nature of the shield material. Hence the exact value of the dose build-up will depend strongly on local conditions. The gamma ray field from induced activity in an accelerator structure will be neither uniform nor will it form a narrow beam and hence buikt-'up factors associated with extreme radiation spatial distributions can be discounted. Average gamma dose build-up factors that might normally be expected for induced activity in accelerator materials are estimated to be in a range from about 1.2 to 3.0 per decade of radiation attenuation.

Data of use for the shielding of 0.8 Me V gamma rays from spallation induced radioactivity and 0.511 MeV annihilation gamma rays from positron emitters are given in Table 4.3. This table lists the narrow beam attenuation mean free paths for common accelerator materials together with typical absorber thickness required to attenuate 0.8 Mev and 0.511 MeV gamma ray dose coming from accelerator activated components by a factor of 10. As the gamma radiation coming from induced radioactivity will have a wide energy spectrum, any shielding added will tend to filter out the lower energy photons and hence harden the radiation so that the second or higher 10th value layers may need to be 10% or more thicker than those given in the Table 4.3.

4.1.5. Dosefrom beta activity The terms beta radiation and beta dose rate are used

loosely as they are taken to include both beta particles and positrons as well as the energy deposition by X rays of energy less than about 50 ke V.

The beta dose rate on the surface of a uniformly activated piece of

101


material is estimated in the same way as for gamma rays where the dose rate in contact with an activated piece of material will correspond to an energy absorption equal to 50% of the energy released per gram of the material. In practical situations and where beta dose is an important consideration the activity will not normally be uniformly distributed and the point at which the dose rate is to be estimated will not normally be in hard contact with the active surface. Hence for dose calculations it is assumed that the energy deposition that constitutes the surface dose will be one third rather than one half of that in the activated material. Using the conversion factors given in Table 1.4, the beta dose rate at the surface of a spallation activated slab of material will be given by

DB = 0.19 E R Q ~SV.h-l per Bq.g-l (4.10)

where E is the average beta particle energy per disintegration in MeV which was shown in Section 4.1.2 to be 0.5 MeV, R is the ratio of the particle stopping power in tissue to that in the active material, which to a first approximation is assumed to be energy independent and to have an average value of 1. Q is the effective quality factor for the beta radiation which is assumed to be 1.

For mixtures of spallation produced isotopes it is further noted that any soft X rays (below about 50 ke V) emitted by isotopes after decaying by electron capture will make a negligible contribution to the surface dose.

Hence the beta dose rate at the surface of a thick slab containing spallation produced radioactivity becomes

DB = 0.1 ~SV.h-l per Bq.g-l (4.11)

For thin foils the beta dose rate will depend on the thickness of the foil. If the beta surface dose has an apparent attenuation mean free path of A g.cm-2 in the foil material then the dose rate on the surface of a foil of thickness X g.cm-2 will be

Dx =O.l (l_e-XfA,) ~Sv.h-lperBq.g-1 (4.12)

Experimentally determined values for A vary between 0.095 g.cm-2 for aluminium to 0.135 g.cm-2 for the attenuation of the surface dose from activated iron and copper(6). Assuming an average value of 0.12 g.cm-2

, the beta dose rate on the surface of foils of thickness X g.cm-2

, (less than 0.1 g.cm-2) becomes

Dx = 0.85 X ~SV.h-1 per Bq.g-l (4.13)

102


4.1.6. Ratio between beta and gamma dose Comparison of the beta dose on the surface of thin

materials as given by Equation 4.13 with the gamma dose given by Equation 4.8, shows that the beta dose rate on foils of less than about 100 mg.cm-2 could exceed that due to gammas by a factor of about 25. The two dose rates are expected to become equal at material thickness in the region of 3 g.cm-2

• However the beta dose on the surface of thick uniformly irradiated materials, as given by Equation 4.11, will be only 20% of that of the gamma dose as given by Equation 4.5. The above generalities concerning the beta and gamma surface dose represent the 'average' properties to be expected from induced radioactivity. In practice these properties will depend on the material that has been activated and on the irradiation conditions. In particular, the ratio between beta and gamma dose rate will vary with time as different isotopes assume prominence during the decay of the induced activity.

4.2.

4,2.1.

Radioactivity in targets and dumps

Radioactivity induced by high energy particle interactions The nuclear fragment remaining after an interaction by a

high energy hadron will most likely be an isotope of an element lighter than the target nucleus. Inspection of the list of possible isotopes below iron or copper in the isotopic table suggest that there is a 35% chance that the isotope will be radioactive and with a half-life in the range from 10 min to 2 y. Furthermore, it is observed that over this half-life range, the probability of an isotope having a given half-life is inversely proportional to the half-life(7,8). The number of isotopes of half-life 't in a range from 't to 't + &t, N('t)&t, will be proportional to &t/'t and the probability that a nuclear fragment will have a half-life 't will be

which, with 't l = 2 Y and 't2 = 10 min,

P( 't) ()'t = 0.031 ()'t/'t

103

(4.14)

(4.15)


The activity of a radioactive isotope will build up and decay according to its half-life and for isotopes of half-life in the range 't to 't + &t the activation resulting from one spallation interaction per second for a time T and after a decay time t (T, t and 't all in same time units) will be

S('t)&t = P('t) e-O·693tlt (1- e-O·693T1"t)&t Bq (4.16)

The total activity per interaction per second will be obtained by integrating Equation 4.16 over all values of't, which gives

J 2y exp(-O.693t/'t) [1- exp(-O.693T/'t)]

S = 0.031 d't Bq (4.17) 10 min 't

The above integral, but over a half-life range from zero to infinity, gives an induced activity from one spallation interaction per second of

S = 0.031In[(T+t)/t] Bq (4.18)

The effect of integrating over a greater half-life range than that for which the isotope half-life distribution was reasonably valid will result in an overestimation of the activity with irradiation times beyond about 3 y. This overestimation will be less than a factor of 2 for an ,irradiation time of 10 y provided the decay time is less than 6 mon or for a 5 y irradiation when the decay time is kept to less than 2 y. These time range limits correspond well with those of interest in most accelerator applications.

4.2.2. Radioactivity in iron or copper targets The nl,1mber of spallation interactions per second in a

target of thicklless of 1 g.cm-2 irradiated in a high energy proton beam of protons per second will be equal to the beam strength divided by the interaction mean free path as given in Table 4.1, expressed in g.cm-2

• Taking a mean value for the mean free path in medium atomic number materials of 133 g.cm-2 the activation per g.cm-2 of target in a beam of protons per second reduces to

S = 2.4 X 10-4 In[(T +t)/t] (4.19)

This activity will also be that of a 1 g target irradiated in a uniform flux of high energy protons.cm-2.s-1•

104


Values for S, the radioactivity level per gram of target irradiated for different times in a flux of 1 high energy hadron.cm-2.s-1 are plotted in Figure 4.4 as a function of the time after the end of the irradiation.

4.2.3. Dose rate from targets and beam dumps The dose rate at 1 m from a target with a known amount of

spallation induced radioactivity can be calculated. In Equation 4.3 it was shown that the dose rate from spallation product radioactivity will on average be 220 fSv.h-1 at 1 m from a source with an emission of 1 Bq, making the dose rate at 1 m from a 1 g target irradiated with proton.cm-2.s-1 for a time T and after a decay time t (T and t in common time units)

D =Do In[(T+t)/t] (4.20)

when Do has a value of 5.2 x 10-17 Sv.h-l .g-l .m2•

The above relation should be essentially independent of

Decay time (d)

Figure 4.4. The specific activity of a medium atomic weight target as a function of time, after being irradiated in a high energy proton flux of 1 proton.cm-2.s-1

for the times indicated. (This is also the activity of a 1 g.cm-2 target after exposure in a beam of 1 proton.s- I

.)

105


incident hadron energy above about 200 Me V and apply equally to neutrons as well as protons incident on any medium atomic weight target material provided the target is thin compared to the hadron interaction mean free path and to the incident proton range.

The dose rate at 1 m from a one g target at different times after irradiation is shown in Figure 4.5 as a function of irradiation time with a beam of I proton.cm-2.s-1. (This is also the dose rate from a target of I g.cm-2 irradiated in a beam of I proton.s-1.)

Using the relation between surface dose and dose at I m, given by Equation 4.6, the gamma dose rate on the surface of a large uniformly irradiated slab of iron or copper, due to activation by spallation interactions will be given by Equation 4.20 but with Do = 1.3 X 10-10 Sv.h-1

When the irradiation time is short compared to the decay time, i.e. t» T, then Equation 4.20 reduces to

,-~

110-'6

:> ~

~ CLl en o

"0

"210-17 () :l "0 .E

Do<PT D=--

t (4.21)

1 0-18!-_...I--.l.......L.....J......I...l..I...l:-I::-_-.l...--1--l..~L...U~o----L_.l.-L...J...w....J..,JJ 1 10 100 1000

Irradiation time (d)

~igure ~.5. The induced radioactivity dose rate at 1 m from a one gram target at tmles glven after the end of an irradiation in a flux of 1 proton.cm-2.s-1 as a function of irradiation time. (This is also the dose rate from a 1 g.cm-2 target

after exposure in a beam of 1 proton.s-1).

106


where, if T and t are in seconds, <P x T will be the total number of protons into the target. Hence after a short irradiation the induced activity dose rate will be proportional to the total number of protons incident and is expected to decrease inversely with time after the end of the irradiation.

While the activation of a thin target is expected to be practically independent of hadron energy (above about 200 MeV) that of a beam dump will be influenced by secondaries produced in the dump and hence depend on the incident proton energy. If Do is the induced activity dose rate factor per unit beam to be used in Equation 4.20 for the dose at I m from a I g.cm-2 target, then as a fIrst approximation the factor for the dose rate at I m in front of a beam dump will be given by

Sv.h-1 at I m (4.22)

where "',; is the induced activity gamma ray attenuation mean free path with a value of 14.9 g.C!!!o-2 for iron (see Table 4.3). Q is the hadron multiplication per interaction which depends on the incident proton energy and is given by Equation 1.10. Ap is the high energy proton interaction mean free path with a value of 132 g.cm-2 for iron as given in Table 4.1. Putting in these values leads to the relation for dose rate at 1 m in front of the point of entry of the beam into the dump of

D = 1.4 X 10-15 EO

O.15 (4.23)

where Eo is the proton beam energy in Ge V. The dose rate at 1 m in front of a beam dump irradiated for a

time T with a beam of <P protons per second and at a time t after the beam has been switched off will therefore be given by

D =1.4 X 10-15 EO

O.15 <P In[(T+t)/t] Sv.h-1 (4.24)

where T and t are in the same time units . Typical dose rates in front of an iron dump after a one year

irradiation with beams of 1012 protons per second of different energies are plotted in Figure 4.6 as a function of time after the end of the irradiation.

4.2.4. Effective half-life The rate of decay of spallation induced radioactivity

decreases as the decay time increases(9). However, at any given

107


time after the end of an irradiation, the effective half-life, or time it will take for the radioactivity to decay by a further factor of 2, can be estimated. If a dose rate D, due to induced radioactivity, is measured at a time t after the end of an irradiation, then if the effective half-life is 't (in the same units as t), the dose rate at a time t+'t will be D/2. This observation, using Equation 4.20, leads to the relation

(4.25a)

or

(4.25b)

which reduces to

't = ...J[(t+D t] (4.26)

Hence, with t, T and 't all in the same time units, a dose rate

'I .c :>

C/)

g

~ Q)

gs o

100r---~-T~~~~--~~~~~rn~---r--~~~'Tn

10 100 Decay time (d)

Figure 4.6. The expected dose rate at 1 m in front of a beam dump irradiated for 1 year with average beam intensity of 1012 protons.s-1 of energy indicated.

108


measured at a time t after an irradiation that lasted a time T will take a further time, 't, as given by Equation 4.26, to decay by a further factor of 2. This half-life is plotted in Figure 4.7 as a function of decay time for the activity resulting after different irradiation times.

From Equation 4.26 it can be seen that for targets irradiated for long periods compared to the decay time the half-life approximates to

(4.27)

and for the case where the irradiation time is short compared to

Figure 4,7. The dependence of the effective half-life of induced radioactivity in medium atomic number materials on decay and irradiation times.

109


the decay time the effective half-life will be equal to the time the radioactivity has already decayed.

The above half-life estimations will be only very approximate as, in addition to variations in real isotope half-life distributions, the formulation assumes that the irradiations are uniform with time which is rarely the case for accelerator activation.

4.2.5. Activation of heavy element targets As was shown in Equation 4.21, the activation of medium

atomic weight materials is expected to decay with an effective 1/t decay law when the decay time is long compared to the irradiation time, a decay law that has been confirmed experimentally. On the other hand, the observed decay of the induced activity dose rate measured near heavy element targets, lead(lO), rhenium(ll), tungsten(l2), etc. irradiated for short periods, shows a dependence on decay time after about one hour decay that is approximately proportional to rIA . (It is of interest to note that mixed fission product radioactivity decays with an approximate r1.2 Iaw(13).)

1O-15r--'--.-.-rrrrTL-_=-:_==_~r::::::!:I!:!J:q::=::::r==r::::J:::r:rr:~ ------------

Decay time 3 h

1;10-16 ~----'I .c

::> ~

~ 0,)

~ 10-17 o

--------------------------d .---

1 mon

1 0-18L1

---I-..I..--.L.....1-l....WJ.1:l:0,.---II..-..l-.J.....Iw....I....I.:I1~OO:::---J....-....I........I.....I..J,.""":-1 o*'!oo Irradiation time (d)

Figure 4.8. Estimated dose rate at 1 m from a 1 g heavy element target irradiated in a high energy proton flux of 1 proton.cm-2.s-1

, or from a target of thickness 1 g.cm-2 irradiated in a beam of 1 proton.s-I

, as a function of irradiation time and at different times after the end of exposure.

110


Quantitative interpretation of these measurements indicates that the induced activity dose rate at 1 m, per incident proton on a 1 g.cm-2 heavy element target, and at a time t days after a short irradiation will be given by

1.8 x 10-21

Sv.h-1 per proton (4.28) D= t1.4

The above relation implies a dose rate at 1 m from a 1 g.cm-2

heavy element target, at a time t after an irradiation in a beam of 1 proton.s-1 for a time T, will be

D = Do [{-DA - (T + t)--DA] Sv.h-1 per proton.s-1 (4.29)

where Do = 4xlO-16 Sv.h-1 at 1 m per g.cm-2 of target per incident proton per second when t and T are in days. Other values for Do that can be used with Equation 4.29 are listed in Table 4.4.

Dose rates expected at 1 m from irradiated heavy element targets are shown in Figure 4.S-lit different times after beam-off as a function of irradiation time.

Comparison of the dose rate given by Equation 4.29 with that from a medium element target suggests heavy elements will be more active after short irradiation times than medium atomic weight targets but that the activity induced in heavy elements will decay more rapidly. This effect can be seen in Figure 4.9 where the expected induced activity dose rates at 1 m from targets of one interaction length of iron and lead (see Table 4.1) irradiated for 10 h and 10 d in a proton beam of 1013 proton.s-I have been plotted.

Assuming that the gamma k factor of 220 fSv.h-1.Bq-1 at 1 m, as found for isotopes produced in medium atomic number materials also applies to heavy element activation, then the specific activity of a heavy element target after irradiation in a

Table 4.4. Values for Do, the dose rate at 1 m from heavy element targets to be used in Equation 4.29 with times measured in hours and days.

Heavy element target

1 g.cm-2 target One interaction length target

111

Dose constant fSv.h-1 per proton.s-1

hours 1.4 300

days 0.4 85


beam of protons per cm2 per second becomes

S = 1.8 X 10-3 [t-OA _ (T+t)-OA] Bq.g-l

when t and T are in days.

4.2.6. Comparison of calculated dose rates with measurements

(4.30)

Induced radioactivity measurements are only very rarely made under controlled irradiation conditions and where the target is removed from the activated beam area for measurement. However, induced activity measurements reported in the literature tend to conrlITll the validity of the formulation presented(9,14). The results of measurements made under controlled conditions of the dose rate at 1 m from slabs of steel and lead irradiated in a 15 GeV proton beam(lO) are compared with those calculated using the above data in Figure 4.10. These curves, where the decay of the dose rate has been followed for over a year, show the

Decay time (h)

Figure 4.9. Estimated induced activity dose rate at 1 m from one interaction length iron and lead targets irradiated for 10 h and 10 d in a beam of

1013 proton.s-l.

112


approximate nature of the analysis. As can be seen, there appear to be systematic differences of the order of 20% but at no time does the 'theoretical' dose rate deviate from that measured by more than a factor of two. Such an accuracy appears to be well within the range of uncertainty to be expected in the prediction of the dose rate from any real-life target irradiated under normal accelerator operating conditions.

4.2.7. Beta dose from thin targets As was shown in Section 4.1.6, the dose from beta £articles

(including positrons) can exceed that of gamma rays( )on the surface of targets of thickness less than about 3 g.cm-2

• The dose rate on the surface of thin targets (e.g. vacuum windows) can be obtained by combining the specific activity given by Equation 4.19 with the beta activity to dose conversion factor given by Equation 4.13, which for targets of thickness X g.cm-2 (less than 100 mg.cm-2) leads to __

D = 3 X 10-10 X In[(T+t)/t] Sv.h-1 (4.31)

1~2L1--~~WU~1~O--~~~~10~O~~~~~1000U-~~-L~1~OOOO~

Decay time (h)

Figure 4.10. Comparison of measured and calculated dose rates from irradiated steel and lead blocks as a function of time after exposure.

113


 is the flux of protons in the beam in protons.cm-2 .S-I, and T and t are the irradiation and decay times in common units. The surface dose rate due to beta particles on 0.1 mm thick steel and aluminium vacuum windows after irradiation in a beam of 1012

protons.s-1, spread over 1 cm2

, is shown in Figure 4.11 as a function of time after irradiation assuming the beam had been operating for 1000 h. As can be seen, very high local beta dose rates are possible on vacuum windows or other thin foils irradiated in beams of small cross sectional area.

Measurements of the attenuation of this surface dose indicate dose attenuation mean free paths of between 95 and 135 mg.cm-2

in plastic, making the tenth value absorption thickness for the beta radiation about 300 mg.cm-2•

4.3.

4.3.1.

Activation by secondary hadrons

Activating particles The estimation of the amount of activity induced in

! 102 f-- ------___ ~ ___ ~~eel

en ----__ o -_ "0 -----____ _

~ ~ .jg r--__ -

-

::::J ---~____ Aluminium ----__.,. (f) _ .• ~______ - ............

-----------~--------------.... _---------

Decay time (h)

Figure 4.11. Estimated dose rate on the surface of 0.1 mm thick vacuum windows of steel and aluminium irradiated in a beam of 1012 proton.s-I over

1 cm2 for 1000 h as a function of decay time.

114


materials by secondary hadrons off the beam line is more complicated than that in targets on account of the broad energy spectrum and non-uniform distribution of the secondary hadrons causing the activation.

The· activation can be divided into two main components, that due to spallation reactions by high energy secondary hadrons and that due to capture reactions particularly of thermal neutrons. Low energy neutron effects will depend critically on the energy spectrum and on the exact composition of the material irradiated, including the possible presence of trace elements. Hence caution is necessary in making generalisations and only guidelines can be given as to what may be expected in the way of induced activity levels in accelerator materials near to where beam losses have occurred.

Induced activity levels depend more on the particle fluence rate or hadron flux rather than the fluence itself. For reasons of convention the hadron flux used for induced radioactivity determinations will be expressed as hadrons.cm-2.s-1 even though the secondary particle fluence levels determined for shielding purposes have previously been given in the recommended SI units ofparticles.m- .

The fluence of secondary hadrons of energy greater than 40 MeV at R metres and at an angle e degrees from a high energy particle interaction in iron or copper will be given by (see Equation 1.8, Chapter 1)

hadrons.cm-2 (4.32)

where E is the interacting proton energy in Ge V (greater than 1 GeV).

The resulting activating flux of secondary particles at 1 m from a target in which there are 1010 interactions per second by protons of energy E GeV is shown in Figure 4.12 as a function of emission angle.

The energy of this secondary radiation may be high enough for further particle multiplication to occur when it interacts in an absorber. Secondary particle equilibrium will be reached after passage through at least 2 mean free paths of absorber when the hadron fluence, at X mean free paths into the shield will become

115


(see Chapter 1, Equation 1.24)

!is = !is(9) e-x (1 + 0.24 IfJ·7) hadrons.cm -2 (4.33)

where E is the energy of the primary protons in Ge V. This buildup factor, by which the flux calculated using Equation 4.32 needs to be multiplied after the radiation has passed through at least 2 mean free paths of absorber, is shown as a function of the energy of the primary proton beam in\Figure 4.13.

4.3.2. High energy particle activation A uniform flux of cf> high energy hadrons.cm-2.s-1

incident on iron or copper will result in an activation of these materials where the specific activity S, determined using Equation 4.19, will be given by

S = 2.4 X 10-4 cf> In[(T+t)/t] Bq.g-l (4.34)

"j "1

'l' E S. ~107 c:: e "0 <II I

Figure 4.12. Flux of activating secon~ hadrons (in particles.cm-2.s-l) at 1 m

from a target in which there are 1010 interactions per second as a function of emission angle.

116


where T is the irradiation and t the decay time in common units. If the radiation field and the irradiated surface are sufficiently

large and the material being activated is more than about 30 g.cm-2

thick, then the induced activity dose rate near the surface will be (see Equation 4.5) 0.5 S J..lSv.h-1

, which combined with Equation 4.34 gives for the gamma dose rate near the surface of a uniformly irradiated thick piece of copper or iron

D = 1.2 X 10-4 cf> In[(T+t)/t] (4.35)

where cf> is the activating hadron flux in hadrons.cm-2.s-1 that can be determined from Equation 4.32.

The above relation is for iron or copper plates of thickness equal to at least one gamma ray tenth value attenuation layer as given in Table 4.3. As was shown in Section 4.1.3, the induced activity dose rate builds up exponentially with plate thickness according to

(4.36)

.... ~ .l!! C.

~ '5 .c >< ~ u::

10 1()2 Primary photon energy (GeV)

Figure 4.13. Factor by which the secondary high energy hadron flux multiplies on passing through an absorber.

117


where X is the plate thickness in cm and A the linear gamma mean free path as given in Table 4.3.

For iron sheets less than 1 cm thick, the gamma surface dose rate will be

D = 6 X 10-5 <l>X In[(T+t)/t] /-LSv.h-1 (4.37)

where X is the plate thickness in cm. The gamma surface dose rate, calculated using the above

relations for iron or copper plates of different thicknesses exposed at 1 m and perpendicular to a target in which there are 1012 interactions per second, will be as shown in Figure 4.14.

Also of interest is the likely contribution to the induced activity dose rate of the activation by secondary hadrons from a target striking a block, such as a collimator or beam dump, immediately down beam from the target. The expected gamma dose rate at the surface of a such a block after exposure to secondary hadrons in the forward direction from 1012 interactions per second in a target at 1 m in front of the block is shown as a function of radius from

., .J:: :>

(f)

E

20r-~.-~~~~~~~~r-~.-~~-r-T~~--~

.. ----_ .. .----

1000 GeV

---------------___ .... _w...-_w.-

-;10 - 10 GeV .. --_ .. -

.---" ~ Q) C/)

o o

.. " .• /_.--., .... 1 GeV-~~·--

Plate thickness (mm iron)

----------

20

Figure 4.14. Estimated dose rate from induced activity near the surface of an iron or copper plate placed at 1 m to the side of a target irradiated by protons of different energies. Dose rates given are for a 30 d irradiation resulting from 1012

interactions per second in the target by protons of energy indicated.

118


the beam line in Figure 4.15. The secondary hadrons have an energy spectrum with an

average energy very much less than that of the interacting proton, (see Section 1.2.2) and hence will tend to produce a more limited range of isotopes in spallation interactions than do the primary hadrons interacting in a target. In particular, if protons of a few tens of Me V make up a significant part of the spectrum then (p,n) reactions may predominate to produce excessive amounts of 56CO

in iron and 65Zn in copper. This, together with any thermal neutron activation that may occur, will result in an isotope distribution that is very different from that expected from spallation interactions and consequently deviations are to be expected from the spallation product activity decay law as given by Equation 4.20 over limited irradiation and decay time ranges.

4.3.3. Activation by thermal neutrons Thermal neutrons are expected to be present in the

spectrum of secondary radiation- inside an accelerator enclosure.

., .J:: :> ~ Q)

~ Q) C/)

o o

···1000 GeV

100..... -' . ......................

.... , ......... _-. -0, ••••• ___ ...... '-.......

......... 10. ..-... ::::::::~:_.~ ... _. ~ ... -.. -.. -~.----.----------- -'-. -'-"-

------_._'-'-'--===::::::::::::::-:.::::::.-.--==------------------ - --

----.1 __ ------------------

---------------------

10~~--~--~--~~--~---L--~~--~---L--~----J o 20 30 40 50

Distance off-axis (cm)

Figure 4.15. Surface gamma dose rate one day after the end of an. irradiation, as a functi?n o~ r~dius of an iron or copper block, at 1 m down beam from a target after IrradiatlOn by the secondary hadrons resulting from 101"2 iilteradioils per

second by protons of different energies in the target for 30 d. .

119


These may cause significant induced radioactivity over and above that caused by spallation reactions on account of the high capture cross section of some materials for thermal neutrons.

The ratio between the thermal and high energy hadron fluxes near an accelerator can vary widely with the layout and energy of the machine as well as depending on position and the nature of the surrounding environment. Experimental data(l5) suggest 1 to 4 thermal neutrons will be formed per high energy neutron incident on concrete. However, for the purposes of comparing thermal neutron with spallation activation in accelerator components, equal fluxes of thermal neutrons and high energy hadrons are assumed.

The principal accelerator materials with significant thermal neutron activation cross section are:

(a) 63CU in natural-copper (b) Sodium in concrete (c) Argon in air (d) Zinc in copper (e) Manganese and cobalt in iron or steel (1) Antimony in lead (g) Trace quantities of manganese, cobalt, caesium and

europium in earth and concrete (h) Possibly tungsten-186 in natural tungsten

The properties of the isotopes that will be formed by thermal neutron capture and that can seriously influence induced radioactivity levels near high energy particle accelerators are listed in Table 4.5 together with their corresponding gamma dose rate constants or k factors(16). Also listed is the dose rate at 1 m per gram of the natural parent element irradiated in unit thermal neutron flux for a time that is long compared to the isotope halflife. This quantity gives an indication of the relative importance of different elements in enhancing radiation levels due to thermal neutron activation and hence indicates what elements are to be avoided in accelerator materials. For comparison, 1 g of iron irradiated for 2 y in unit flux of high energy particles would result in an induced activity dose rate of 0.6 fSv.h- at 1 m.

The gamma dose rate from material containing 1% by weight of an isotope of atomic weight A which has an activation cross section, cr barn, and whose activation product has a gamma dose

120


rate constant k fSv.h-I.Bq-1 at 1 m will be given by

Qfcr k c:P e-M ,

D = (1 - e-II.T) fSv.h-1.Bq-l A

(4.38)

where A is the isotope decay constant given by 0.693 divided by the half-life, t is the decay time and T the irradiation time, c:P the thermal neutron flux in neutrons.cm-2.s-1 and A the atomic weight of the activated material.

When D is dose rate at 1 m from 1 g of material (in fSv.h-1) and the parameters are expressed in the units as given above, then Q will be 10-26 x Avogadro's number (6.02 x 1023 atoms per mole), making

Q = 6 X 10-3 (4.39)

To obtain the gamma surface dose rate on a large uniformly activated block of medium or low atomic number material in fSv.h-1 using the ratio gjyen by Equation 4.6, then:

Q = 1.5 X 104 (4.40)

and to obtain the dose rate on the surface of a uniformly irradiated lead block

Q = 7.5 X 103 (4.41)

Table 4.5. Isotopes that could contribute to accelerator radioactivity by thermal neutron activation. The dose rates at 1 m are per Bq of the active isotope and per g of the natural parent element irradiated to saturation in a

thermal neutron flux of 1 n.cm-2.s-1•

Parent Natural cr Active Half- fSv.h-1 at 1 m isotope (%) (barn) isotope life perBq perg

23Na 100 0.53 24Na 15 h 560 7.7 40Ar 99.6 0.61 41Ar 1.8 h 150 1.4 44Ca 2.0 0.70 4SCa 165 d 50Cr 4.3 17 SICr 28d 4 0.04 sSMn 100 13 S6Mn 2.6h 250 35 S9CO 100 37 6OCO 5.3 Y 340 128 63CU 69 4.5 64CU 13h 28 0.84 64Zn 49 0.46 6SZn 245 d 76 0.16 121Sb 57 6.1 122Sb 2.8d 60 1.0 123Sb 43 3.3 124Sb 60d 200 1.4 l33Cs 100 31 134CS 2.1 Y 116 17 lSlEu 48 8700 lS2Eu 12 y 45 750 lS3Eu 52 320 l~U 8y 286 190 186W 28 40 187W Id 73 2.6

121


Thermal neutron fluxes are difficult to assess as is also the possible presence of trace elements with a high thermal neutron capture cross section in accelerator materials. Hence only nominal dose rates due to thermal neutron activation of accelerator materials can be estimated.

Some idea of the importance of thermal neutron activation can be obtained by comparing the induced activity dose rate from spallation products with that from thermal neutron induced isotopes after irradiation with equal fluxes of high energy hadrons and thermal neutrons. Such a comparison is made in Figure 4.16 where the surface gamma dose rate due to thermal neutron activation of 1 % of manganese and cobalt alloyed into iron, after 1 y irradiation in a flux of 106 thermal neutrons.cm-2.s-1

, is compared with that from spallation products after an equal irradiation with high energy particles, as a function of decay time.

The induced activity dose rate due to thermal neutron activation of 63eu in natural copper is compared to that expected from spallation products after 30 days irradiation in fluxes of 106 cm-2.s-1

thermal neutrons and high energy hadrons in Figure 4.17 where the relative importance of the thermal neutrons can be seen. The

1:: :> (f)

.s (i) f-~ ______ _

~ 1 ::-_~_ ~------Spallation -

~ "' _ -----------------__ 1 % manga:::----~~-_________ _

~ ............. ~ ............ ~ :J 1 % cobalt ""

(f) .,'\\

\

I >\ I 0.1.'-::--~~..J_.I_'_l ......... ~--'--....... ...I...I.-J...I~!:_-"-....I-.J-.I'-'-~ 0.1 10 100

Decay time (h)

Figure 4.16. Surface dose rates from spallation products induced in iron after a 1 y irradiation by 106 high energy hadrons per cm2 per second compared to that expected from the activation of 1 % manganese and cobalt incorporated in the

iron by a similar flux of thermal neutrons.

122


possible effect of thermal neutron activation of antimony in lead is compared to high energy particle activation after a one year irradiation in Figure 4.18. 10~--~~~~~~----r--r~~~~--~--~~~~

Decay time (h)

Figure 4.17. Gamma surface dose rates from spallation products and thermal neutron activation of 63CU in natural copper after a 30 d irradiation by high

energy and thermal neutron fluxes of 106cm-2.s-l•

'TlTj J I I , 1 i i J

1% antimony r------------__ ~ ____ _______

_._------------------10~~--~~~~~~~--~--~~~U7~--~--~~~~

1 10 100 1000 Decay time (h)

Figure 4.18. Gamma surface dose rate due to spallation products in lead compared to that from thermal neutron activation of 1 % antimony for high

energy and thermal neutron fluxes of 106 cm-2.s-1 after 1 y irradiation.

123


Despite the uncertainties in estimating thermal neutron fluxes, the data given above indicate where the possibility exists that thermal neutron activation of trace or alloying elements in

-accelerator materials can be a major contributor to induced radioactivity dose rates and should be taken into consideration when selecting materials for accelerator components.

4.3.4. The activation of aluminium The activation of light elements is characterised by the

relatively few radioactive isotopes that it is possible to produce by spallation reactions and hence the continuous isotope distribution that was assumed when determining the activation of iron or copper tends to break down. The principal radioactive isotopes found in aluminium, together with their assumed average high energy particle production cross sections, appropriate gamma k factors and half-lives are given in Table 4.6. The cross section for the production of 24Na includes an allowance for (n,a) reactions in aluminium which has a resonance at a neutron energy in the region of 10 to 20 MeV. The above data enable the dose rate to be calculated and the expected gamma dose rate on the surface of a large aluminium block following an irradiation with a uniform flux of 106 secondary hadrons.cm-2.s-1 for different times is shown in Figure 4.19 as a function of decay time. Also shown is the expected surface dose rate from iron irradiated in the same high energy particle flux for one year as calculated using Equations 4.6 and 4.20. As can be seen, the dose rate from aluminium appears to be 10 to 30% of that of iron for equal irradiations. However, after irradiations lasting many years and after long decay times the dose rate from aluminium may again approach or-"e-ven exceed that of iron on account of the build-up of 22Na, with its 2.6 y half-life, in the aluminium.

Table 4.6. Principal radioactive isotopes formed by secondary high energy radiation in aluminium. The !INa cross section includes allowance for n,C(

reactions by neutrons in the region of 10 to 20 MeV.

Average cross kfactor Isotope section Half-life (fSv.h-1.Bq-l

(mb) at 1 m)

18F 20 1.8 h 132 24Na 40 15h 560 22Na 20 2.6y 298

124


4.3.5. The activation of concrete Normal concrete is more than 50% by weight oxygen and

contains about 30% silicon, existing mainly as Si02, together with various other elements. Activation of oxygen will not contribute significantly to the long-lived induced activity and activation of Si should not be very different from that of aluminium. In addition, it has been found(l7) that activation of marble (CaO), depending on irradiation conditions, is on average only about 30% of that of quartz (Si02). Hence limestone based concrete with its high Ca and low Si content is to be preferred to that with the more normal sandstone aggregate to minimise induced activity(lS). As an approximation for getting a fIrst order estimate of dose rates to be expected from activated concrete, the accuracy of which will depend on irradiation conditions, the dose rate from spallation produced isotopes in normal concrete will be of the order of 30% and for limestone aggregate 15% of that from iron irradiated under similar conditions.

Hence the radiation level due to spallation interactions by high

------==:;:== _______ ~____ --____ ~ 1 Y ----..::.'- --- ---------.

'-==:::::'_ .... ___ --. --.-.-.. -._ ~ ___ A_I_T_=_5~Y __ ---__ - __ "":_:::: __ ~~--I '-..-.. -, ""'~:~_AI_T_=_1_Y ___ ~ __ -;I

""

AI T= 1 mon

Decay time (d)

Figure 4.19. Gamma surface dose rate on a thick block of aluminium irradiated for different times in a flux of 106 secondary hadrons.cm-2.s-1 compared to that

expected on iron irradiated in the same flux for 1 y.

125


energy secondary hadrons in concrete can approximately be calculated by an equation of the form

D = Do In[(T+t)/t] (4.42)

where is the activating hadron flux (hadrons.cm-2.s-1) and Do has the values given in Table 4.7. The secondary hadron fluxes at I m from a target, from which can be determined, are plotted in Figure 4.12. Deviations of the order of a factor of 3 are to be expected over limited irradiation and decay time periods when using this 'continuous' half-life distribution decay relation on account of the relatively few radioactive isotopes likely to be present in concrete.

Concrete can contain significant quantities of sodium(19) which may result in thermal neutron produced 24Na, with its 15 h halflife, being the major contributor to the dose rate near the walls of an accelerator tunnel shortly after the beam is switched off. The induced activity dose rate near concrete containing 1 % sodium, after irradiation in a uniform thermal neutron flux of 106 cm-2.s-1

for 30 days, is compared to the spallation product dose rate caused by the same flux of high energy hadrons in Figure 4.20. As can be deduced from the data given in this figure, thermal neutron activation can easily give rise to dose rates of the same order or greater than that from spallation products and could be the major contributor to the dose rate from concrete at short times after the end of an irradiation.

In the case of a target in a beam surrounded by a concrete enclosure, it is useful to know the relative importance of the induced activity dose rate from the wall of the enclosure to that from the target. The contribution of the activation of the concrete wall of an accelerator tunnel to the induced activity dose rate in

Table 4.7. Summary of induced activity dose rate constant for use in 'Equation 4.42.

Material irradiated

Iron/Copper Concrete Marble

Near surface (pSv.h-1

)

130 40 20

126

per kg at 1 m (fSv.h-1

)

52 16 8


the tunnel depends on many factors. A figure of merit, which will be independent of tunnel size, could be the ratio between the dose rate at the tunnel wall due to an activated target compared to that at the target position due to the activated tunnel wall. Assuming the distance between the target and wall is the same in all directions and that the wall was only irradiated with secondaries from the target, then the dose ratio will be approximately given by

R = DO(conc) 'A(y,c) DO(trJrg) 'A(h,t) Q

(4.43)

where DO(conc/DO(trJrg) is the ratio of the induced activity dose rate constants for concrete and the target material given in Table 4.7, 'A(y,c) is the gamma ray attenuation mean free path of concrete given in Table 4.3, and 'A(h,t) is the hadron interaction mean free path in the target given in Table 1.3. Q is the hadron multiplicity in the target given by Equation 1.10. The above ratio of the dose

i [ iii I j I I

-------______ Spallation

Q)

1§ 0.1 r-Q) rJl o "0 Q) u

~ ::l

(/)

------------------------1% sodium __

------------~---...~-------------------~~

\

Decay time (h)

Figure 4.20. Gamma surface dose rate from a concrete block containing 1 % sodium, irradiated for 30 d with fluxes of 106cm-2.s-1 thermal neutrons and high

energy hadrons.

127


rates from a concrete wall to that from an iron or copper target, after times when any 24Na activity that may have been present has had time to decay, will be as shown in Figure 4.21 as a function of the energy of the protons hitting the target. However, this ratio is merely an indication of the relative importance of the activation of accelerator tunnel walls as in real life targets may be changed whereas the activity in the wall will continue to accumulate.

The use of heavy concrete containing barium in target areas is not recommended on account of the long-lived radioactive isotopes that have been found. Long-term irradiation of baryta in an accelerator tunnel showed the presence of the radioactive isotopes listed in Table 4.8(20) where significant quantities of l37es can be noted.

4.3.6. Earth activation The radioactivity induced in earth or fill forming the bulk

shield over an accelerator and particularly around a target area is of special interest on account of the possibility of this activity

1·°r---r---r--,-,""'nT,....---r--r-.,.....,rr-rTT,....---r--r--r-rr-17I"TII

0.8 -

·gO.6 ~.

~ Q) (J)

80.4

0.2

/ / .... /

.. ,/"

J

//?

// /

~~--~~~~~10~~--~~uu~1~~~~~~~~1~

Proton energy (GeV)

Figure 4.21. The ratio of the induced activity dose rate at the target position due to activation of the concrete wall to that at the wall due to activation of the target,

assuming a spherical target enclosure with the target at its centre.

128


being leached into ground water or otherwise entering the environment. Although the activation will depend on how and where beam is lost and the effects of local shielding, an indication of the types and quantities of activity that have been found in target area shields could serve as a base for estimating the degree of severity of any problems that may arise.

The long-lived isotopes that have been found in earth surrounding target areas(21,22), are listed in Table 4.9 together with the estimated saturation activities when the long term average beam was 2xlO12 protons.s-1 of 26 GeV onto a target with approximately 50% of the protons interacting (4 kW beam power lost on target) and where there was a shield of 80 cm concrete

Table 4.8. Long-lived radioactive isotopes induced in baryte concrete.

Specific Isotope Half-life activity

(%)

I3lBa 12d 19.5 136CS 13d 1.1 127Xe 36d 1.8 134CS 2.1 Y 8.7 22Na 2.6y 1.7 6OCO 5.3 Y 0.5

133Ba 1O.7y 51.5 152Eu 12.0y 9.8 l37Cs 30.0y 5.4

Table 4.9. Apparent production rate and saturation activities of long-lived isotopes found in earth around a target area for long-term average beam

power dissipation of 4 kW at 26 Ge V.

Isotope Half-life

53 d 84d

165 d 303 d 2.6y 5.3 y

12.3 Y 12.0y 8.0y

Production rate

(Bq.S-l)

820 75

590 170 170 43 72

130 7

Trace amounts of 48Va, 57CO, 59pe andl34Cs were also noted.

129

Saturation activity (GBq)

5.4 0.8

12 6.4

20 11 40 71 2.5


between the target and the earth. The uninteracted beam and the strongly forward directed secondary particles from the target are assumed to be absorbed in a sealed beam dump. The total activity in the earth, per watt of beam power lost in target interactions, computed from the data in Table 4.9, is plotted in Figure 4.22 for various irradiation periods as a function of decay time and is given as an example of the order of magnitude of earth activation that can occur around a target shield.

The above data are based on measurement of activities around a 26 Ge V machine. If it is supposed that the activation mainly

1oor-----~--~~~~rT~----~~~--~~~~n

----___ 20 Y irradiation ------------

-------- - ..... 10 Y . __ --......_-.. ----__ -.. ____ .~ __ .

~-......... --........ '""-, -------------. 3 Y

-----~ -----......... _--'1

11~----~--~~--~~·1~0------------~~~~1~OO

Decay time (mon)

Figure 4.22. Estimation of the activation of earth by isotopes of more than 50 d half-life, per watt of beam power lost on a target with 80 cm concrete shield between the earth and the target (as extrapolated from the measured activities

around a target area given in Table 4.9).

130


occurs in the part of the shield near the target perpendicular to the beam direction, then the earth activation could be expected to depend on the incident proton energy as does the dose at 90 deg from an interaction as was given by Equation 2.4. Combining this energy dependence of the activation with decay of the measured activities given in Table 4.9 leads to a relation for an accelerator of energy E Ge V of

S = 15 y-O.2 ln[(T+t)/t] MBq.WI (4.44)

where S is the total radioactivity at a time t years after the end of the irradiation, due to isotopes of half-life greater than 50 days induced in earth by secondaries that penetrate an 80 cm concrete shield per watt of beam power lost in a target for a time T years. The residual earth activation after one year decay following a 10 year irradiation period is shown in Figure 4.23 as a function of the primary proton beam energy. It should be noted that Equation 4.44 is based on an empirical fiLm measured data and can be extended into the region of decay and irradiation times up to 10 years. 100r-~--~~nTnl---.~~~TnTI---.-.-r~~

I I 11~--~~~~~~10----~~~~~~10~2~~--~~~uuu103

Proton beam energy (GeV) Figure 4.23. An estimate of the total long-lived radioactivity (half-life greater than 50 d) induced in earth outside an 80 cm concrete shield near a target per watt of beam power lost in the target as a function of the interacting proton beam

energy, following a 10 y irradiation period and after I y of cooling down.

131


The principal isotopes of long tenn interest, 6OCO and 152Eu, are fonned by thennal neutron capture in trace amounts of cobalt and europium in the ea.rt11. It should also be noted that these isotopes tend to be found near the inner wall of the shield whereas the spallation produced isotopes are more widely distributed through the shield, approximately according to the high energy hadron attenuation mean free path(21,22).

4.4. Accelerator activation

4.4.1. Total activity in an accelerator An assessment of the total amount of radioactivity that

may exist in an accelerator structure after a period of operation will give an overall idea of the magnitude of any induced activity problems, particularly in the case where the machine will need to be decommissioned or dismantled. The total radioactivity in the machine will be primarily that of the remnant nuclei following high energy spallation interactions to which should be added a component due to interactions by the low energy evaporation neutrons(24) emitted following a spallation interaction.

A first order estimate of the total number of spallation interactions or 'stars' produced in the cascade by hadrons following an initial interaction by a proton accelerated to an energy of Eo GeV can be obtained using Equation 1.21 and will be given by

Nsec = 3.5 Eoo.92 stars per proton (4.45)

The activation resulting from a spallation interaction per second is given by Equation 4.18 and the spallation induced activitY per proton of energy Eo Ge V lost per second becomes

S = 0.12 Eoo.92 ln[(T + t )ft] Bq per proton.s-1 (4.46)

where T is the irradiation time and t the decay time (T and t in the same time units with T less than 10 years and t less than 6 months).

Low energy neutron activation is more difficult to estimate as it is a strong function of the composition of materials in the machine. The low energy neutrons will interact in the accelerator structure principally by way of (n,p),(n,a) or (n;y) reactions. The most important of these reactions will be the (n;y) capture reaction that occurs when neutrons have been slowed down to thennal energies. The probability of a thennal neutron interaction

132


in nonnal accelerator materials resulting in the production of a radioactive isotope with a half-life greater than 10 min is low and the principal reactions will be with the elements listed in Table 4.5. Inspection of the likely neutron capture cross sections of elements in accelerator materials suggests that less than 20% of thennal neutron capture reactions will result in an isotope that will contribute to the overall activity of the machine. Assuming on average 2.5 low energy (evaporation) neutrons are emitted per spallation reaction(23,241, the quantity of activity estimated as being due to spallation needs to be increased by a factor of the order of 50% to take into account the activity created by the associated low energy neutrons. Hence the effective total activity that can be expected in an accelerator structure for a machine where the average beam power dissipated is equivalent to 1 W, becomes

S = 1.1 Eo~·08In[(T + t)ft] GBq.W1 (4.47)

Results of calculations of the expected total radioactivity in an accelerator per watt of beam power used, after 5 years' operation and for cooling down times of 6 months and 1 and 2 years for machines working in the range from 1 to 1000 Ge V are shown in Figure 4.24.

.... _------------..----1: .-.-._._. ___ ._ Decay

0- -. ___ 6 mon ffi·2 ===_ -------- ---- ----------------I -~-~-~-------=~_-_-_. c:: ---------------_~_ 2 Y - -~1 ------_____ ~ __

~

Proton energy (GeV)

Figure 4.24. The estimated total radioactivity induced in a proton accelerator structure per watt of beam power after 5 y operation and cooling down periods of

6 months and 1 and 2 years.

133


Comparison of the total accelerator activity with that in typical earth shielding as shown in Figure 4.22 suggests that the bulk earth shield around an accelerator could contain of the order of 1 % of the total activity of half-life less than about 3 years but will contain a larger proportion of the longer-lived activity on account of the relatively long half-lives of the trace element activation induced by thermal neutrons in the earth.

4.4.2. Induced activity dose rate near a beam line An estimate of the order of magnitude of the induced

activity dose rate due to beam losses in an accelerator or along a beam line can be made if the losses are known or conversely loss rate can be estimated from measured induced activity levels. Most of the activity will be buried in the machine structure. If it is assumed that some 10% of the activity is visible at the ends of magnets and in sections between magnets then using Equation 4.47 for the total activity and with a dose conversion constant of 220 fSv.h-1 at 1 m from 1 Bq, the dose rate at 50 cm from a beam line of protons of energy Eo Ge V, at a time t days after the beam is switched off and where beam losses have been 1 W per metre for a period of T days, approximates to

D = 30 EO-D·08 In[(T + t)/t] (4.48)

However, this assumes the beam losses have been constant over a long period of time, which is never the case in real machines. The loss rate in the· period just before beam-off is normally much higher than the long-term average and is of more importance f6r the short-term induced activity level. To compensate for this non-uniform irradiation, the effective value for irradiation time is considered to be one year and the beam loss is taken as the average occurring over the two months prior to shutdown. This procedure should allow a more realistic estimate of dose rates due to induced radioactivity in the period up to at least a month after the beam is switched off.

Taking the above into account, the induced activity dose rate at 50 cm from a beam line and between beam elements, where the recent beam power loss has been p watts per metre of beam path (at Eo GeV) and t days after beam-off, reduces to(25)

134


D = 0.19 p EO-D·08 (1 - 0.17In(t)) mSv.h-1 (4.49)

This relation has been plotted in Figure 4.25 which shows the magnitude of the dose rates to be expected near a beam line from radioactivity induced by beam losses at 1, 10 and 1000 Ge V and how these dose rates should decay with time. The order of dose rate and its decay with time has been confirmed by measurements near a 26 GeV proton synchrotron(25).

4.4.3. Activation in high energy electron accelerators An estimate can be made of the radioactivity induced in

electron machines by way of the so-called giant resonance interactions of gamma photons with nuclei. An analysis has been made of the isotope yields in various materials due to this effect following high energy electron bombardment(26). The expected radioactivity induced by electrons in different materials, assuming all the electron beam energy is' lost in a target for a period of 2 years, is shown in Figure 4.26 as a function of decay time. The gamma dose rate expected at 1 m from this activity, calculated

0.3 _···_·--·'·-r···· "'oTT T '1-·_·-.,....·-.. ..,..·.". TT r ,---...... _'--. .... "

1: :> .. --. -------§. 0.2

E o a U)

co Q)

"§ 0.1 Q) C/l o a

Decay time (d)

Figure .4.25. The estimated induced activity dose rate at 50 em from a proton beam Ime for proton beams of (a) 1, (b) 10 and (c) 1000 GeV, as a function of decay time following a long period of operation and with losses corresponding to

1 W.m- l of beam path averaged over the previous 2 months operation.

135


assuming all the activity is concentrated at a point and without any'self-shielding, is shown in Figure 4.27. The above calculations are only for activity induced following giant resonance reactions, which will be the principal source of activity. However, additional radioactivity can be expected due to isotopes formed by the capture of the neutrons emitted in the giant resonance reactions and also at very high energies spallation interactions will occur due to hadron cascades initiated by high energy photopions.

Activation of antimony in lead has been found to be an important contributor to activity levels near a high energy electron beam target and the use of antimony-free lead is recommended for target shielding.

Comparison of the data for total activity due to a high energy electron beam, shown in Figure 4.26, with that due to spallation in proton machines as given in Figure 4.24, suggests that for equal beam power the activation of an electron machine will be less than 5% of that of a proton accelerator.

.... ~ _____ i I I Ilill .

\ \Copper \

iii IIIII

1000 Decay time (d)

Figure 4.26. Estimated activity induced by gamma giant resonance reactions in different materials per watt of high energy electron beam power dissipated as a

function of decay time.

136


4.5. Activation of air and water

4.5.1. Radioactivity production in air and water The air surrounding an accelerator and cooling water in

the machine will become activated due to high energy hadron interactions. Although only another component of the induced activity in the machine, air and water activity presents an additional hazard that needs to be studied separately in that this radioactivity is readily transportable through the shield and hence may escape to irradiate the environment and other occupied areas where the allowed radioactivity levels may be particularly low.

The principle radioactive isotopes of immediate interest that are found in irradiated air and water are the short-lived positron emitters that are produced in oxygen and nitrogen by spallation reactions. These isotopes are produced with a cross section that can be considered practically independent of the incident hadron energy above about 100 Mey(27). The production of 7Be and tritium by spallation reactions iii -air ·and water, as well as 41 Ar by

'I .s:: :>

(J)

~ E

.. _, I , i i'l I i I I Ii'

100 Decay time (d)

Figure 4.27. Gamma dose rate at 1 m from activity induced in various materials per watt of high energy electron beam power loss and after 2 y operation as a function of decay time, assuming all activity created is concentrated at one point.

137


thermal neutron capture in the natural argon in air, has also to be considered in an overall assessment of the radioactivity in the air and water that is irradiated near a high energy particle accelerator. The main radiological properties of the isotopes of interest for assessment of air and water radioactivity together with their assumed production cross sections(28) are summarised in Table 4.10.

The production rates of these isotopes and equilibrium activities expected to result from the passage of 1012 high energy hadrons and thermal neutrons through 1 m of air per second have been calculated from the data given in the Table 4.10. and are listed in Table 4.11. Similarly the resulting activities to be expected from the passage of 1012 hadrons per second through 1 cm of water are given in Table 4.12.

4.5.2. Air and water activation in electron machines Air and cooling water near a target in a high energy

electron accelerator may become radioactive primarily on account of bremsstrahlung gamma rays interacting with oxygen or nitrogen nuclei in so-called giant resonance reactions. These interactions produce mainly 150 in water and l3N in air with 2.1 min and 10 min

Table 4.10. Principal radioactive isotopes produced in air and water. All W emitting isotopes are assumed also to emit 2 x 0.511 Me V photons.

kgamma Production Isotope Half- Emission (fSv.h-l. cross section(mb)

life beta/gamma Bq-lat 1 m) N 0

140 1.2 min.~ _ 1.8 MeV B+ 450

150 2.3 MeVy

2.1 min 1.7 MeV B+ 140 40

13N 10 min 1.2 MeV B+ 140 10 9

llC 20 min .97 MeV B+ 140 10 5

7Be 53 d EC 8 10 5

3H 10.3% 0.48 MeVy

12.3 y 19keV B 30 30

4lAr 1.83 h 1.2 MeV B 150 Thn610mb 1.3 MeVy in 40Ar

138


half-lives respectively. As practically every gamma interaction results in the production of a neutron and a radioactive nucleus, the equilibrium activity in air and water should just equal the neutron yield in these materials. These yields are estimated to be 3 x 108 neutrons.s-1 per watt of electron power dissipated in air and 2x 108 neutrons.s-1 per watt for water(29) and are applicable to electron accelerators of energy above about 100 MeV. For lower energies the neutron yield (and activation) is reduced and ceases altogether when the gamma energy falls below the neutron production threshold of 11 Me V in nitrogen and 16 Me V in oxygen.

Table 4.11. Air activation for 1012 high energy hadrons and thermal neutrons passing through 1 m path length in air per second.

Isotope

Total short lived positron emitters

Half-life

1.2 min 2.1 min

10 min 20 min

53 d 12.3 Y 1.83 h

Production rate

(kBq.S-I)

12 250

60 30

352

7xl0-3

3xl0-4 1.9

Equilibrium activity (MBq)

1.2 45 52 48

146

48 160

13

Table 4.12. Activation of water by 1012 high energy hadrons traversing 1 cm of water per second.

Isotope

Total short lived positron emitters

Half-life

1.2 min 2.1 min

10 min 20 min

53 d 12.3 Y

139

Production rate

(kBq.S-I)

320 7300

320 90

8010

0.025 0.0018

Equilibrium activity (MBq)

33 1320 270 165

1788

165 1000


At very high energies multiple neutron production will result in lle being produced but the saturation activity of this isotope is only expected/to be a few per cent of the 150 activity in water and will be negligible compared to the 13N activity in air. The production of radioactive air due to any hadron cascade initiated by photopion production will always be small compared to that produced by gamma interactions.

The production of radioactivity in air or water near a target in a high energy electron beam can be readily calculated for the idealised case of a target surrounded by aIm layer of air or 1 cm of water where the activity A per watt of beam power loss will be given by

A = fY P A-I (4.50)

f is the fraction of electron energy that converts to gamma rays of energy above the nuclear interaction threshold, Y is the neutron yield in air or water per watt of electron power dissipated, P is the path length of the gamma rays in g.cm-2 in air or water and A the corresponding attenuation mean free path for gamma rays in the 10 to 30 Me V energy range.

The assumed values for these parameters are f = 0.3 (which is expected to depend on electron energy and target material), Y is the yield as given above and the path length Pis 0.129 g.cm-2 for air and 1 g.cm-2 for water. The mean free path of gamma rays is reasonably independent of gamma energy in the tens of Me V range and is taken as 56 g.cm-2 for both air and water.

The above data lead to the activities in air and water listed in Table 4.13 which gives the rate at which the activity is produced as well as the equilibrium activity that would occur in a spherical shell of 1 m of air or 1 cm of water surrounding a target in which the electromagnetic cascade is complete but where there has been

Table 4.13. Activation of a 1 cm layer of water and the activity produced in a layer of 1 m of air surrounding a target in which 1 W of power from high

energy electrons is dissipated.

Principal Half- Production Equilibrium Material isotope life rate quantity

(min) (Bq.S-I) (MBq)

Water 150 2.1 6100 1.1

Air 13N 10 240 0.2

140


no attenuation of the radiation by any intervening material. In a real situation appropriate corrections will have to be made for the actual quantity and position of any air or water near a target as well as any attenuation of the gamma rays by intervening material around the target. This attenuation can be determined using the gamma attenuation mean free paths as given in Table 3.3 (4.7 cm for iron and 21 cm for concrete).

4.5.3. Dose rates from activated air and water The beta and gamma dose rates in a very large cloud of

uniformly radioactive air and on the surface of a large volume of activated water have been determined using data given in Sections 4.1.3 and 4.1.4 which lead to values summarised in Table 4.14.

The dose rate at the surface of finite volumes of air or water will be, for a hemisphere of radius r g.cm-2

D = Do (1- e-r(A.) ~SV.h-I per MBq.m-3 (4.51)

where Do is the dose rate per unif activity at the surface of a large volume as given in Table 4.14 and A is the dose attenuation mean free path of air or water in g.cm -2 which is assumed to have a value for both media of 0.1 g.cm-2 for beta radiation (see Section 4.2.7) and 11.5 and 10.3 g.cm-2 for the 0.511 MeV gamma rays from positron annihilation in air and water (se~ Table 4.3).

In particular, this leads to a gamma dose rate at the centre of a cloud of radius R metres (less than about 200 m) of accelerator produced positron emitting isotopes of

D = 3.2 R ~SV.h-I per MBq.m-3 (4.52)

Using the above estimation for the gamma dose rate it can be seen by comparison with the data for beta radiation given in Table 4.14 that the beta dose rate will exceed that of the gamma rays in clouds of diameter less than about 66 m.

Table 4.14. Dose rates from large volumes of activated air and water.

IlSV.h-1 per MBq.m-3

Position Beta Gamma

Semi-inf"mite cloud 100 270

Water surface 0.13 0.35

141


4.5.4. Passage of radioactive air through a ventilation system When operating a target area, it may be necessary to

extract any radioactive air before entry can be allowed and it may also be required to extract a proportion of the air surrounding a target during operation in order to maintain a slight underpressure in the target enclosure. Under these circumstances it is essential to be able to estimate the quantities of radioactivity that are being released.

If there is an exchange of radioactive air inside a closed volume with fresh air from outside such that there are r air changes per hour, then for a gaseous isotope of decay constant A h-1, (A =

Air changes per hour

Figure 4.28. The equilibrium activity of air outside an enclosure as a function of air exchange rate for the activity produced when 1012 high energy hadrons and thermal neutrons traverse 1 m air path per second. The 13N curve also corresponds to the air activity produced in a one metre radius sphere of air surrounding a

target in a high energy electron beam where the beam power loss is 250 W.

142


0.693 divided by the half-life expressed in hours) and for which the total equilibrium activity is A Bq, the activity inside the area at a time t after switching on the beam becomes

A A(t) =A -- (l_e-(A+r)t)

A+r Bq (4.53)

This activity will build up with time until equilibrium is reached, which inside the area will be

102

0: !Xl

~ ~ '> ~ Ol Q)

"'0 Ow E

10

A A(in)=A -

A+r Bq


(4.54)

Figure 4.29. The equilibrium activity of air inside an enclosure as a function of air exchange rate for activity produced when 1012 high energy hadrons and thermal neutrons traverse 1 m air path per second. The 13N curve also corresponds to the air activity produced in a one metre radius sphere of air surrounding a

target in a high energy electron beam where the beam power loss is 250 W.

143


and that outside the area

r A(out) =A -

A+r Bq (4.55)

The equilibrium activities of the gaseous isotopes resulting from a continuous irradiation of air by 1012 hadrons traversing a one metre air path were listed in Table 4.11. The equilibrium activity of the various isotopes that will exist outside the enclosed volume for different ventilation speeds is plotted in Figure 4.28 and that remaining inside the volume in Figure 4.29. The

102

I f/J

0-m C.

~ Q) 0. al () f/J W

10


Figure 4.30. The rate at which air radioactivity 'escapes from a closed volume as a function of the air exchange rate for the activity produced when 1012 hi~h energy hadrons and thermal neutrons traverse aim air path per second. The 1 N curve also corresponds to the air activity produced in a one metre radius sphere of air surrounding a target in a high energy electron beam where the beam power

loss is 250 W.

144


equilibrium activity of 41 Ar has been included assuming there is one thermal neutron for every high energy hadron.

Of particular interest for calculating activity concentrations near the point of air release is the rate of escape of the radioactivity from the enclosure. The radioactivity escape rate, Q Bq.S-l, of an isotope of decay constant A will be the product of the equilibrium activity outside the area as given by Equation 4.55 above multiplied by A expressed in S-I and is plotted for the various radioactive gaseous isotopes and for the total activity as a function of air exchange rate in Figure 4.30.

It should be noted that the I3N data in the three preceding figures will also correspond to the air activity in aIm thick layer surrounding a target in a high energy electron beam where the beam power loss is 250 W.

4.5.5. Activity concentration and dose rate from a release of radioactive air

(a) Activity concentration--At a distance X metres downwind from a release of radioactive

air, the cross sectional area of the plume will be given by(30)

S = 1t C C X 2-

n m 2 (4.56) y z

where C and Cz are diffusion constants in the y and z planes and n is an iridex that takes into account turbulence.

Typical values for these parameters for use near ground level releases under widely different atmospheric conditions(31) are given in Table 4.15, which when put in the plume size equation, show that at about 30 m downwind the average radius of the plume will be practically independent of atmospheric conditions with a mean value of 5.7 m. Hence as a first approximation the average plume radius, R, at a distance X metres downwind can be

Table 4.15. Typical values of air plume parameters for a release near to ground level.

Atmospheric Plume parameters Mean radius conditions at30m

C Cz y n (m)

Very unstable 1.46 0.01 -0.25 5.53 Unstable 1.52 0.04 0.14 5.83 Neutral 1.36 0.09 0.38 5.50 Stable 0.79 0.04 0.63 5.78

145


represented by

R=5.7/30X=0.19X metres (4.57)

For a release of air activity at a rate Q Bq.S-l when the wind speed is u m.s-1

, the average activity concentration in the plume will be q Bq.m-3 given by

q = Q / rr R2u Bq.m-3 (4.58)

However, near ground level the plume is assumed to have a semicircular cross section where activity that touches the ground is reflected back into the plume, making the concentration twice that given above. It is also assumed that the activity is unifonnly distributed over the plume cross section. Substituting for R from Equation 4.57, the activity concentration at X metres downwind from a release of Q Bq.S-l with the wind speed u m.s-1 becomes

q = 18 Q / u X2 Bq.m-3 (4.59)

At large distances and low wind speeds the activity will significantly decay in transit. Reference to the isotopic composition of the radioactive air that is shown in Figure 4.30 suggests that an adequate approximate decay correction will be obtained at all air evacuation rates if the activity is assumed to be equal parts of 150, 13N and lle. The resulting concentrations of radioactivity in the plume downwind from the point of release are plotted in Figure 4.31 as a function of distance from the source for different wind speeds.

(b) Dose rate in a cloud. Using dose rate conversion factors given in Table 4.14, the

beta dose rat~ !n the plume at a distance X metres downwind from a release of Q Bq.S-l when the wind speed is u m.s-1 becomes

DB = 100 q = 1.8 Q / u X2 nSv.h-1 (4.60)

and the gamma dose rate, where the plume radius is given by Equation 4.57 approximates to

Dy= 1.2R q = 2.0 Q / uX pSv.h-1 (4.61)

(c) Long-tenn integrated gamma dose. The dose rates calculated above are those in an average plume

of radioactive air and would represent the possible instantaneous

146


values that occur during the release. In the case where wind frequency and speed is known as a function of direction Equation 4.61, with a suitable activity decay correction, could be used to estimate the integrated gamma dose in different directions and at different distances downwind from the point of release. However, as the concentration of the radioactivity in the plume is inversely proportional to wind speed, it will be in calm conditions that dose rates will be highest and at low wind speeds the wind direction tends towards being random.

Assuming all wind directions are equally likely, then at a distance X metres from the source the released activity could be considered to pass through a circular plane of length 2 rr X and height ...,frr R with velocity u. The long-tenn average radioactivity concentration at X metres from a release of Q Bq.S-l then becomes

q= Q/l1XRu (4.62)

where R is the plume radius in- ~etres and u the wind speed in m.s-1

• The resulting gamma dose rate corresponding to this

1'--,

...... Wind speed ~"'--.

----" '. ······ .. -.L~..:.~_._._._._._ ..

---"'--------------

....... -.. -... -.

........... -.-~ 0 m.s-1

----.

._----...._. __ ._._._---------------_ ...

500 Distance down wind (m)

Figure 4.31. The estimated activity concentration in a radioactive plume as a function of distance downwind from a release at a rate of 1 MBq.S-l.

147


concentration will be given by Equation 4.52 making the longterm integrated gamma dose D(tot), per GBq of activity released

D(tot) = 0.11 / uX J..lSV.GBq-1 (4.63)

A reasonable conservative assumption for the long-term average wind speed, which will tend towards overestimating the dose, would be 1 m.s-1

• A correction has also to be applied for the decay of the radioactivity in transit, as was made when considering the concentration in a radioactive plume.

The resulting long-term integrated dose for different total releases of activated air is shown as a function of distances from the source in Figure 4.32. The dose rates indicated in this figure are those occurring under the most adverse conditions and should be used merely to indicate at what level of emission and at what distances significant doses could occur.

4.5.6. Activation of cooling water Accelerator cooling water, particularly that used for

cooling targets, will be the major source of radioactive water

,~

----'-R;i~ase = 10000 TBq

-----.... _- ------'-. -------..._-.. _------

--------------- 3000 _____

------------------'---,---------

~-----~----~_____________ ---300 -___ ~_

------1 00 -~---------------, -------------------------....------------

'--"--------------_ -------30 -. --------------..... ------------------

--.. -----------.....: ----10 __

---------------

Distance from source (m)

Figure 4.32_ The long-tenn average gamma dose for different quantities of radioactive air released as a function of distance from the point of release and

assuming an average wind speed of 1 m.s-I.

148


from an accelerator. An estimation of the gamma dose rate expected at 1 m from a given volume of this water, for example from a heat exchanger, could be of interest for assessing the magnitude of any radiation problem that could arise.

If for a typical target cooling system it is assumed that: (i) 1012 high energy hadrons traverse 1 cm of water per second.

(ii) 50% of the total cooling water is in the heat exchanger at any one time.

(iii) There is self shielding of the gamma rays by the water and its container that reduces the dose by a factor of 2.

(iv) The water has an average transit time from the point of irradiation to heat exchanger of 2 min.

Then, using a dose rate constants from Table 4.10 and activation data from Table 4.12, the expected gamma dose rate at 1 m from the heat exchanger due to the various radioactive isotopes

100

Beamon Beam off

Total

'i _--- 150 .c // ... -cr.i I

-3 ,I

E 10

1a 13N (J)

~ (J) C/) 0 0

// /,./~'"

140

10 20 30 40 50 60 Irradiation time (min)

Figure 4.33. Dose rate at 1 m from a container in a water circuit after 1012 high energy hadrons per second have passed through 1 cm of water, showing the component activities and how the dose rate is expected to build up and decay with time after beam-on and beam-off_ It is assumed that the container holds half of the total water in the circuit, there is a 2 min transit time and 50% self

shielding by the water in the container.

149


induced in the water and its variation with time will be as shown in Figure 4.33.

The same water circuit would also be expected to accumulate:

2.2 MBq.d-1 of 7Be and

0.15 MBq.d-1 of tritium

The dose rate from 150 activity given in Figure 4.33 would also represent the dose rate from a similar heat exchanger circuit when cooling a 1 cm layer of water surrounding a high energy electron beam target in which 1.2 kW of beam power is lost.

References 1. Barbier, M. Induced Radioactivity (Amsterdam: North Holland) (1969). 2. US DREW. Radiological Health Handbook No. 137 (US Dept. of Health,

Education and Welfare, Maryland) (1970). 3. Evans, R. D. X-Ray and Gamma-Ray Interactions. In: Radiation Dosimetry,

Eds F. H. Attix and W. C. Roesch, Ch.3 (New York: Academic Press) (1968).

4. US DREW. Dose Buildup Factors. In: Radiological Health Handbook, p. 145 (US DREW, Maryland) (1970).

5. Fano, U., Spencer, L. V. and Berger, M. J. Penetration and Diffusion of xrays. In: Handbuch der Physik, Ed. S. Flugge, Vo!' 38, Part II, pp. 690-817 (Berlin: Springer) (1959).

6. Sullivan, A. H. Dose Rates from Radioactivity Induced in Thin Foils. Radiation Protection Group Report HS-RP/IR 82-46 (CERN, Geneva) (1982).

7. Sullivan, A. H. and Overton, T. R. Time Variation of the Dose Rate from Radioactivity Induced in High Energy Particle Accelerators. Health Phys. 11, 1101 (1965).

8. Sullivan, A .. H. An Approximate Relation for the Prediction of the Dose Rate from RadioaCtivity Induced in High Energy Particle Accelerators. Health Phys. 23, 252 (1972).

9. Freytag, E. Halbwertszeiten der Activierung bei Beschleunigern. Health Phys. 14, 267 (1968).

10. Sullivan, A. H. Induced Radioactivity Dose Rates in Steel and Lead. Radiation Protection Group Report HP-72-106 (CERN, Geneva) (1972).

11. Sullivan, A. H. The Release of Radioactivity from Rhenium Targets in AA. Radiation Protection Group Report TIS-RP/TM/85-40 (CERN, Geneva) (1985).

12. Hoefert, M., Yu-cheng, Chu, Hanon, J. M. and Sanchez, J. Radiation Protection Calculations and Measurements around the e-J6 Beam in the PS East Experimental Hall. Radiation Protection Group Report HSjRP/044 (CERN, Geneva) (1979).

150


13. Way, K. and Wigner, E. P. The Rate of Decay of Fission Products. Phys. Rev. 73,1318 (1948).

14. Goebel, K., Ranft, J. and Stevenson, G. R. Remnant Radioactivity in the Accelerator Structure. In: Radiation Problems Encountered in the Design of Multi-GeV Research Facilities, Ch. VIllA CERN Yellow Report 71-21 (CERN, Geneva) (1971).

15. Ishikawa, T., Sugita, H. and Nakamura, T. Thermalisation of Accelerator Produced Neutrons in Concrete. Health Phys. 209(2), 60 (1991).

16. Barbier, M. Induced Radioactivity. Appendix A (Amsterdam: North Holland) (1969).

17. Barbier, M. Induced Radioactivity. Ch. 1.5, p. 36 (Amsterdam: North Holland) (1969).

18. Yamaguchi, C., Hoefert, M., Schonbacher, H. and Stapleton, G. Induced Radioactivity in Concrete Blocks of Various Compositions Irradiated in the CERN Neutrino Facility. HS Division Report HS-RP/058 (CERN, Geneva) (1981).

19. Nachtigall, D. and Charalambus, S. Induced 24Na Activity in the Concrete Shielding of High Energy Accelerators. CERN Yellow Report 66-28 (CERN, Geneva) (1966).

20. Tuyn, J. W. N. Spectrometrie Gamma d'un Echantillon de Beton. Private communication (CERN, Geneva) (290).

21. Renaud, C. and Sullivan, A. H. Demantellement d'un Tunnel Utilise comme Blindage pour un Faisceau de Protons de Haut Energie. Rayonments Ionisants 4, 83, 261 (1983).

22. Sullivan, A. H. Decommissioning of a Tunnel used for a Shield for a HighEnergy Proton Beam. In: Proc. 6th Int. Conf. on Radiation-Risk-Protection, IRPA, Berlin (1984).

23. Metropolis, N., Bivins, R., Storn, M., Turkevich, A., Miller, J. M. and Friedlander, G. Monte Carlo Calculations on Intranuclear Cascades. Phys. Rev. 110, 185 (1958).

24. Skyrme, D. M. The Evaporation of Neutrons from Nuclei Bombarded with High Energy Protons. Nuclear Phys. 35, 177 (1962).

25. Sullivan, A. H. Induced Radioactivity and its Relation to Beam Losses in the CERN 26 GeV Proton Synchrotron. Nuc!. Instrum. Methods A257, 185 (1987).

26. Barbier, M. Induced Radioactivity. Ch.5.4, p. 228 (Amsterdam: North Holland) (1969).

27. Rindi, A. and Charalambus, S. Airborne Radioactivity Produced at High Energy Accelerators .. Nuc!. Instrum. Methods 47, 227 (1967).

28. Rindi, A. La Radioactivite Induite dans l' Air de l' Accelirateur de Protons de 300 GeV du CERN. Radiation Protection Group Report LABII-RA/72-5 (CERN, Geneva) (1972).

29. Swanson, W. P. Radiological Safety Aspects of the Operation of Electron Linear Accelerators. STI/DOC/1O/188, Ch. 2.5.3 (Vienna: IAEA) (1979).

30. Stem, A. C. Air Pollution, Vo!' 1 (New York and London: Academic Press) (1962).

31. International Atomic Energy Agency. Atmospheric Dispersion in Nuclear Power Plant Siting: A Safety Guide. 50-SG-S3-STI/PUB/549 (Vienna: IAEA)(1980).

151

152

Subject Index

A

Accelerator activation, 132 Absorbed dose

in a charged particle beam, 22 near a target in a hadron beam, 23 near a thick target in an electron

beam, 76-79 relation to hadron fluence, 22-24 units and conversion factors, 8

Activity in an electron accelerator, 135 in a proton accelerator, 132 produced by low energy

neutrons, 132 produced in a spallation

interaction, 94, 104, 132 Activating particles, 114 Activation - see also Induced

radioactivity by low energy neutrons, 133 of a proton accelerator, 132 of air, 136 of aluminium, 124, 136-137 of an electron accelerator, 135 of baryte concrete, 129 of concrete, 126 of copper, 123, 136-137 of earth, 128 oflead, 123,136 of water, 137-141

Air activation, 137 activation by electrons, 138 beta dose in activated volume of, 141

critical energy of electrons in, 75 dose rate from a release of, 148 gamma dose rate from activated

volume of, 141 gamma ray attenuation by, 100, 140 passage through a ventilation

system, 142 photoneutron production threshold

in, 75 radioactivity concentration in, 145 radiation length of electrons in, 75

Aluminium activation, 124

153

Index

activation by electrons, 136-137 charged particle range in, 5 density of, 8 gamma ray attenuation by, 100 high energy hadron attenuation mfp

in, 8,94 nuclear inelastic cross section of, 6-8

principal isotopes fonned in, 124 relative secondary particle yield

in, 32 spallation mfp of hadrons in, 94 vacuum window surface dose, 114

Angle of maximum dose, 40-41 Angular distribution

of hadron fluence, 11-13,49 of muons, 57

Antimony activation in lead, 120, 123, 136

Argon-41 isotope properties, 121 production cross section by

thennal neutrons, 138 production in air, 138, 144-145

Attenuation mean free path for beta surface dose, 114 for gamma rays of 0.5 and 0.8 MeV, 100

for hadrons, 8, 13, 53 for muons, 54, 81 for secondaries from electron

interactions, 81 Attenuation of X rays, 85

B

Baryte concrete activation of, 129 density of, 8 high energy hadron attenuation mfpin, 8,94

isotopes produced in, 129 muon beam energy loss rates

in, 55 range of charged particles in, 5 spallation mfp of hadrons in, 94 transmission of hadrons

through, 36 Beam line

induced activity dose rate near, 134-135

shield for point losses, 39 shield for unifonn losses, 42, 52

Index

Beam dump dose equivalent outside, 43-44 gamma ray dose rate from, 106,

119 length to range out muons, 56 muon isofluence contours in, 60

Beta particle activity, 95 dose, 101 dose at surface of activated

water, 141 dose from activated materials, 102 dose from thin targets, 113 dose in a radioactive cloud, 141 dose relative to gamma dose, 103 emission, 95, 138 energy, 95 surface dose attenuation, 114

Bequerel, 8 Beryllium

density of, 8 high energy hadron attenuation mfp in, 8

nuclear inelastic cross section of, 6-8

relative secondary particle yield in, 32

threshold for photoneutron production in, 76

Beryllium-7 gamma k factor, 95, 138 in a cooling water circuit, 150 in accelerator structures, 95 in air and water, 138-139 in an earth shield, 129 isotope properties, 95, 138

Bremmstrahlung from electrons, 5, 76, 138 from muons, 56

Build-up -.: ... of dose.equivalent in a shield, 38 of dose in an absorber, 38 of gamma ray dose, 85-86,101 of secondary hadron fluence, 20 of secondary hadron flux, 115-116

c Carbon - see graphite Carbon-II

in accelerators, 95 in air and water, 137-140 in cooling water, 149

154

Cascade neutrons, 45-47 number and energy of secondary hadrons in, 17

Charged particle (s) ionisation by, 3 minimum ionising, 3-4 range, 3-5,

Chicanes, radiation transmission through, 67

Cobalt contribution to surface dose on iron, 122 thermal neutron capture cross

section, 121 Cobalt-60

gamma k factor, 95 in accelerators, 95 in baryte concrete, 129 isotope properties, 95, 121 production of by thermal neutrons,

121 surface dose contribution in

iron, 122 Concrete

activation, 126 density of, 8 dose rate from activity induced

in, 126 gamma ray attenuation by, 100 high energy hadron attenuation mfp

in, 8 muon beam dump length in, 58 muon beam energy loss rates in, 55 production of sodium-24 in, 126 range of charged particles in, 5 spallation mfp of hadrons in, 94 transmission of hadrons through, 36

X ray attenuation by, 85 Copper

activation by electrons, 136-137 charged particle range in, 5 density of, 8 dose rate from activity induced

in, 105,117-119, 126 gamma ray attenuation by, 100 high energy hadron attenuation mfp

in, 8 nuclear inelastic cross section, 6-8

spallation mfp of hadrons in, 94 surface dose rate on, 123

target activation, 104-107 thermal neutron activation of,

121-123 Critical energy

for electrons 75 for synchrotron radiation, 86-87

Cross section for isotope production in air and

water, 138 high energy hadron inelastic, 6-8 thermal neutron capture, 121

Curie, 8

D

Damage - see Radiation damage Decay products from unstable

particles, 2 Delta rays, 4 Density

of target and shielding materials, 8 Deuterium

threshold for photoneutron production in, 76

Dose equivalent conversion from hadron fluence, 26 in a beam, 28 near a beam line, 30 near a target, 29 outside a beam dump, 43 source term for hadrons, 37, 40,

50-51 source term for secondaries from

electrons, 80 Dose rate constant for induced

activity in concrete, 126 in copper, 105, 126 in heavy elements, III in iron, 105, 126 in marble, 126

Ducting - see holes through a shield

E

Earth activation, 128, 134 density of, 8 charged particle range in, 5 gamma ray attenuation by, 100 high energy hadron attenuation mfp

in, 8 muon beam dump length, 58

155

Index

muon beam energy loss rates in, 55 saturation activities in, 129 spallation mfp of hadrons in, 94 transmission of hadrons through, 36

Electron capture, 94 critical energy of, 75, 86 low energy, 83 mass, 2 radiation length in targets, 75 range, 4

Electronics radiation damage to, 25-26

Energy beta particle average, 95 gamma ray average, 95 of secondary hadrons, 13-18, 46 of synchrotron radiation, 86 relation to particle momentum, 2

Epoxy resines radiation damage to, 25-26

Equivalence of continuous and point beam losses, 43

Europium in an earth shield, 129, 132 in baryte concrete, 129 isotope properties, 121, 129 thermal neutron capture in, 121

F

Fluorine-18 in accelerators, 95 in aluminium, 124 isotope properties, 95

Fluence angular distribution of secondary hadron, 11-13,49

build-up of secondary hadron in an absorber, 20

conversion to hadron absorbed dose, 22-24

conversion to hadron dose equivalent, 26-27,50

equilibrium hadron, 22 of muons outside a shield, 54 of neutrons from proton

interactions at E<l GeV, 44 Flux

build-up, 116-117 conversion to absorbed dose, 23 equlibrium, 115 of particles in a beam, 22-23

Index

of panicles near a target, 115 of thennal neutrons, 120, 122

G

Gamma ray - see also X rays dose build-up factor, 85-86 dose rate near active materials,97 dose rate near thin materials, 99 induced activity dose rate

constant, 96, 121 k-factor, 96, 121, 138 mass-energy absorption

coefficient, 96 mean energy, 95 mean free path

in air, 140 in concrete, 81, 141 in iron, 81, 141 in lead, 81 in water, 140

relation between dose rate and activity, 96

tenth value layers, 85 Giant resonance reactions, 76,

136, 138 Gold

critical energy of electrons in, 75 photoneutron production threshold

in, 75 radiation length of electrons in, 75

Graphite density of, 8 high energy hadron attenuation mfp in, 8

Gray, 8-9

H

Hadron(s) attenuation mfp of high energy, 8 conversion of fluence to absorbed

dose, 22-24 conversion of fluence to dose

equivalent, 26-27 inelastic nuclear cross sections

for, 7-8 secondary fluence of, 13 transmission down chicanes, 67 transmission through a shield, 36 tenth value attenuation thickness

of, 8

156

Half-life effective, 107-109 of isotopes in activated air and

water, 138-139 of isotopes in activated baryte,

129 of isotopes in activated earth,

129 of isotopes produced by

spallation, 95 of isotopes produced by thennal

neutron interactions, 121 ffealth risk of radiation, 10-11 Heavy element

activation, 111 dose rate from activity induced

in, 110-111, 113 Holes in a shield,

radiation at entrance to, 61 neutron and X ray scatter down, 63 source tenns for calculating transmission down, 62

I

ICRP, 10 Induced radioactivity

dose rate near a beam line, 134 dose ratio at surface to at 1 m, 99 gamma ray dose rate at surface of

large activated volume, 98 in heavy element targets, 1 10-113 properties, 93-95, 103 in iron and copper down beam from

a target, 117-119 in iron and coppertargets, 104-107

Interaction length, 6, Ill, 112 Iron - also see Steel

activation of alloying elements by thennal neutrons, 120-122

activation by electrons, 136-137 attenuation of muons from proton

interactions in, 54 charged particle range in, 4-5 critical energy for electrons, 75 density of, 8 dose rate from activity induced

in, 105, 112, 117-119, 126 gamma ray attenuation by, 100 gamma ray dose rate at surface of

large activated volume, 98 high energy hadron attenuation mfp

in, 8

low energy neutron absorption in, 83 muon beam dump length, 58 muon beam energy loss rates in, 55 nuclear interaction cross section

of, 6-8 photoneutron production threshold

in, 75 radiation length of electrons in, 75 relative secondary hadron yield

in, 32 shielding for X and gamma rays, 81, 85, 100

spallation mfp of hadrons in, 94 target activation, 104-107 transmission of hadrons through,36

K

Kapton radiation damage to, 25-26

k factor for gamma emitters, 95-96, 121, 138 for isotopes fonned in air and

water, 138 for mixtures of spallation

produced isotopes, 97, III

L

Lead activation by electrons, 136-137 activation of antimony in, 123, 136 attenuation of muons from electron

interactions in, 81 attenuation of muons from proton

interactions in, 54 charged particle range in, 5 critical energy of electrons in, 75 density of, 8 dose rate from activity induced

in, 111-113 gamma ray attenuation by, 100 gamma ray dose rate at surface of

large activated volume, 98 high energy hadron attenuation mfp

in, 8 muon beam energy loss rates in, 55 nuclear inelastic cross section, 6-8 radiation length of electrons in, 75 relative secondary particle yield in,

32 shielding for X and gamma rays,

85, 100

157

Index

spallation mfp of hadrons in, 94 target activation, 112 threshold for photoneutron production in, 75

Leptons, 1-2 Lifetime

of muons, 2 of neutrons, 2 of pions 2, 54

Linear energy transfer (LET), 9

M

Magnet coil insulation radiation damage to, 25-26

Manganese contribution to surface dose on

iron, 122 thennal neutron capture cross

section in, 121 Manganese-54

in accelerators, 95 isotope properties, 95

Manganese-56 production by thennal neutrons,

121-122, isotope properties, 121

Marble activation, 125-126 dose rate from activity induced

in, 126 Mean free path

for hadron interactions in target and shielding materials, 7, 8

for spallation interactions, 94 of beta particle surface dose, 114 of gamma rays of 0.5 and 0.8 MeV of high energy hadrons, 8, 94 of muons from electrons, 79 of muons from protons, 56 of secondaries from electron

interactions, 81 of secondaries from protons of

less than 1 GeV, 52, 53 Minimum ionising particles, 4 Momentum

relation to panicle energy, 2 Mortality risk factor, 10 Multiplicity

in high energy proton interactions, 13-15

in proton interactions below 1 GeV, 46-47

Index

Muon (s) angular distribution, 57 attenuation, 54 beam strength, 59 from electron beams, 76, 79 isofluence contours, 60 lifetime, 2 mass, 2 mean free path (electron), 80-81 mean free path (proton), 56 production, 54 range, 3-4 ranging out, 56 source term (electrons), 80

Mylar radiation damage to, 25-26

N

Natural background radiation, 10 Neutron

cascade, 45, 47 dose rate at a distance, 71 evaporation, 29, 132-133 giant resonance, 76, 136 lifetime, 2 mass, 2 attenuation mfp in concrete, 81

in iron, 81 in lead, 81

photo production threshold, 139 thermal - see thermal neutrons transmission along ducting, 66 skyshine, 71 yield from electron interactions,

79, 139 yield from proton interactions

below 1 GeV,46 Nitrogen ..

isotope. production cross section in, 138

photoneutron production threshold in, 139

Nitrogen-13 in activated air, 138-140 in activated cooling water, 149 in air activated by electrons,

138, 142-145, Nuclear interaction (s)

by electrons, 76 cross section, 8 mean free path, 8

158

Nuclear interaction length, 6, Ill, 112 Nylon

radiation damage to, 25-26

o Occupational dose limit, 10-11 Oils

radiation damage to, 25-26 Organic cables

radiation damage to, 25-26 Oxygen

isotope production cross section in, 138

photoneutron production threshold in, 139

Oxygen-14 in activated air and water, 138-139

Oxygen-15 in activated air and water, 138-140 in electron target cooling water, 150 in target cooling water, 149

p

Paint radiation damage to, 25-26

Photonuclear interactions, 76 Photoneutron

production threshold, 75, 76 Photopions, 76 Pion

flight path, 54 lifetime, 2, 54 mass, 2 range, 3-4

Plastic scintillator radiation damage to, 25-26

Platinum density of, 8 high energy hadron attenuation mfp

in, 8 inelastic nuclear cross section, 8

Polyeurathane radiation damage to, 25-26

Polythene radiation damage to, 25-26

Positron annihilation, 94, 101, 141 emitters, 94, emitters in air and water, 137-139 mass, 2

Prefixes for SI units, 9

Proton mass, 2 range, 4-5 range in iron of protons of energy

less than 0.8 GeV, 5 stopping power in iron and water, 3

Q

Quality factor of beta particles, 102 of charged hadrons, 8 of charged leptons, 8 of high energy secondary hadrons,

8, 37 of X or gamma rays, 8

R

Rad, 8-9 Radiation damage

to accelerator materials, 25-26 to integrated circuits, 26

Radiation length of targets in electron beams, 75

Radioactivity - see induced radioactivity

Range of charged particles relative to

iron, 5 of protons, muons and electrons, 4,5

Relativistic increase of particle lifetime, 1, 54 of particle mass, 1

Rem, 8-9 Rhenium activation, 110 Rubber

radiation damage to, 25-26

Scatter coefficient for neutrons, 64

s

for X or gamma rays, 64 Secondary hadron(s)

angular distribution of, 11-12 energy of, 13-17, 46 eqUilibrium, 35 fluence build-up in an absorber, 20 flux, 115 fraction emitted into a forward

cone, 14

159

Index

from interactions by protons of E<l GeV, 46-49

multiplicity in an interaction, 13, 46 number in a cascade, 17

S.I. units of absorbed dose, 8 of dose equivalent, 8 of radioactivity, 8 prefixes for, 9

Sievert, 8-9 Single event upsets, 26 Skyshine, 71 Sodium-22

gamma k factor, 95, 124 in accelerators, 95 in aluminium, 124 in baryte concrete, 129 in earth, 129 isotope properties, 95

Sodium-24 gamma k factor, 95, 121, 124 in accelerators, 95 in concrete, 125-127 isotope properties, 95 production by thermal neutrons,

121, 127 production by (n,a) reaction

in aluminium, 124 Source term

for beam line shields, 39, 52 for high energy protons, 37, 44, 49 for protons below 1 GeV, 49 for secondary radiation from

electron interactions -gamma rays, 77-78,80 high energy neutrons, 79,80 low energy neutrons, 79,80 muons, 79-80

Spallation isotopes produced by, 95 mean free path, 94

Spallation products dose rate from, 95, 122, 123, 127

Stars number in a cascade, 20-21, 132

Steel - see also Iron gamma ray dose rate from, 112, 113 surface dose from vacuum window,

114 Stopping power of protons and

muons, 3 Surface dose

due to spallation products, 98

Index

on activated aluminium, 114, 125 on activated concrete, 127 on activated copper, 119, 123 on activated iron, 119, 122 on activated lead, 123 on activated steel, 114 on activated water, 141 on vacuum windows, 114 ratio to dose at 1 metre, 99 ratio to specific activity, 102

Synchrotron radiation critical energy, 86-87 dose rate, 90 energy, 86 energy spectrum, 88 heating, 87 production, 86

T

Teflon radiation damage to, 25-26

Tenth value layer for gamma rays of 0.5 and 0.8 MeV,

100-101 for high energy hadrons, 8 for surface dose in plastic, 114 for X and gamma rays, 85

Thermal neutron activation, 119-124 capture cross sections, 121 flux relative to high energy neutrons, 120

Tissue sphere, 26 Transmission

along ducting for neutrons and X or gamma rays, 65-66

down multi-legged chicanes, 67 of high energy hadrons through a shield, 35-36 .;-

Tritium gamma k factor, 138 in a cooling water circuit, 150 in an earth shield, 129 isotope properties, 138 production in aii '!lld water, 138-139

Tungsten activation of, 110 charged particle range in, 5 critical energy of electrons in, 75 density of, 8 high energy hadron attenuation mfp in, 8

160


radiation length of electrons in, 75 spallation mfp of hadrons in, 94 threshold for photoneutron production in, 75

Tungsten-187 isotope properties, 121 production of by thermal neutrons,

121

u Uranium

charged particle range in, 5 density of, 8 high energy hadron attenuation mfp in, 8


relative secondary particle yield in, 32

spallation mfp of hadrons in, 94

v Vacuum windows

surface dose on, 114 Ventilation systems, 142-145

w Water

activation of, 137-141, 148 activation of by electrons, 138 critical energy of electrons in, 75 gamma ray attenuation by, 100, 140 gamma ray dose rate at surface of

large activated volume, 98 muon beam energy loss rates in, 55 photoneutron production threshold in,75

radiation length of electrons in, 75 ratio of activity to dose rate in, 141 spallation mfp of hadrons in, 94

x Xray

attenuation, 85 dose rate from high voltage

discharges, 84 production, 83-84

scatter down holes, 65-66 synchrotron radiation, 86-91 tenth value layer attenuation

thickness, 85

y

Yield of high energy secondary particles, 32

of neutrons from electron interactions, 79, 139

161

of neutrons from proton interactions, 46

z Zinc-65

in accelerators, 95 in copper, 119-120 isotope properties, 121

Index

production of by thermal neutrons, 121

Date post:	01-Nov-2021
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

A Guide to Radiation and

Documents