A Guide to Radiation and
Radioactivity Levels Near High
Energy Particle Accelerators
A. H. Sullivan
Nuclear Technology Publishing
Ashford, Kent, TN23 IJW
England
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A Guide to Radiation and
Radioactivity Levels Near High
Energy Particle Accelerators
~
I
"A little inaccuracy sometimes saves tons of explanation"
H.H. Munro in Short Stories of Saki
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
iii
THE AUTHOR
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.
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.
Typesetting by Lin-Art, Ashford, Kent.
Printed by Geerings of Ashford, Ashford, Kent.
Published by Nuclear Technology Publishing, Ashford, Kent.
ISBN 870965 183
iv
v
Contents
Contents
Preface
Chapter 1
1.1
vi
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
3
4
6
9
10
1.2
Secondary radiation from high energy interactions
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
1.3
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
equivalent
1.3.5 Dose equivalent in a beam
1.3.6 Dose equivalent near a target
1.3.7 Dose equivalent rate near a beam
line
1.3.8 Dose near targets of different
materials
References
Vll
22
23
25
26
28
29
30
31
33
Contents
Contents
Shielding for high energy particle accelerators
Chapter 2
2.1
2.2
2.3
2.4
2.5
Chapter 3
3.1
Shielding for high energy protons
2.1.1 Radiation attenuation in a shield
2.1.2 Source terms for shielding
calculations
2.1.3 Dose build-up in an absorber
2.1.4 Beam line shields
2.1.5 Dose equivalent outside beam dumps
Shielding for protons below 1 Ge V
2.2.1 The secondary radiation distribution
2.2.2 Source terms for shielding
calculations
2.2.3 Secondary particle attenuation
Shielding for muons
2.3.1 Muon production
2.3.2 Muon attenuation
2.3.3 Ranging out the muons
2.3.4 Angular distribution of muons
2.3.5 Muon beam strength
2.3.6 Isofluence contours
Radiation transmission through holes and
chicanes in a shield
2.4.1 Radiation at the entrance to a hole
in a shield
2.4.2 Radiation scatter down holes
in a shield
2.4.3 Transmission down multi-legged
chicanes
35
35
38
39
43
49
52
3.4
54
54
56
57
59
60
Chapter 4
61
4.1
63
67
71
73
Shielding for high energy electron machines
viii
3.3
45
Skyshine
2.5.1 Neutron dose rate at a distance
References
Electron interactions
3.1.1 Critical energy
3.1.2 Radiation length
3.1.3 Nuclear interactions by electrons
3.2
4.2
75
75
76
3.1.4 Radiation near a target in an
electron beam
76
Shielding for high energy electrons
3.2.1 Source terms for shielding
calculations
3.2.2 Muons from electron beams
3.2.3 Secondary particle attenuation
77
79
81
Low energy electrons
3.3.1 X ray production
3.3.2 X ray attenuation
83
85
Synchrotron radiation
3.4.1 The production of synchrotron
radiation
3.4.2 Synchrotron radiation energy
3.4.3 The synchrotron energy spectrum
3.4.4 Synchrotron radiation levels
3.4.5 Dose rate outside the vacuum
chamber
References
86
86
88
89
90
91
Radioactivity induced in high energy
particle accelerators
Properties of induced radioactivity
4.1.1 High energy particle activation
4.1.2 The activity produced in an
interaction
4.1.3 Relation between activity and
gamma ray dose rate
4.1.4 Shielding for induced activity
gamma dose
4.1.5 Dose from beta activity
4.1.6 Ratio between beta and gamma
dose
93
94
96
100
101
103
Radioactivity in targets and dumps
4.2.1 Radioactivity induced by high energy
particle interactions
103
4.2.2 Radioactivity in iron and copper
targets
104
ix
Contents
4.2.3 Dose rate from targets and beam
dumps
4.2.4 Effective half-life
4.2.5 Activation of heavy element targets
4.2.6 Comparison of calculated dose rates
with measurements
4.2.7 Beta dose from thin targets
4.3
4.4
4.5
I
Activation by secondary hadrons
4.3.1 Activating particles
4.3.2 High energy particle activation
4.3.3 Activation by thermal neutrons
4.3.4 The activation of aluminium
4.3.5 The activation of concrete
4.3.6 Earth activation '
Accelerator activation
4.4.1 Total activity in an accelerator
4.4.2 Induced activity dose rate
near a beam line
4.4.3 Activation in high energy
electron accelerators
Activation of air and water
4.5.1 Radioactivity production in air
and water
4.5.2 Air and water activation in
electron machines
4.5.3 Dose rates from activated air and
water
4.5.4 Passage of radioactive air through a
ventilation system
4.5.5 Activity concentration and dose rate
from a release of radioactive air
4.5.6 Activation of cooling water
References
x
105
107
110
112
113
114
116
119
124
125
128
132
134
135
137
138
141
142
145
148
150
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
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.
I
!
J
I
(
1
II
l
xiii
CHAPTER 1
High Energy Particle Interactions
1.1.
Properties of high energy particles
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.
1.1.1.
1.1.2.
Energy and momentum
The degree of acceleration of a charged particle is often
expressed as its momentum, whereas calculations of radiation
xiv
1
Radiation and Radioactivity Levels near High Energy Particle Accelerators
High Energy Particle Interactions
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
Figure 1.1 for commonly encountered high energy particles.
III
1.1.3.
10~L-~~~di~l---~~~~~--~~~~1~03~~~~~·1~04
10
102
Momentum (MeV/c)
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
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
4
Protons
of'
E
()
"Ol 3
:>
6
Q)
Table 1.1. High energy particles of interest for shielding calculations_._"
Particle
Charge
Symbol
Mass
(MeV)
Mean life
at rest
(s)
Principal
decay
products
\\
\
'.
\
\
"
=ci 2
1i:J
"0
Muons
,Iron ___ _
--._------..-... ......
-- -
._--_.
Hadrons
Proton
Neutron
Pion
Pion
Leptons
Muon
Electron
Positron
0
p
n
±
7r
0
1[;0
+
±
+
+
+
)r
e
e+
2
938
940
140
135
stable
900
2.6x 10-8
8.4xlO- 17
106
0.511
0.511
2.2xlO-6
stable
stable
p,e
+
)r
gamma rays
e-+
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
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 e V.g-I .cm-2
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
(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
= 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
102w-~~-rrn~--~-r"~~---r-r~~~---r-rrT~~
(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 GeV 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.
c
:se 10-
1
Material
Q)
OJ
c
&. 10-
2
K
(m.GeV- 1)
Densiti:
(g.cm- )
Relative
range
.~.,
Proton
10-3
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
Water
Earth
Concrete
Aluminium
Baryte
Iron
Copper
Lead
Uranium
Tungsten
1.0
1.8
2.35
2.7
3.2
7.4
8.9
11.3
19.0
19.3
4.0
2.5
1.8
1.8
1.7
0.70
0.60
0.55
0.32
0.30
5
5.7
3.6
2.6
2.6
2.4
1.0
0.86
0.79
0.46
0.43
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
in cm2, on the
dependence of the interaction cross section,
atomic mass of the target nucleus A of
°
0=
42 AO.7 x 10-27
where N is Avogadros number with a value of 6.02 x 10" atoms
per mole, A is the atomic weight of2 the material and 0 is the
nuclear interaction cross section in cm • 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
(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 cm 2) 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
c
~
-
1.0 t--
c:
o
t5
Be
..,/
_,.,-·,.~C
Q)
(/)
(/)
(/)
&0.1 ~
::-............
...-."
-
_.....-
0.01 '":1;--------.........----:-:10:---"'O'----;""O"...l-'-U-I.1..l..~0-......--~.............1...:..JOOO
Atomic weight
A
Ie = ~.-
(l.6)
N0
6
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
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Table 1.3. High energy particle interaction cross sections and attenuation
mean free paths in various target and shielding materials.
Inelastic
cross section
(bam)
Material
Beryllium
Graphite
Water
Concrete
Earth
Aluminium
Baryte
Iron
Copper
Tungsten
Platinum
Lead
Uranium
0.20
0.23
0.42
0.70
0.78
1.61
1.78
1.77
1.98
Nominal
densit¥
(g.cm- )
Attenuation
mfp
(g.cm-2 )
(cm)
75
86
85
100
100
106
112
132
135
185
190
194
199
42
43
85
43
56
39
35
17.8
15.2
9.6
8.9
17.0
10.5
1.8
2.0
1.0
2.35
1.8
2.7
3.2
7.4
8.9
19.3
21.4
11.3
19.0
Tenth
value
(cm)
96
100
195
99
128
90
80
41
35
22
20
39
24
Table 1.4. SI units, conversion factors and assumed quality factors.
(a) Beam power
1 kW = 6.24 X 10 12 GeV.s- 1
1 ampere = 6.24 x 10 18 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
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.
(e) Radioactivity
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
Symbol
Value
Tera
Giga
Mega
kilo
milli
micro
nano
pico
femto
T
10 12
109
106
103
10-3
10-0
10-9
10- 12
10- 15
G
M
k
m
~
n
p
f
9
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
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)
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
<pee)
=
5000
(e +
hadrons.m-2
35/oJEi
(1.8)
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
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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)
hadrons.m-2
= (i~ 0.4/~E)2
(1.9)
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
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'
~
~100
o deg
(f)
c
e
"'E
ui
1:l
CIl
c
e
E
E
-g
:S
E
Cii
(])
u
10
10
c
(])
:J
u:::
10-1
90
H!Q
10-2
1
10
102
Proton energy (GeV)
103
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.
Figure 1.6. Secondary hadron fluence per proton interaction at different angles as
a function of incident proton energy.
12
13
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
rJJ
(1.10)
Q)
.~
10
"0
C
o
<.>
Q)
rJJ
'0
iii
.0
E
:J
Z
40
20
60
80
100
120
Angle (deg)
140
160
180
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.
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
40
0
1000
rJ)
Q)
"fa
-g 0.6
0
()
Q)
rJ)
en
/
0.8
Q)
.~
"0
~11
'0
iii
1 GeV
z
c 30
0
<.>
/
0
C
gO.4
.<
Q)
/10
rJJ
,.e
E20
:J
()
<1l
u::
10
20
40
60
80
100
120
140
160
180
Interacting proton energy (GeV)
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.
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.
14
15
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 GeV. 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
(1.11)
GeV
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)
E sec = 0.12 E 0.76 = (0.06 E)0.76
GeV
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 GeV in a cascade initiated by a proton of energy Eo GeV can
be estimated. Using Equation 1.12, the effective energy of the
secondary hadrons after one interaction, E 1, will be
S2-
E - (aE)p
>-
1 -
2'
Q)
(1.12)
°
(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
c
Q)
i::'
rn
"0
c
o<)
Q)
(1.14)
(f)
after q interactions the average energy of the hadrons in the
cascade will be
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
(LISa)
where
p
= 13+132+133+... 13q = 13 (1
- u)/(1
17
-13)
(l.lSb)
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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»)
N(E) = (EJE)o.92
(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
( 1.17)
N(E) = EJE (0.8)Q
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
(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 GeV 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
N sec
where q is the average number of collisions required to reduce the
= 2 E00.92
(1.19)
3
(/)
(/)
Q)
Ow
-0
0
o
c 2
0
.~ 102
C
o
0
Q)
'0
(/)
'0
Qi
Qi
.D
E
.D
~
E 10
z
~
z
10
Proton energy initiating cascade (GeV)
10
102
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.
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.
18
19
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 = 0.24E o.7 <PI hadrons.m-2
(1.23)
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
= 0•24E°0.7
N
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
sec
= 3.5 E°0.92
(1.21)
o
and the total hadron fluence inside the shield after equilibrium is
reached will be given by
<P = <PI + <P2 = <PI (1 + 0.24E o.7 ) hadrons.m-2 (1.24)
o
5
The expected number of spallation interactions or stars in a
cascade per GeV of primary energy is plotted as a function of the
initiating proton energy in Figure 1.13.
4
~3
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
m 2 ) of
= <pee) e-tf)..
<P
I
(1.22)
R2
20
(')
Q;
0.
00
!§2
(f)
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
High Energy Particle Interactions
as particles per cm2 per second. In which case the appropriate
factor to convert flux into absorbed dose rate becomes
This equilibrium fluence is plotted in Figure 1.14 as a function
of incident proton energy for various directions from the target.
1.3.
(1.26)
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··/
.-----------
---~-~
-
:
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 <I> minimum ionising particles per second, the
particle flux <p particles.cm-2 .s- 1 at a radius r cm from the beam
axis will be given by
<I> exp(-r/a)2
(1.27)
<p=
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 10 12 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.
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.
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
22
23
Interacting proton energy (GeV)
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
2
interaction in a target, ~ hadrons per m , is given by Equation
I. 2. 'E ~ and the absorbed dose at 1 m per primary interaction in the
target will be
D
= 32 ~
(1.28)
fGy per proton
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
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-~~~~~~~--
,..c
~5
:>,
e:l
.S;
::10
I
.c
4
2
:>.
~
Q.
Q)
(f)
Q)
o
~3
Ol
o
Ii!
Q)
(f)
o
-0
....J
-0
Q)
.0
2
o
(f)
.0
«
1
o
2
4
14
10
12
8
6
Distance from beam axis (cm)
16
18
20
30
90
60
120
150
180
Angle (deg)
Figure 1.15. The absorbed dose rate as a function of distance from the beam line
in a beam of 10 12 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.
Figure 1.16. The absorbed dose rate as a function of emission angle to a sample
placed at 1 m from a target, per 10 10 interactions per second in the target by
protons of different energies.
24
25
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
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
C = 40(1 + E- 6 ) fSv per hadron.m-2
0.29)
H
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
C H = 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~
Table 1.7. Radiation levels at which damage to various materials may start
___________ to become significant.
Material
Dose Gy
------
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
Eo
c
2
~ 10
.t::
Q;
">
'2.
103
10-3
105
Hadron energy (MeV)
Figure 1.17. Fluence to dose equivalent conversion factors for low energy
neutrons and high energy hadrons.
26
27
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 10 12 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-~~~~__~~~~~~
~
________
(f)
"3
0.
10
(j;
0.
(f)
C
o
(5
S
9
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 GeV) 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
+ 35/...JEo)2
(a
(1.31)
The corresponding dose rate at 1 m from a target in which there
are 10 12 interactions per second is plotted as a function of the
interacting proton energy in Figure 1.19. However, in addition to
Possibly lethal
--__ ~v
11
Q)
High Energy Particle Interactions
Requiring medical
supervis~
~
Requires investigation
/.-/........
~.,
~
.../
---.
....
Ol
/~......---
o
1 mSv
8
-~
-------
------~-----
No serious consequences
------.....--..-----
...-----------
~-.----
~----~------
..J
10
..------------30_----90
----------------
______
_------------------180---
-------
10L---~~~~~U---~~~~wu~--~--~~~uu
102
10
Proton energy (GeV)
1
102
10
103
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.
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.
28
29
High Energy Particle Interactions
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
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.
57.3 tane - e
Dose near targets of different materials
The above dose estimates are essentially those of high
energy secondary hadrons from protons interacting in iron or
1.3.8.
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
~
'",10
ui
c
-§ 9
0.
c
L:
0,
c
2
Ui
E
<1l
-------
Ql
2-
""1
Ql
---
<1l
""(5
"1
--=
1011SV.h-
102
10
Proton beam energy (GeV)
-
"'-.,
,
"
-
"
~
~
I-
C
40 -
-
~" ",
j
1
, i
"',
<ii
()
lmSv.h-1
Controlled
Open
-
T
I
-.",
"'\
-OJ. 50
0,.
-I
1
~
§
r
4
,
Strictly controlled
7r
=5
Lethal
"-.
-
- - --
8r-
OJ
0
60
' §
1 SV.h- 1
r-
6r
....J
I
f~
Ql
e
"
(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.
1.3.7.
11
= 35/..JEo
-
~
'.
"",,-
..
"'
,-
"-.
, ,
103
I
30
1
10
Proton energy (GeV)
100
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.
Figure 1.21. The emission angle at which the dose equivalent will be maximum
at I m from a beam line.
30
31
Radiation and Radioactivity Levels near High Energy Particle Accelerators
103~__~--~I~i~i~iTT
I
High Energy Particle Interactions
'-
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
Relative yield
Cu
Fe
Be
AI
Pb
U
1.0
1.0
0.4
0.6
1.5
1.7
32
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
CHAPTER 2
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).
Shielding for High Energy Particles
2.1.
Shielding for high energy protons
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
2.1.1.
H
-t/A
H- ~
R2
(2.1)
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.
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
2.1.2.
34
35
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
---.--r----
Shielding for High Energy Particles
given by Equation 1.12 and assuming a quality factor of 4, the
dose equivalent source term H o' 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/--JE o)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
T
o deg
10-1
--.-....
...-_..,-
o'
-"'"
';
\,
\
--_.-..-
-......
---.--
.--------------------------.-
'--.
"'.
Earth
/_----/----- 30 ----------.
' ' ,.
\
\.\
...•,
Concrete
'-..
"',
Iron',.
...
-~.
-: -.-:::-.::=---::---~--
Baryte·· ...
10-5
'-..
-
'
\
10---<;
-
10-2
-.-:...~6~--~7~---~8
.. I
~O----~----~----3~--~----~Shield thickness (m)
..'
1
.,'
I
....L..l-l....L
I
I
I
I
I I I I I
10
102
Interacting proton energy (GeV)
I I
103
Figure 2.1_ The transmission factor for dose from high energy hadrons in various
materials as a function of shielding thickness.
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.
36
37
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
radiation emitted at 90 deg, the dose equivalent source term can
be approximated by
H o(90) = 1.7 x 10- 14 E oo. 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
R
eVA)
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.
F
I~-
~
x
.,
.c
:>
(f)
10- 1
10-2
' -_ _-'---_-L_ _
o
J
----'1_ _-'-_--'-.
--'-_---I.I__._J_
2
3
4
Distance into shield (mfp)
5
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 10 10 interactions per second.
39
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 10 12 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.
I
I
I
--------
g> 80
:g.
E =1 GeV
-~-.,
Q)
....
'
<n
o
"E:::>
.~ 70
'E"
'0
.!!!
0>
.:'i
60
2
3
5
6
4
Shield thickness (mfp)
8
7
10
9
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.
III
1.8
.,
.-.---
o deg
rf)
~ 10
5
//-/1'0
.9
2
_/
a.
-_..... -.....
~o 104
Q;
Cl.
., 103
.c
:>
.-.-.-
....-
, ..- /
~-----
-------------
_----------.
.---------------.---~------
--.-
.--.---.-----------~------
---
~---.-.------ 30·------__-.---.-.
--------------90----------------
~
102
10 1
10
Interacting proton energy (GeV)
o
2
3
5
4
6
7
8
9
10
Shield thickness (mfp)
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
12
of 10 protons per second in a copper or iron target, as a function of beam energy.
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.
40
41
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Particles
(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
H
1
=2
R
fl80Ho(e)exp(-(t cosec e)/A) sin e de
2
(2.6)
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
0
(2.7)
F = 1.5 exp(-O.06t/A)
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
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
H
F R H 0 (90)
=
R
2
exp( -t/A)
Sv. per proton
(2.8)
which can be represented by
2.0
H=
1.8
1.6
"'
1.4
li...
H (cont)
0
R
(2.9)
exp( -t/0.94 A)
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.
"-
1.2
~co 1.0
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
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
H(A)
Ho(e)
=7
exp[-(x/A 1 + Xi A2)]
43
Sv per proton
(2.10)
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
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.
----"..--'"
1~'
1-----------____ 1W per m
- .. _---------------------~__~~~~~~I__~~~~~ul____~~~~~
103
102
10
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 -__- .__~
Interacting proton energy (GeV)
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
----------------.._--...,
10
.."
Shield mfp A2
-'-'"
....•••....
.•..•
"-
Beam
.............
Distance along dump (m)
1,.,
Figure 2.9. Simplified geometry for the estimation of dose near a shielded target
or beam dump.
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 10 12 protons per second of different
energies.
44
45
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 GeV(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
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 GeV) this
ratio can be approximated by
R/A=5.7x 10-5 EI.6 withE in MeV
(2.15)
R/A= 3.6E1.6
(2.16)
or
withE in GeV
-
-
o
-
-
(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 .t:-rtl.63
-
-
(2 . 12)
-
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 sec
= 10 IfJ.37
neut rons per proton
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)
I
I I I .l Lll1
I
I
I
I I I I I
0.1~----~--~~~~~~~--~--~~~~~~
10
102
103
Energy (MeV)
where R is the proton range m the target material (given by
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.
46
47
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
incident on a target. This fluence, at I m and an angle 8 to the
direction of an incident proton of energy E GeV, will be given by
5000 (1 - e-m
10(8) = (8 + 40/...)E)2
)
neutrons.m-2
(2.17)
where
m = 3.6 E1.6
(2.18)
This angular distribution is plotted in Figure 2.13 for incident
protons in the 50 to 1000 MeV range.
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
2.2.2.
(/)
Q)
.~
"0
1 GeV
C
8
Q)
(/)
o
~//
Q;
.0
E
/
500 MeV
::l
z
0.1
o
If
/
!
/
/6
Cii
Q)
o
~-~
10-2
100 MeV
0/0
i
50 MeV ___________
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.
Figure 2.13. Angular distribution of neutron fluence per proton incident on a
thick copper or iron target for various energy incident protons.
48
49
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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.
Shielding for High Energy Particles
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 10 12 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
Odeg
Q;
Q.
>
90 deg
C/)
.s
Q)
o
..J
10-1
-18~--~~~~~~~~
10
____~~~~~~~
102
Incident proton energy (MeV)
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.
Figure 2.15. Source term for shielding calculations expressed as dose rate at 1 m
and 0 and 90 deg for a beam of 10 12 protons per second incident on a thick target.
50
51
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 GeV 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
H =
1.5 H (90)
R
0
Sv.m-1 per proton
exp(-t/0.94A)
Shielding for High Energy Particles
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.
1.0
/
II
0.8
(2.19)
V ,/
where H o(90) is the source term for 90 deg emission as given in
Figure 2.14.
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
2.2.3.
FO~1
0.6
V
,;'"
7
tJ
[l'
f
:/ ) r~ide
a.
E
Q)
>
'@
Qi
0:
V
0.4
~~
0.2
-
~~
/
/
-:::
V
V
VV
...
(2.20)
o
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
10
102
Incident proton energy (MeV)
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
2.3.
Shielding for muons
2.3.1.
Muon production
of1 =
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-
Shielding for High Energy Particles
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
?
(e
- e )
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
11.3
2.35
3.2
1.8
23
29
9.0
10.4
6.4
1~
55
~O
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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.
T= 1.8 A+ 16E/a
(2.25)
metres
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
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
o
E
£
::::l
(!)
()
c
(!)
::::l
Ol
o
....J
(2.24)
Metres of iron
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
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.
56
57
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
d
= 4.6 X/-V(Eat)
metres
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
2.3.5.
(full width at half maximum) of
(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
I = 2q
!1
e-atlE
at
(2.28)
muons per proton
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
:[
a.
E
::::l
U
'0
.<:
c
.8
e
0,
c
(lJ
....J
0..
10
Q)
0..
if)
c
0
:::::>
EO>
0
....J
1~
1
____~~__~~~~~____~__~~~~~~
10
Proton energy (GeV)
~,
~,,~, ~
30
50
100 GeV
~~
"'-
Metres of iron
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.
Figure 2.19. Intensity of surviving muon beam as a function of thickness of an
iron beam dump per incident proton of energy indicated.
58
59
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Particles
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
2
r2 = X/E (0.77 n - 1.16 - 7.7 X/E + 0.33In(E/X2)
m (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.
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
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.
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-
60
61
2.or------.,---,.--,----r--.,---r--r---r---;--.---,----,
Ic
~·10-11
~---~
-",
e
~ 1.0
(J)
~
-~
~."-.,.
10-10
~
OJ
'6
~ ~
<Il
a:
~ ~10/~
10-5
7
10-9
8
10-
\
""\
10--6
\
\
.
\
\,
2
4
6
8
10
12
14
16
18
20
22
24
Depth in iron (m)
2.4.1.
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
matically in Figure 2.22. For the purposes of estimating the
radiation scattered down such a hole, it is assumed that all
10
,.
..c
:>
~
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 10 10 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).
<J.)
"§
~
m
>
2.4.2.
1-
·s
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
0<J.)
<J.)
(/J
o
o
Radiation scatter down holes in a shield
If the average diameter of a hole is small compared to the
...- ....
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)
o~::::···--,--. .--_______
.'-"~.....-.
~--...---------::'---1 0 ____..._
__...,.----______~____________
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
'"'
,E=1000GeV
., .
". 1
"-~1~~-==--==-----=---_====_
~---.----------------------
Shield mfp A
10-1 ------0.1 - _____~
---------------_.-
10~~~~--~~--~~~--~~~--~~~~~~--~~~
~
~
90
o
Source
e
W
Emission angle (deg)
Fi.gure '2.'2'2. Diagram showing radiation incident at an angle to a hole of length
X and cross section area A in a shield where the radiation interaction mean free
path is A.
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.
62
63
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 H m ,
H=H.
m
K.A ff.-VA
e
L3
n
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-
(2.32)
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
en
'\
en
c:
\\
c:
o
·iii
\' ,
\
·E
jg
~..... ~eutrons
\.
(])
sc:
'-
'~
(])
"-
~',
~'''-''
~
l:
(])
a.
",
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Particles
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.
.~
'j
---.--"
--
--------'........
~-10----------------------
--
_.,.,..-'
3
10-
,/_-----/.----------
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).
2.4.3.
Transmission down multi-legged chicanes
The layout of a multi-legged chicane is shown diagrammatically 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~
----------- --------...-------
-----_-..--/-.. -..---..-.. 50-----
10~~~~~~~~~~-L~~-L~~~~~~--~~--~
40
50
60
70
80
100
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).
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.
66
67
Shielding for High Energy Particles
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
= Ho/LI2
HI
(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
H -H
n -
(n-I)'
KA( n- I) ....JA n
L 3
(2.36)
n
the radiation level at the exit of the chicane will therefore be
H =H
I
n
xr-
I
Al . ( ...JA2 . ...JA3 ... ...JAn )
An
L2 L3
Ln
(2.37)
where HI is the radiation level at the end of the first leg.
2
If the chicane has a constant cross sectional area of A m , 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)
(2.35)
= (KxA 3!2t-I
(2.39)
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
/.
i-------,.-rI
0.1
Protons
E(GeV)
i
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
2
3
Tunnel area, A (m 2)
4
Figure 2.29. Transmission factors for neutrons along a chicane with n legs (n
4) as a function of cross sectional area of the tunnel.
69
5
=2 to
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 m 2 , 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
First leg
.-.-&'-
-'--...Q
-------:;----______________ Second leg
(/)
c
o
o
ea.
\
\C)
" \'"
o
~ 10-1
'-~ Third leg
-
o~
CD
a.
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
H=
\"
'",,-
·'. . .-.._~.\.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.
10-11
>.
~10-2
Shielding for High Energy Particles
R2
e-Rf)...
Sv.h- 1 per neutron.s- 1
(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)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
where 2.EoA is the hadron dose equivalent rate in
times
2
surface area (m ) 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
1
2.5 )lSv.h- averaged over 1000 m 2 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.
SV.h- 1
,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
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.
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.
3.l.2.
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
material
Air
Water
Iron
Tungsten
Gold
Lead
74
Critical
energy
(MeV)
Radiation length
(g.cm-2)
102
92
27
10.2
9.7
9.5
36.6
36.1
13.8
6.76
6.46
6.36
75
(cm)
30,000
36.1
1.9
0.35
0.33
0.56
Neutron
threshold
(MeV)
10.5
15.7
11.2
6.2
8.1
6.7
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 GeV 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.
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
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 MeV and 9 the emission angle
in degrees. The resulting dose rates at 1 m from targets in
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.
76
77
Shieldingjor High Energy Electron Machines
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
(3.3)
where E is the electron energy in GeV.
(ii) At 90 deg to the target
Sv.h-l.kW-1 at 1 m
(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).
-------1-----HE limits
_________l.;_--
........ ...
E
10-1
",
,
, .- "
----------
.,1
(c) High energy neutrons
The source terms for the two neutron components, those in the
energy range 25-100 MeV 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
H
=
0.36
1
1
SV.h- .kW- at 1 m
(1- 0.72 cosei
(3.5)
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).
",
",
Cii
(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 10 12 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.
/'
"
-":
.r=
:>
Cf.)10-2
3.2.2.
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
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=----
(3.6)
r
79
Shielding for High Energy Electron Machines
Radiation and Radioactivity Levels near High Energy Particle Accelerators
where E is the electron energy in GeV (greater than 3 GeV) 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
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
Gamma rays
Neutrons < 25 MeV
Neutrons 25-100 MeV
Neutrons> 100 MeV
Muons
Concrete
Iron
Lead
21
18
28
43
0.26E
4.7
16
2.4
18
0.1 E
17
0.077 E
E=500MeV
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
Figure 3.2.
Secondary
radiation
Sv.h-l.kW- 1 at 1 m
at 90 deg
at 0 deg
Gamma rays
Neutrons < 25 Me V
Neutrons 25-100 MeV
Neutrons > 100 Me V
Muons
3x105 E
10
4.6
0.5 E
80
50
10
1.2
0.36
0
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 MeV incident electrons.
81
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Electron Machines
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 GeV
E
=10co
1
"k1O-'"
2
10~~--~--~--~~--~
o
__-L__~____~~~__~__~
2
3
Metres of concrete
4
5
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.
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
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
3.3.1.
~
~
.,.:.:;
.r:.
10 GeV
:>
~10.,,;l
~<l>
~
a
Muons
10-2
Sv.h- l at 1 m per rnA.
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
(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)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
Shielding for High Energy Electron Machines
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
1~~·O~-~2--~~~~~~1~O~-1--~~~~"~1~--~~~~~~10
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.
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.
84
85
Accelerating voltage (MV)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
Shielding for High Energy Electron Machines
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
Ec
= 2.2 J3/R
keY
(3.9)
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
Electron energy (GeV)
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Electron Machines
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 Ec keV.
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
Electron energy (GeV)
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 keV are absorbed and
rest scattered into the surroundings,
the
10~~0--~--~--~--~--~--~6~~--~8--~---1~0---L---J
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.
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.
88
89
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Shielding for High Energy Electron Machines
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.
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.
3.4.5.
Figure 3.11. The synchrotron radiation power of photons of energy greater than
50 keV from an electron beam of 1 J.lA circulating on arcs of different radii.
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 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).
90
91
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
Electron energy (GeV)
0
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
92
93
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 .., _
Water
Concrete
Earth
Aluminium
Baryte
Iron
Copper
Tungsten
Lead
Uranium
Spallation
mfp
Nominal
density
(g.cm-3)
2
(g.cm-
1.0
2.35
1.8
2.7
3.2
7.4
8.9
19.3
11.3
18.8
85
100
100
106
112
132
135
185
194
199
94
)
(cm)
85
43
56
39
35
18
15
10
17
11
Radioactivity Induced in High Energy Particle Accelerators
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
7Be
llC
18F
22Na
24Na
46SC
48SC
48V
51Cr
52Mn
54Mn
56CO
6OCO
65Zn
Half-life
Decay
mode
53 d
20 min
1.8 h
2.6 y
15 h
84d
1.8 d
16 d
28 d
5.7 d
303 d
77d
5.3 Y
245 d
EC
13+
13+
13+
13'
B'
13'
13+
EC
13+
EC
13+
B'
EC
95
fSv.h-1.Bq-l
at 1 m
7.8
140
132
298
560
283
455
397
4.3
326
114
350
340
76
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 keV 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 MeV 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
.,:!.c- 10
2
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
1
0.26 J.1Sv.h- 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
d s = 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
Radioactivity Induced in High Energy Particle Accelerators
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 keV. 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
/
Water /
/
./
,/
/
~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)
1 O~O-2
10-1
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.
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.
98
99
Radioactivity Induced in High Energy Particle Accelerators
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)
~SV.h-1
= 0.036 X
per Bq.g-l
(4.8)
2
when X is the plate thickness in g.cm- •
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 MeV gamma rays. Narrow beam
attenuation mean free paths and the average shield thickness required to
obtain a factor of 10 dose attenuation.
Narrow beam
mfp
(g.cm-2)
Shield
material
Lead
Copper
Iron
Aluminium
Concrete
Earth
Water
Air
Tenth value
layer
(cm)
0.5 MeV
0.8 MeV
0.5 MeV
0.8 MeV
6.2
12.0
11.9
11.8
11.4
11.4
10.3
11.5
11.3
15.1
14.9
14.2
14.1
14.1
12.7
14.3
1.4
4.0
4.8
14
15
19
35
290m
2.6
5.0
5.9
16
18
23
40
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 keV.
The beta dose rate on the surface of a uniformly activated piece of
101
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 keV) 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
D x =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
102
(4.13)
Radioactivity Induced in High Energy Particle Accelerators
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.
Radioactivity in targets and dumps
4,2.1.
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
(4.14)
which, with 't l = 2 Y and 't2 = 10 min,
P('t) ()'t = 0.031 ()'t/'t
103
(4.15)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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·693 T1"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
S = 0.031
2y
J
exp(-O.693t/'t) [1- exp(-O.693T/'t)]
10 min
d't
Bq (4.17)
'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)
Radioactivity Induced in High Energy Particle Accelerators
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 <I> proton.cm-2 .s- 1 for a time T and after a
decay time t (T and t in common time units)
(4.20)
D =Do <I> In[(T+t)/t]
17
l
l
2
when Do has a value of 5.2 x 10- Sv.h- .g- .m •
The above relation should be essentially independent of
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 <I> 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
2
per g.cm- of target in a beam of <I> protons per second reduces to
S = 2.4 X 10-4 <I> In[(T+t)/t]
(4.19)
Decay time (d)
This activity will also be that of a 1 g target irradiated in a
uniform flux of <I> high energy protons.cm-2 .s-1•
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 .)
104
105
Radiation and Radioactivity Levels near High Energy Particle Accelerators
incident hadron energy above about 200 MeV 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
Do<PT
D=--t
(4.21)
,-
~
Radioactivity Induced in High Energy Particle Accelerators
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 E O. 15
(4.23)
O
110-'6
:>
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
Sv.h-1
(4.24)
D =1.4 X 10-15 E O. 15 <P In[(T+t)/t]
~
~
CLl
en
o
"0
17
"210()
O
:l
"0
.E
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 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.
Effective half-life
The rate of decay of spallation induced radioactivity
decreases as the decay time increases(9). However, at any given
4.2.4.
107
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Radioactivity Induced in High Energy Particle Accelerators
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)
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
or
(4.25b)
which reduces to
't
= ...J[(t+D t]
Hence, with t, T and
(4.26)
't
all in the same time units, a dose rate
100r---~-T~~~~--~~~~~rn~---r--~~~'Tn
'I
.c
:>
C/)
g
~
Q)
gs
o
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.
Figure 4,7. The dependence of the effective half-life of induced radioactivity in
medium atomic number materials on decay and irradiation times.
108
109
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
-------
d .---
--------------------
1;10-
16
~----
'I
.c
::>
~
~
0,)
~ 10-17
o
1 mon
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
D=
x 10-21
t1.4
Sv.h-1 per proton
(4.28)
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.
10-18L---I-..I..--.L.....1-l....WJ.1:l:0,.---II..-..l-.J.....Iw....I....I.:I1~OO:::---J....-....I........I.....I..J,.""":-1o*'!oo
1
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
Dose constant
fSv.h- 1 per proton.s-1
Heavy element target
hours
1.4
300
1 g.cm-2 target
One interaction length target
111
days
0.4
85
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
beam of <I> protons per cm2 per second becomes
S = 1.8 X 10-3 <I> [t-O A _ (T+t)-OA]
Bq.g-l
(4.30)
when t and T are in days.
4.2.6.
Comparison of calculated dose rates with
measurements
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)
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 <I> In[(T+t)/t]
Sv.h-1
(4.31)
1~2L1--~~WU~1~O--~~~~10~O~~~~~1000U-~~-L~1~OOOO~
Decay time (h)
Figure 4.9. 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 .
Figure 4.10. Comparison of measured and calculated dose rates from irradiated
steel and lead blocks as a function of time after exposure.
112
113
Radiation and Radioactivity Levels near High Energy Particle Accelerators
<I> 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 10 12
1
protons.s- , 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.
Activation by secondary hadrons
4.3.1.
Activating particles
The estimation of the amount of activity induced in
!
en
10
2
f-- - - - - - -___
~___~~eel
~
.jg
::::J
(f)
- _-----_____
r--__
---~_____
Aluminium
.•
~-
----__.,.- ............
~______
-----------
~------
- --
------- ...._---- ---
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 10 12 proton.s- I over
2
1 cm 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
-
----__
o
"0
Radioactivity Induced in High Energy Particle Accelerators
(4.32)
where E is the interacting proton energy in GeV (greater than
1 GeV).
The resulting activating flux of secondary particles at 1 m from
a target in which there are 10 10 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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
(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 GeV. 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)
Radioactivity Induced in High Energy Particle Accelerators
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)
"j
"1
'l'
....
~
E
S.
~107
c::
.l!!
<II
'5
C.
~
e
"0
I
.c
><
~
u::
10
1()2
Primary photon energy (GeV)
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.
Figure 4.13. Factor by which the secondary high energy hadron flux multiplies
on passing through an absorber.
116
117
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
10 12 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 10 12 interactions per second in a target
at 1 m in front of the block is shown as a function of radius from
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 MeV 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.
20r-~.-~~~~~~~~r-~.-~~-r-T~~--~
···1000 GeV
---------------___ .... _w...-_w.-
.,
.----
.J::
.,
..----_..
1000 GeV
:>
:>
(f)
E
~
C/)
o
....
,
.."
.•/_.--.,....
o
.---"
--
----------
........._-.
••••• ___ ......
' -.......
..-...::::::::~:_.~..._.
~...- ..-.. -~.----.-----------'-. -'-"-
......... 10.
~
..--_..
1 GeV-~~·--
-0,
Q)
10 GeV
-'.
......................
~
-;10 Q)
100.....
.J::
Q)
------_._'-'-'--===::::::::::::::-:.::::::.-.--==---
C/)
o
o
- --
---------------
----.1 __
--------------------------------------
10~~--~--~--~~--~---L--~~--~---L--~----J
20
Plate thickness (mm iron)
o
20
30
Distance off-axis (cm)
40
50
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 10 12
interactions per second in the target by protons of energy indicated.
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. .
118
119
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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)
(b)
(c)
(d)
(e)
63CU in natural-copper
Sodium in concrete
Argon in air
Zinc in copper
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
M
D
= Qf cr k c:P e-
,
(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
isotope
23Na
40Ar
44Ca
50Cr
sSMn
S9CO
63CU
64Zn
121Sb
123Sb
l33Cs
lSlEu
lS3Eu
186W
Natural
(%)
100
99.6
2.0
4.3
100
100
69
49
57
43
100
48
52
28
cr
(barn)
0.53
0.61
0.70
17
13
37
4.5
0.46
6.1
3.3
31
8700
320
40
Active
isotope
Halflife
24Na
41Ar
4SCa
SICr
15 h
1.8 h
165 d
28d
2.6h
5.3 Y
13h
245 d
2.8d
60d
2.1 Y
12 y
8y
Id
S6Mn
6OCO
64CU
6SZn
122Sb
124Sb
134CS
lS2Eu
l~U
187W
121
fSv.h- 1 at 1 m
perBq
perg
560
150
7.7
1.4
4
250
340
28
76
60
200
116
45
286
73
0.04
35
128
0.84
0.16
1.0
1.4
17
750
190
2.6
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
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 •
J
'TlTj
I
I
, 1 i i J
1::
:>
(f)
.s
(i)
f-~
______ _
~ 1 ::-_~_
~
~------Spallation
"' _ -----------------__ 1%
~
-
manga:::----~~-__________
.............~............
~
1% cobalt
:J
""
(f)
.,'\\
1% antimony
r------------ _ _
\
>\ 10
~
____ _______
_._------------------
I
I
0.1.'-::--~~..J_.I_'_l.........~--'-..........I...I.-J...I~!:_-"-....I-.J-.I'-'-~
0.1
100
Decay time (h)
10~~--~~~~~~~--~--~~~U7~--~--~~~~
1
10
100
1000
Decay time (h)
Figure 4.16. Surface dose rates from spallation products induced in iron after a
6
1 y irradiation by 10 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.
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.
122
123
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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.
Radioactivity Induced in High Energy Particle Accelerators
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
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.
Isotope
18F
24Na
22Na
Average cross
section
(mb)
Half-life
(fSv.h-1.Bq-l
at 1 m)
20
40
20
1.8 h
15h
2.6y
132
560
298
kfactor
124
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
energy secondary hadrons in concrete can approximately be
calculated by an equation of the form
=Do <I> In[(T+t)/t]
(4.42)
2
1
where <I> is the activating hadron flux (hadrons.cm- .s- ) and Do
has the values given in Table 4.7. The secondary hadron fluxes at
I m from a target, from which <I> 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
D
Radioactivity Induced in High Energy Particle Accelerators
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)
DO(trJrg)
'A(y,c)
'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
---------
1% sodium
---------------__
-
Q)
1§ 0.1 r-
-----------~---...~------------------~~
Q)
rJl
o
"0
\
Q)
u
~
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)
per kg at 1 m
(fSv.h- 1)
130
40
20
52
16
8
126
::l
(/)
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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.
Radioactivity Induced in High Energy Particle Accelerators
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.
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
J
-
//?
//
/
·gO.6
~.
~
Q)
(J)
80.4
/
.., / "
/
....
/
Isotope
(%)
I3lBa
136CS
127Xe
134CS
22Na
6OCO
133Ba
152Eu
l37Cs
~~--~~~~~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
12d
13d
36d
2.1 Y
2.6y
5.3 Y
1O.7y
12.0y
30.0y
19.5
1.1
1.8
8.7
1.7
0.5
51.5
9.8
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
0.2
Specific
activity
Half-life
Production
rate
(Bq.S-l)
Half-life
53 d
84d
165 d
303 d
2.6y
5.3 y
12.3 Y
12.0y
8.0y
820
75
590
170
170
43
72
130
7
Trace amounts of 48 Va, 57CO, 59pe and l34Cs were also noted.
129
Saturation
activity
(GBq)
5.4
0.8
12
6.4
20
11
40
71
2.5
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 .__--......_-..
----__-..____.~__.
--
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~~
~-.........
---
........
----------. 3 Y
--
.....
Radioactivity Induced in High Energy Particle Accelerators
'""-,
---~
-----........._-'1
11~----~--~~--~~·1~0------------~~~~1~OO
Decay time (mon)
I
I
11~--~~~~~~10----~~~~~~10~2~~--~~~uuu103
Proton beam energy (GeV)
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).
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.
130
131
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 E oo.92
Radioactivity Induced in High Energy Particle Accelerators
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
(4.47)
GBq.W1
S = 1.1 Eo~·08In[(T + t)ft]
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 GeV are shown in
Figure 4.24.
....
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 E o. 92 ln[(T + t )ft]
Bq per proton.s-1 (4.46)
o
1:0-
_------------..----
ffi·2 ===_
-
I
c::
~1
----
.-.-._._.___._-.___
Decay
6 mon
-------
----------------
-~-~-~-------=~_-_-_.
---------------_~_2 Y
- - - - - - -_ _ _ _ _ ~__
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
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.
132
133
~
Proton energy (GeV)
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 GeV, 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 E O-D·08 In[(T + t)/t]
D
= 0.19 p E O-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 , - - -...... _'--....."
(4.48)
1::>
..--.-------
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)
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.
134
135
§. 0.2
E
o
aU)
co
Q)
"§ 0.1
Q)
C/l
o
a
Decay time (d)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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
.
iii
Radioactivity Induced in High Energy Particle Accelerators
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
.. _,
IIIII
I
, i
i'l
I
i
I
I Ii'
\Copper
\
'I
.s::
:>
(J)
~
E
100
1000
Decay time (d)
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.
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.
136
137
Radiation and Radioactivity Levels near High Energy Particle Accelerators
Radioactivity Induced in High Energy Particle Accelerators
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 10 12 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 15 0 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.
Isotope
Halflife
Emission
beta/gamma
kgamma
(fSv.h- l.
Bq-l at 1 m)
1.2 min.~ _
0
150
2.1 min
1.8 MeV B+
2.3 MeVy
1.7 MeV B+
13N
10 min
1.2 MeV B+
140
10
9
llC
20 min
.97 MeV B+
140
10
5
7Be
53 d
8
10
5
3H
12.3 y
30
30
4lAr
1.83 h
EC
10.3% 0.48 MeVy
19keV B
1.2 MeV B
1.3 MeVy
138
450
140
150
Table 4.11. Air activation for 1012 high energy hadrons and thermal
neutrons passing through 1 m path length in air per second.
Isotope
40
Thn610mb
in 40Ar
Half-life
Production
rate
(kBq.S-I)
1.2 min
2.1 min
10 min
20 min
12
250
60
30
Total short lived
positron emitters
53 d
12.3 Y
1.83 h
Production
cross section(mb)
N
140
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.
Equilibrium
activity
(MBq)
1.2
45
52
48
352
146
7xl0-3
3xl0-4
1.9
48
160
13
Table 4.12. Activation of water by 1012 high energy hadrons traversing 1 cm
of water per second.
Isotope
Half-life
1.2 min
2.1 min
10 min
20 min
Total short lived
positron emitters
53 d
12.3 Y
139
Production
rate
(kBq.S-I)
Equilibrium
activity
320
7300
320
90
33
1320
270
165
8010
1788
0.025
0.0018
165
1000
(MBq)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
At very high energies multiple neutron production will result in
being produced but the saturation activity of this isotope is
only expected/to be a few per cent of the 15 0 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
lle
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.
Material
Water
Air
Principal
isotope
150
13
N
Halflife
(min)
Production
rate
(Bq.S-I)
Equilibrium
quantity
(MBq)
2.1
6100
1.1
10
240
0.2
140
Radioactivity Induced in High Energy Particle Accelerators
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 =
Radioactivity Induced in High Energy Particle Accelerators
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
A
A(in)=A - -
A+r
Bq
(4.54)
102
0:
!Xl
~
~
'>
~
Ol
Q)
"'0
Ow
E
10
Air changes per hour
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 10 12 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.
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.
142
143
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 10 12 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
Radioactivity Induced in High Energy Particle Accelerators
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.
(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)
102
I
Activity concentration and dose rate from a
release of radioactive air
f/J
S = 1t Cy Cz X 2- n
0m
C.
m2
(4.56)
where C and C z 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
~
Q)
0.
al
()
f/J
W
10
Table 4.15. Typical values of air plume parameters for a release near to
ground level.
Air changes per hour
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
Atmospheric
conditions
Very unstable
Unstable
Neutral
Stable
Plume parameters
Cy
Cz
n
1.46
1.52
1.36
0.79
0.01
0.04
0.09
0.04
-0.25
0.14
0.38
0.63
145
Mean radius
at30m
(m)
5.53
5.83
5.50
5.78
Radioactivity Induced in High Energy Particle Accelerators
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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 R 2u
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.
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
(4.62)
q= Q/l1XRu
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'--,
......
(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
=
Wind speed
~"'--.
----"
'.
.......-..
······..-.L~..:.~_._._._._._.
-...-.
---"'-
...........-.-~ 0 m.s-1
-------------
----.
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
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
Radiation and Radioactivity Levels near High Energy Particle Accelerators
concentration will be given by Equation 4.52 making the longterm integrated gamma dose D(tot), per GBq of activity released
= 0.11 / uX
D(tot)
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.
Radioactivity Induced in High Energy Particle Accelerators
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
4.5.6.
Activation of cooling water
Accelerator cooling water, particularly that used for
cooling targets, will be the major source of radioactive water
100
,~
Total
----'-
R;i~ase
-----.... _-
----------..._- _------
= 10000 TBq
---'-.
..
--------------- 3000 _____
10
13N
~
---300 -___~_
-....------------
'--"--------------_
,I
-3
E
15
-_ - - - 0
I
(J)
~-
------1 00
--,
/ /...
.c
1a
~-
---~_____________
'i
cr.i
----------------
--'---,---------
-----
Beam off
Beamon
-------------
(J)
-~-------------
C/)
0
0
//
/,./~'"
------------------
-------30
-.
------.....---------
---------
----10 __
--..
14
0
-----------.....:
---------------
10
60
40 50
30
20
Irradiation time (min)
12
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 .
Figure 4.33. Dose rate at 1 m from a container in a water circuit after 10 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.
148
149
Distance from source (m)
Radiation and Radioactivity Levels near High Energy Particle Accelerators
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:
Radioactivity Induced in High Energy Particle Accelerators
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).
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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).
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
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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
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18. Yamaguchi, C., Hoefert, M., Schonbacher, H. and Stapleton, G. Induced
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(1981).
19. Nachtigall, D. and Charalambus, S. Induced 24Na Activity in the Concrete
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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,
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150
151
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.
Index
Subject 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
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
152
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, 134135
shield for point losses, 39
shield for unifonn losses, 42, 52
153
Index
Index
Beam dump
dose equivalent outside, 43-44
gamma ray dose rate from, 106,
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
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
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
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
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
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
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
Index
of panicles near a target, 115
of thennal neutrons, 120, 122
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
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
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, 110-113
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
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
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
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
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
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
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
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
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
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
158
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
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
s
Scatter coefficient
for neutrons, 64
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
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
nuclear inelastic cross section
of, 6-8
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
scatter down holes, 65-66
synchrotron radiation, 86-91
tenth value layer attenuation
thickness, 85
of neutrons from proton
interactions, 46
z
y
Zinc-65
in accelerators, 95
in copper, 119-120
isotope properties, 121
production of by thermal neutrons,
121
Yield
of high energy secondary
particles, 32
of neutrons from electron
interactions, 79, 139
Uranium
charged particle range in, 5
density of, 8
high energy hadron attenuation mfp
in, 8
nuclear inelastic cross section
of, 6-8
relative secondary particle
yield in, 32
spallation mfp of hadrons in, 94
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
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
160
161