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Paper # SL005

RADIATION PROTECTION AT LOW-ENERGY PROTON

ACCELERATORS

L. E. Moritz

TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada V6T 2A3

E-mail: lutz.moritz@triumf.ca

Running Title: LOW-ENERGY PROTON ACCELERATORS

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RADIATION PROTECTION AT LOW-ENERGY PROTON

ACCELERATORS

L. E. Moritz

TRIUMF, 4004 Wesbrook Mall, Vancouver, B.C., Canada V6T 2A3

ABSTRACT In this paper we provide a sample of the radiological safety issues particular to low-

energy proton accelerators. ‘Low’ energy in this context is taken to mean proton energies

of less than about 1 GeV. Many of the radiation issues are common to all particle

accelerators. In this paper we try to address those issues that may require perhaps not

unique treatment but those which benefit from a different approach. Among the problems

discussed are the generation of prompt radiation and its transmission through shielding,

the estimation of induced radioactivity, and the assessments of both the off-site prompt

radiation hazard and the effect of releases of radioactive effluents to the environment.

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INTRODUCTION This paper is intended as a review of radiation protection at low-energy proton

accelerators. ‘Low’ is of course a relative term and one person’s low-energy regime may

well be seen as high-energy by another. However, for the purpose of this review we take

low-energy to mean less than about 1 GeV and therefore include so-called intermediate

energy accelerators. Also, the separation between radiological safety issues at low-energy

accelerators and high-energy accelerators is not as clear-cut as the title of this paper

might indicate and there are many problems that are common to both. This paper may

therefore be characterized more as a sampling of the author’s interests and experiences,

hopefully presented so as to be a useful guide.

Synchrotrons that accelerate colliding beams of protons currently achieve the highest

center of mass energies, but at low energies there are a great variety of accelerating

schemes available. At the low end of the energy spectrum, direct acceleration by the

application of an electric potential generated either electrostatically or by various high-

voltage transformer schemes is possible. The maximum energy achievable is limited by

the electrical breakdown of the surrounding medium, either air or a high-pressure inert

gas. A factor of two in energy may be gained by accelerating negative hydrogen ions and,

after stripping off the electrons, using the same potential drop again to accelerate the bare

protons. Higher energy acceleration schemes rely on resonant principles, either by

applying the same electric potential to a repetitive structure as in radio-frequency

quadrupoles and drift-tube linacs, or using the same potential repeatedly by magnetically

confining the protons to circular orbits as in cyclotrons or synchrotrons.

The construction of proton accelerators at the high-energy frontier has always been

driven by research into fundamental physics. As the research interests have shifted to

higher energies the low-energy machines are nevertheless still required to provide the

initial boost for the high-energy accelerators. Where the low-energy accelerators are used

to drive such applications as meson factories, spallation neutron sources, radioactive

beam facilities and radioisotope production (or destruction, as in the prototypes of

accelerator waste transmutation) they have required large increases in the beam intensity

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often making the total beam power equivalent to that of the highest energy machines.

Many of the recent applications of low-energy proton accelerators have been in medicine

and industry. Proton accelerators have been used to provide radiotherapy for the

treatment of various cancers, using either the protons directly or using secondary particles

such as neutrons, heavy ions and π-mesons produced by proton reactions. A large number

of proton accelerators are now dedicated to, or purpose-built for, the industrial production

of radioisotopes. Many of the generally neutron-poor radioisotopes produced in this way

decay via electron capture and are used as medical imaging agents that result in little dose

to the patients. A recent novel application uses a high-intensity low-energy proton

accelerator to generate gamma rays via the 13C(p, γ)14N reaction precisely tuned for

absorption by nitrogen. This device has been used as a contraband detector at a North

American airport (1).

GENERATION OF PROMPT RADIATION

It is the interactions of the accelerated protons with matter that lead to the primary

radiological hazard associated with proton accelerators. These interactions produce both

‘prompt’ radiation that persists only while the accelerator is in operation and induced

radioactivity that continues to emit radiation after the accelerator is shut off.

Interaction of Protons with Matter

The interactions of protons with matter degrade the energy of the protons and at the same

time result in the production of prompt radiation in the form of a spray of secondary

particles. At the lowest proton energy the energy loss is primarily due to ionization of the

stopping medium. The specific ionization is in fact greatest for the lowest energy protons

and this results in the characteristic Bragg peak at the end of the proton range. This

property of the energy loss curve for protons has been used effectively to treat deep-

seated cancerous tumours with protons in the energy range of 50-100 MeV. Because the

energy required for creating an ion pair is small when compared to the lowest energy

accelerated protons, the energy loss appears almost continuous and the protons, except

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for minor straggling effects, have a definite range. An approximate expression for the

range in iron is (3)

6.13101.1 ER −×= , (1)

where R is in cm and E is in MeV. For materials other than iron the Bragg-Kleeman (4)

rule may be used to scale the range from that for iron

Fe

FeFe A

ARRρ

ρ= . (2)

For protons whose kinetic energy is sufficiently high so that they are able to penetrate the

Coulomb barrier of the target nuclei, nuclear reactions other than simple Coulomb

scattering become possible. The nuclear reactions compete with the electromagnetic

interactions as the energy of the protons is increased. When the energy of the protons

approaches the upper limit of the range that we are considering, the probability of a

nuclear interaction rises to nearly unity and is more or less independent of the stopping

medium (Fig. 1). At the highest energies the proton range is no longer a useful concept as

the primary protons are effectively removed from the particle stream but are at the same

time to some extent replenished by the secondary protons produced by nuclear

interactions.

Nuclear Interactions An understanding of the generation of the prompt radiation (and induced radioactivity)

requires a basic knowledge of the nuclear reaction mechanisms that apply in the energy

range under consideration. The incident proton, or more generally nucleon, may simply

enter the nucleus, be deflected by the nuclear potential, and emerge again at a different

angle but with the same energy. This is direct elastic scattering. On the other hand, it can

collide directly with a target nucleon and excite it above the Fermi sea forming a

compound state. Two alternatives are now possible: either one or both nucleons have

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energy greater than their separation energy or neither has. In the former case, the

nucleon(s) whose energy exceeds the separation energy may leave the nucleus without

further interaction other than its deflection by the average potential. This is described as a

direct reaction. In those cases where the change in mass 0=ΔA , the reaction is either

inelastic scattering (the outgoing particle is the same type as the incident particle) or a

charge-exchange reaction. Where 0≠ΔA , we refer to transfer reactions (either stripping

or pickup) and knockout reactions. The angular distributions of the scattered particles are

characteristically anisotropic, peaking in the forward direction.

In the latter case, each nucleon will undergo further collisions, gradually spreading its

excitation energy over the whole nucleus. For a time (during the pre-equilibrium phase),

the nuclear state will become increasingly complex, but, after a certain relaxation time,

statistical equilibrium will be reached. A certain fraction of the resultant complicated

admixture of nuclear states consist of configurations in which sufficient energy is

concentrated on one nucleon so that it may escape from the nucleus. Similarly, kinetic

energy may be concentrated on groups of particles and lead to the emission of α-

particles, tritons, deuterons etc. This process is akin to evaporation and may be

characterized by a nuclear temperature Θ ≈ 2-8 MeV, so that the spectrum of the emitted

neutrons may be described by the following Maxwellian distribution:

nnn

n dEEE

Ed ⎟⎠⎞

⎜⎝⎛

Θ−

Θ∝ exp)( 2φ . (3)

Compound reactions may occur during the ‘pre-equilibrium’ phase, before statistical

equilibrium is achieved. In such cases the angle of emission may still be strongly

correlated with the direction of the incident particle. On the other hand, once statistical

equilibrium has been reached, the emitted or ‘evaporated’ particles have no memory of

the direction of the incident particles and the angular distribution is isotropic.

All the scattered and emitted particles can again participate in similar reactions resulting

in an inter-nuclear cascade. Above the pion production threshold, pions also contribute to

the cascade. The neutral pions travel only a short distance before they decay into a pair of

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gamma rays. If the charged pions are allowed a clear flight path, they will successively

decay into muons and then electrons and in this way the energy of the pions in the

cascade is channeled into the electromagnetic sector.

For high atomic mass nuclei, proton or neutron induced fission becomes a possible

reaction. Although there are some low-energy neutrons emitted as a result of the proton-

induced fission of heavy nuclei, the prime radiological significance is that fission may

lead to the production of some of the more radiotoxic isotopes such as the radioactive

species of iodine.

Characteristics of the Prompt Radiation Field From the description above it is evident that the prompt radiation field near a point of

interaction of accelerated protons and matter is complex and becomes more complex as

the energy of the protons is increased. The field consists of a mixture of charged and

neutral particles as well as photons. Several simulation codes are now available that

include all the interactions described above and that allow estimates of the radiation field

near the interaction points, such as those required for calculating energy deposition in

targets and beam dumps. These codes will be discussed in a separate paper in this volume

(5).

At low energies a simplification occurs because the range of the charged particles

produced in reactions of protons with energy less than 1 GeV are such that they are

always ranged out in shielding that is sufficiently thick to provide protection against

neutrons. This means that the radiation field outside accelerator shielding in this energy

range is always determined and dominated by neutrons. Neutrons are nevertheless not the

only contribution to the radiation field because the degraded neutrons may be captured by

the nuclei of the shielding material with the consequent emission of neutron capture

gamma rays.

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Attenuation of the Prompt Radiation Field The accelerator-shielding problem is addressed in detail in a separate paper in this

volume (6). Here we will outline the aspects particular to the low-energy regime. As we

have seen above, neutrons always dominate the prompt radiation field outside sufficiently

thick shielding of proton accelerators in this energy range. The attenuation length of

neutrons in the shielding material therefore determines the attenuation of the dose

equivalent provided by the shielding. Shielding for neutrons must satisfy two criteria: to

interpose sufficient mass between the source and the field point and to effectively

attenuate neutrons of all energies. The first criterion is most easily met by dense material

of high atomic mass, whereas the second is most easily met by hydrogen, which, via

elastic scattering, effectively attenuates neutrons at all energies. The two criteria, and the

additional one of having to provide stable shielding at minimum cost, are simultaneously

and most easily met by concrete because of its relatively high hydrogen content in the

form of water of hydration. If higher density is required, steel is often used as shielding

near the source point. But because the total cross-section for neutrons incident on iron

shows a series of dips between 0.2-0.3 MeV (Fig. 2), steel is essentially ‘transparent’ to

neutrons at this energy. An outer layer of a material containing hydrogen must therefore

always follow steel.

Fig. 3 shows the variation of the attenuation length, ρλ, for mono-energetic neutrons in

concrete as a function of neutron energy. Below about 20 MeV, ρλ has the value

200 kg m-2. Above this energy there is an increase in the attenuation length that reflects

the change from the regime where neutrons interact with the target nuclei as a whole, and

largely by direct elastic scattering, to the regime where the interaction is more likely with

individual constituent nucleons of the target nuclei and may lead to an inter-nuclear

cascade. The attenuation length reaches a limiting value of 1170 kg m-2 above about

150 MeV.

For low-energy accelerators the attenuation of shielding in concrete may therefore be

estimated by a simple exponential function, using the attenuation length appropriate for

the neutrons with energy in the peak of the Maxwellian distribution, i.e. at the nuclear

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temperature Θ. Attenuation curves for mono-energetic neutrons in this energy range have

been tabulated in NCRP Report No. 38 (7). The attenuation length of 200 kg m-2 for a

concrete density of 2400 kg m-3 corresponds to a tenth value layer of about 30 cm. Proton

accelerators with energy below about 50 MeV tend to be rather compact and thus the

shielding cost for an additional 10-30 cm of concrete is not a major factor in the overall

cost.

Above proton energies of a few hundred MeV, neutrons with energy above 100 MeV

propagate the neutron field through shielding because of their greater attenuation length

(Fig. 3). The lower energy neutrons and charged particles are re-generated at all depths in

the shield by the inelastic interactions of the neutrons with the shielding material. In other

words, at any field point outside the shielding, the highest energy neutrons will be those

that have come directly from the source without interaction, or that have undergone only

elastic scattering or direct inelastic scattering with little loss of energy and only small

angular deflection. Any low-energy neutrons and charged particles detected outside the

shielding will have been generated by the inter-nuclear cascade near the outer surface of

the shield. The yield of high-energy neutrons (En>100 MeV) in the primary collision of

the incident protons with the target material therefore determines the magnitude of the

prompt radiation field outside the shield for proton accelerators with energy above a few

hundred MeV. Fig. 4 shows the variation with proton energy of the yield of neutrons with

energy greater than 100 MeV for protons stopping in a number of materials. These yields

were calculated using the FLUKA99 code (9). The neutron yield is normalized per

interacting proton and has a simple dependence on the proton bombarding energy of the

form mpp EnEn 0)( = . (4)

Table 1 lists the parameters n0 and m obtained by a least squares fit to the points in Fig. 4

and it is evident that, except for the lightest elements, the yield is largely independent of

the target material.

Although the ready accessibility of powerful simulation codes allows us to calculate

detailed spatial distributions of any of the radiological quantities of interest, even for

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complex geometries, nevertheless there is still considerable interest in doing simple

point-kernel calculations if for no other reason than to provide a “reality-check” on the

more detailed Monte Carlo results. In general one would like to have an equation of the

type:

2

0 /)/exp(),()/,,( rdEHdEH pp λθλθ −= , (5) where )/,,( λθ dEH p is the dose equivalent at a point outside the shielding, Ep is the

energy of the incident protons, r is the distance from the source point to the field point, θ

is the angle between the line of sight from the source to the field point and the direction

of the proton beam, d is the thickness of the shielding and λ is a suitably defined

attenuation length for dose equivalent. Tesch (8) has proposed a relation of the form:

2/)/exp()2/( rdHH casc λπ −= , (6)

where H(π/2) is the dose equivalent at the surface of a concrete shield at right angles to

the direction of the beam, Hcasc is the dose equivalent per incident proton due to neutrons

with energy greater than 8 MeV at a distance of 1 m from an unshielded target and near

90o to the proton beam. He has tabulated the value of Hcasc and corresponding values of λ

as a function of energy based on a search of the literature. Here we note that the neutrons

included in this energy group contain neutrons on either side of the change in attenuation

length illustrated in Fig. 3. Those in the lower end of this energy range will be attenuated

more quickly than those in the upper end of the energy range and therefore applying a

single attenuation length to the entire range seems questionable. However, if we restrict

ourselves to proton energies above a few hundred MeV, then from the preceding

discussion, it would appear that the energy dependence of H0(Ep,θ) ought to follow the

form of Equation (4) above, as long as we normalize its value to the number of protons

interacting in the target. Also the attenuation of the dose rate should follow that of the

high-energy neutrons, as these are the neutrons that propagate the cascade.

We can investigate the angular distribution of the high-energy neutrons in the interval

60o<θ <120o using the Monte Carlo code FLUKA99. The results are shown in Fig. 5 and

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evidently the angular distribution of the high-energy neutrons may be expressed quite

well as an exponential in θ of the form exp(-βθ). The angular relaxation parameter, β ,

has been obtained by fitting to the points in Fig. 5 and is listed as a function of energy for

a number of different target materials in Table 2. Finally, the dose rate extrapolated to

zero depth in the concrete shield and the attenuation length ρλ for ρ = 2350 kg m-3 are

tabulated in Table 3. These were obtained by fitting the dose equivalent at depths

between 2 m and 6 m, determined at intervals of 0.25 m in a concrete shield at 90o to the

interaction point. We then use the relation

2

0 /)/exp()()/,,( rdEhEfdEH mppnp λλθ −= , (7)

where fn(Ep) is the fraction of protons participating in nuclear reactions (Fig. 1) and all

other quantities have been defined above. This expression merges smoothly into the

Moyer model used at proton energies above about 1 GeV where fn(Ep) → 1, h0 → 0.28

pSv m2, m → 0.8, and β → 2.3.

An application of Equation (7) is illustrated in Fig. 6. A 495 MeV beam is incident on a

graphite beam stop and the dose equivalent as a function of distance along the beam

above a 1.6 m thick concrete shield is shown in Fig. 7. Both the full FLUKA99

simulation is shown as well as the result obtained using the relation Equation (7). The

agreement between the FLUKA99 results and the empirical relation is very good near the

peak of the dose equivalent distribution. On either side of the peak the full simulation

includes contributions from particles that are transmitted along the beam line tunnel and

scattered off the line of sight. These are not accounted for in the simple model developed

above. Measurements made with a moderated BF3 ‘dose equivalent’ meter are also

indicated in the graph of Fig. 7. It is evident that the BF3 counter underestimates the dose

equivalent by about a factor of 2. However, if we fold the neutron spectra calculated by

FLUKA at each of the measurement points with the response of the BF3 counter, the

results agree quite well with the measurements (Fig. 8).

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INDUCED RADIOACTIVITY PRODUCTION The production of induced radioactivity at proton accelerators will be discussed in a

separate paper in this volume (10). Here we again discuss only those aspects particular to

the low-energy regime. At lower incident energies radionuclide production by direct

reactions such as single- and multi-nucleon transfer as well as processes such as (p, γ) are

of principal concern. The systematics and approximate energy dependence of these

processes are generally well understood. The majority of reactions of concern are

endoergic nuclear reactions that have a threshold Eth below which the process is

forbidden by conservation of energy. Eth is related to the mass of the projectile, mp the

mass of the target nucleus, M, and the energy released in the reaction, Q, by

QM

MmE p

th

+= . (8)

The Q-value is the difference between the separation energy of the in-going and out-

going particles in the absence of excitation energy in either the entrance or exit channels.

In endoergic reactions Q is negative for reactions having a positive threshold. Many of

the reactions show a broad resonance above the threshold that may be used to good

advantage for selectively enhancing the yield of certain radioisotopes for the purpose of

medical radioisotope production. Cohen (11) has systematically plotted thick target yields

for a number of useful reaction processes.

At low proton bombarding energies the distribution of the induced radioactivity may be

very localized because of the short range of the protons. This can lead to problems in

dosimetry, as a single dosimeter may not show a true representation of the dose received

while working in a residual radiation field with steep spatial gradients. However, the

practice of wearing multiple dosimeters requires careful record keeping and

interpretation. For the relatively thin sources produced by protons of low energy (at

30 MeV the proton range is less than 2 mm in copper) the beta dose may make a

significantly larger contribution to the residual radiation field at the surface of irradiated

objects than at higher energies where the induced radioactivity is more deeply embedded.

By ‘beta’ dose is meant not only the dose due to beta particles but also that due to

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positrons as well as the energy deposited by X-rays of energy less than about 50 keV.

Sullivan (2) has shown that the beta and gamma dose are expected to become equal at a

material thickness of about 3 g cm-2, which for copper corresponds to a thickness of

3 mm. For materials of lower density or at lower proton bombarding energies the beta

dose can easily exceed the gamma dose by a large factor. Working with such materials

may require eye protection or working from behind a leaded glass window. In the latter

case extremity monitoring using ring-mounted thermo-luminescence dosimeters is often

used.

At energies above about 100 MeV, the semi-empirical recipes of Silberberg and

Tsao (12,13,14) have been widely used to estimate radioisotope production. These are a

much-improved version of the semi-empirical formula initially suggested by Rudstam (15)

and used effectively by Barbier (16) to calculate induced radioactivity for a number of

different materials and for different proton bombarding energies. The code that

incorporates their formulae is continually being updated and is freely available for

downloading via the Internet(∗). The Silberberg and Tsao formulae can be used to explore

the variation of production cross-sections with incident proton energy. Fig. 9 shows the

cross-section for the production of nuclides by the bombardment of 500 MeV protons as

a function of atomic mass for four different target materials. The cross-sections are

summed over the atomic number Z for each value of the atomic mass A. A number of

trends can be discerned from these plots. The highest cross-sections are always those for

the direct or peripheral reactions, i.e. those that yield products near the target mass. For

medium mass targets fragmentation reactions that result in products of very light mass

become possible. For targets of high atomic mass such as lead, fission reactions are also

an important production mechanism. Targets at the upper end of the range of stable

elements, such as uranium and thorium, display the full range of available product

masses, with fission and fragmentation products being produced at rates comparable to

the peripheral reactions. Such target materials are of great interest for radioactive ion

beam facilities and accelerator driven waste transmutation.

∗ http://spdsch.phys.Isu.edu/SPDSCH_Pages/Software_pages/Cross_Section/SilberburgTsao.html.

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The production cross-sections may also be calculated using Monte Carlo techniques.

Calculations (17) of the production cross-sections for 500 MeV protons bombarding

uranium using the Silberberg and Tsao formulae and Monte Carlo techniques using the

LAHET code system (LCS) (18) and FLUKA show good agreement for the peripheral and

fission reactions (for which there are also relatively good experimental values available).

The agreement is less good in the product mass region near A=180. It is perhaps not

surprising that this is the region where there is also a lack of experimental data.

Unfortunately it is also the region of interest for the production of radiotoxic α-emitters

such as the polonium isotopes. The Monte Carlo codes do not contain a good model for

fragmentation reactions and therefore a comparison to experimental data or even to the

Silberberg and Tsao formulae for these reactions is not meaningful.

For critical calculations involving the production of specific radionuclides, such as those

required to estimate inventories for possible releases to the environment, it is still

advisable to rely on experimental data where available. A number of good compilations

exist, such as that edited by Schopper (19, 20).

Prediction of Residual Radiation Fields Although it is possible in principle to perform calculations of induced radioactivity and

the corresponding residual radiation fields from knowledge of the cross sections and the

particle fluence, in practice the beam losses have not been or cannot be predicted with

sufficient detail to warrant the effort required. A useful practical, operational technique

for predicting residual radiation fields for different beam loss scenarios is to make

measurements during commissioning of the facility, at the locations where the

information is required, using a high-resolution gamma-ray detector. The detector

coupled to an analysis system will yield measurements of count rates in photo-peaks that

may be identified with specific radioactive species. Although the geometry is usually too

complex to be able to derive an actual activity for each species, one can assume that the

radiation originates from a virtual point source located at a standard distance for which

the detector efficiency is known. The activities Ai may be converted to dose rates using

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the so-called gamma factors Γi that give the dose per unit activity at a fixed distance from

a point source. The sum

∑∑==

=Γ=n

iii

n

ii hAH

11 (9)

should then correspond to the total gamma dose rate at that location. But because the

activities Ai are determined from the count rates in the photo-peak, this sum ignores all

scattered radiation. A simultaneous measurement of the gamma field with an ionization

chamber can be used to normalize the components hi =Γi Ai so that the sum in

Equation (9) agrees with the field measurement. Historical information of the variation of

beam intensity (or more appropriately beam loss) with time then allows calculation of

saturation values hsat,i per unit beam loss. The dose rate at any later time t for an arbitrary

irradiation history may then be obtained from

[ ]{ } ( )[ ]jiji

m

jisatj

n

ittthbH −−Δ−−= ∑∑ λλ expexp1, , (10)

where bj is the beam loss in interval Δtj and λi is the decay constant for the ith radioactive

component. Such calculations can easily be implemented using a commercially available

spreadsheet program and can be a useful tool for planning maintenance activities in high

radiation areas.

ENVIRONMENTAL IMPACT The environmental impact of proton accelerator operation that concerns us here is that of

the prompt or direct radiation as well as the possibility of the emission of radioactive

effluents, each of which may have an off-site radiological impact.

Skyshine The off-site component of the prompt radiation field is usually referred to as ‘skyshine’,

because in most cases sufficient shielding must be provided in the horizontal direction

(often by having the accelerator located below ground level) to protect the personnel

working at the facility. However, the shielding in the vertical direction is not always

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constrained in this way so that more radiation (usually neutrons) may be emitted from the

roof shielding of an accelerator at levels that may have an off-site impact.

Much has been written about the neutron skyshine phenomenon, often with confusing

terminology and unnecessary complications. Because the threshold for nuclear reactions

for neutrons with the constituents of air all lie near or above 20 MeV, the interactions

below this energy are restricted to elastic scattering. The high-energy nuclear interaction

lengths for N2 and O2 are of the order of 90 g cm-2, which for the density of air

(ρ = 1.2 × 10-3 g cm-3) is of the order of 750 m and hence the high-energy neutrons

effectively escape to great distances. Because only low-energy neutrons can be scattered

into the backward direction, near the source it is only these neutrons that are important.

At distances that may be reached by a shallow angle scatter, i.e. distances comparable to

the nuclear interaction length, the high-energy neutrons will predominate. Due to the

mass ratio of neutrons to nitrogen and oxygen nuclei, many elastic scatters are needed in

order to reduce the neutron energy significantly. It follows that, as a first approximation,

there is no effective attenuation of neutrons in air and the primary reduction in fluence

out to a few hundred metres derives from geometrical factors. (What little attenuation

there is must depend on the relative humidity, i.e. the hydrogen content of the air as has

been demonstrated in the atomic bomb dosimetry studies (21). Unfortunately this

parameter has not been reported in any of the accelerator skyshine measurements). The

dependence of neutron dose on distance from the source is therefore in the first instance a

purely geometrical effect. As particle number must be conserved, the dose is inversely

proportional to the area over which the particles are dispersed

22 rQH

π= , (11)

where AhQ a= is the dose ah averaged over the roof area A and r is the distance from the

source to the field point of interest. For large distances there is some attenuation

characterized by an attenuation length λ that is of the order of several hundred to 800 m.

A more complete expression is therefore

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)/exp(2

)( 2 λπ

rr

QrH −= . (12)

This simple expression ignores the fact that the neutron spectrum will be affected by the

scattering off the air. The high-energy neutrons will disappear to great distances and the

lower energy neutrons will be further degraded. A number of authors have investigated

the variation of the source term Q and the attenuation length λ as a function of the energy

spectrum of the neutrons emerging from the area A. The most complete analysis is that

due to Stapleton et al.(22) who have used the importance functions calculated by Alsmiller

et al.(23) and folded them with a composite spectrum that approximates the sea-level

cosmic ray neutron spectrum and has an angular distribution that varies as cos(θ). They

determined the equivalent dose as a function of distance from the source point and use a

function of the form

2)()](/exp[

)(rb

ErarH c

+−

=λ

per skyshine neutron (13)

to represent their results. They claim that the factor b accounts for the fact that skyshine

will produce a virtual source in the air at some height above the ground. (However, it

should be noted that for a virtual source at some height above the ground, the correct

variation with distance would be ∝ 1/[b2 + r2]). They chose a = 2 fSv m2 and b = 40 m to

be appropriate values to give a reasonable representation of their results. However, a

detailed analysis that determines the parameters as a best fit to their results (Fig. 10)

yields the values for a, b and λ listed in Table 4. The average value for a is

(2.41 ± 0.29) fSv m2 and for b it is (49.1 ± 3.7) m; the values for λ are plotted as a

function of maximum neutron energy in Fig. 11. In this method, if the source Q is known

only in terms of the equivalent dose, then it must first be converted to neutrons using the

g factors of the last column of Table 4. These factors are the averaged equivalent dose

over the composite spectrum with cut-off energy Ec. The method attributed to Stapleton

et al. is compared to the simple approach of Equation (11) in Fig. 12 where we plot the

equivalent dose per unit source strength Q as a function of distance r. At large distances

and high cut-off energies there is very little difference between the two methods. At short

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distances the offset b limits the magnitude of H(r) and gives a more believable shape to

the attenuation curves. For low-energy accelerators, which are compact and sited such

that boundaries are often within less than 100 m from the source, the geometrical factors

always dominate the reduction in equivalent dose with distance and it is usually not

necessary to include the exponential attenuation term.

Emission of Radioactive Effluents Because of their compact size and location in built-up urban areas, radioactive emissions

to the atmosphere can dominate the radiological off-site impact of high-power low-

energy proton accelerators. This is especially true if the target materials being bombarded

include high-Z materials that may produce exotic radioactive species such as radioactive

isotopes of iodine or α-emitters. On the other hand, releases to ground and surface water

can often be mitigated by minimizing water inventories and holding up the effluent until

such time that the radioactivity content has decayed below the levels of concern. Such an

approach is also feasible for releases of air from the exhaust of vacuum systems as this is

often the greatest source of airborne radioactivity and the total volume is usually small.

The vacuum exhausts from the radioactive beam facility at CERN (ISOLDE) and that at

TRIUMF (ISAC) are held up in this way.

The NCRP has produced a guide (24) that can be used to screen the magnitude of the

potential off-site impact of the release of radioactive effluents to the environment and to

select a model for estimating that impact. In this approach one starts with a crude model

that assumes that a member of the public is continuously ingesting or inhaling the

maximum concentration at the point of release. If this crude estimate does not yield a

significant dose then the process stops. On the other hand if this estimate fails to meet the

regulatory requirements of the local jurisdiction then one proceeds through a series of

ever more detailed calculations, at each stage verifying whether the regulatory limits can

be met. In this way one needs to refine the calculation only to the extent required by the

identified risk.

19

The transport of the radioactive releases may be modeled using an environmental

pathway model. A generic model is illustrated in Fig. 13. The release proceeds from the

source through a number of environmental compartments to produce a dose in a typical

member of the ‘critical group’, i.e. the most exposed homogeneous group of people in the

public. The transfer of radioactive material between compartments is modeled by

evaluating the transfer factors Pij that determine the fraction of radioactivity transferred

from compartment i to compartment j. For the short-lived positron emitters and noble

gases (e.g. 41Ar) that are usually the products of direct air activation at accelerators, only

the external dose via the immersion pathway determined by P(e)19 and P(e)29 are

significant. For long-lived, and biologically active isotopes, all possible pathways need to

be considered.

For example, in the release of an airborne radionuclide, the calculation of the transfer of

radioactivity from source to the environment at the point of interest, say the residential

community where vegetables are grown and consumed, would proceed as follows:

)()(

)(

0341314013341144

1133

0011

aXPPPPXPXPXXPX

aXPX

+=+===

where X0(a) is the source release rate, and the Xi is the radioactivity concentration in

compartment i. We have neglected here the contribution via irrigation of contaminated

surface water.

The equivalent dose to a member of the critical group from this pathway would then be

given by X9=P49X4, where P49 is the dose equivalent per unit intake multiplied by the

quantity of vegetation consumed per person per year. Methods for calculating the various

transfer factors are given in NCRP Report No. 123. A number of countries have devised

their own specific pathway models that include the preferred values or methods for

calculating these factors.

(14) (15) , (16)

20

Of particular interest is the factor P01 or the atmospheric dispersion factor. This factor

may be derived from an atmospheric dispersion model such as that described in the IAEA

Safety Guide No. 50-SG-S3(24). The long-term average centre-line atmospheric dispersion

factor at ground level for a continuous point release is (25)

⎟⎟⎠

⎞⎜⎜⎝

⎛ −= 2

2

01 2exp

zzy

hU

fPσσπσ

, (17)

where U is the mean wind speed, h is the height of the effluent release, σy,σz are the

horizontal and vertical turbulent diffusion parameters and f is the fraction of the time the

wind blows towards the receptor (i.e. critical group). For the default case of neutral

atmospheric stability and smooth terrain the diffusion parameters are given by

xx

y 0001.0108.0

+=σ , (18)

xx

z 0025.0106.0

+=σ (19)

and x is the downwind distance from the release point to the point of interest. IAEA

Safety Guide No. 50-SG-S3 provides values for these parameters for other stability

classes and for rough terrain. The diffusion parameters may be modified to account for

variable terrain, but of interest here is the concern for small facilities where the distance

to the point of interest may be rather short and where the release point may be only

slightly higher than the height of the building from which the release takes place. In those

cases it becomes important to account for the downdraft of the released air in the wake of

the building. This wake effect can produce dispersion in the lee of the building that is

greater than that calculated using the parameters above. When the height of the release h

is less than 2.5 times the height of the building it is assumed for calculational purposes

that the release and receptor heights are the same (i.e. h = 0). To account for the increased

dilution downwind of the building the standard value of σz is replaced with a modified

dispersion parameter Σz given by

21

πσ G

zzA

+=Σ 2 , (20)

where AG is the cross sectional area of the building influencing the flow in m2. An

alternative approach is to assume that a fraction ET of the release is ‘entrained’ by the

building so that the source is made up of a source at height h that is (1-ET)X0 plus a

virtual source at ground level of strength ETX0. The entrainment factor is given by

⎟⎠⎞

⎜⎝⎛−=

UW

ET058.158.2 ; for 5.10.1 0 ≤≤

UW

(21)

⎟⎠⎞

⎜⎝⎛−=

UW

ET006.030.0 ; for 0.55.1 0 ≤≤

UW

, (22)

where W0 is the velocity of the exhaust air. Fig. 14 illustrates the magnitude of this effect

for different ratios of W0 / U. Near the source the effect may be as large as an order of

magnitude. Note that for a given exhaust speed the entrainment factor ET increases with

wind speed.

SUMMARY Many of the radiological safety issues at low- and intermediate-energy proton

accelerators are similar in kind to those at all particle accelerators. We have pointed out a

few of the areas where the details of the problem are, if not unique, then at least requiring

a different approach. Among these are the problems of estimating the magnitude of the

prompt and residual radiation, and their environmental consequences.

22

REFERENCES

1. Ruegg, R., et al. Contraband Detection based on 13C(p,gamma)14N. Proceedings of the 3rd International Conference on Isotopes, Vancouver (1999)

2. Measday, D.F. and Richard-Serre, C. Loss of Protons by Nuclear Interactions in

Various Materials. CERN Yellow Report 69-17, CERN (1969).

3. Sullivan, A.H., A Guide to Radiation and Radioactivity Levels Near High Energy Particle Accelerators. Nuclear Technology Publishing (Ashford). ISBN 1 870965 18 (1992).

4. Evans, R.D., The Atomic Nucleus. McGraw-Hill Book Company (New York).

(1969)

5. Ferrari, A., Radiation Transport Codes. These Proceedings. (2001).

6. Stevenson, G.R., Accelerator Shielding. These Proceedings (2001).

7. National Council on Radiation Protection and Measurements. Protection Against Neutron Radiation. NCRP Report No. 38 (1971).

8. Fasso, A., Ferrari, A., Ranft, J. and Sala, P. New Developments in FLUKA

Modeling Hadronic and EM Interactions. Proceedings of 3rd Workshop on Simulating Accelerator Radiation Environments, Tsukuba, KEK (1997).

9. Tesch, K. A Simple Estimation of the Lateral Shielding for Proton Accelerators in

the Energy Range 50 to 1000 MeV. Radiat. Prot. Dosim. 11(3), 165-172 (1985).

10. Stevenson, G.R. Induced Activity in Accelerator Structures, Air and Water. These Proceedings (2001).

11. Cohen, B.L. Nuclear Cross Sections. Handbook of Radiation Measurement and

Protection, Section A: Volume I. Physical Science and Engineering Data. Brodssky. A. Ed. CRC Press, Inc. (West Palm Beach, Florida). 91-212. (1978).

12. Silberberg, R. and Tsao, C.H. Partial Cross-sections in High-energy Nuclear

Reactions, and Astrophysical Applications. I. Targets with Z<28. Astro. Phys. J. Suppl. 25, 315-333 (1973)

13. Silberberg, R. and Tsao, C.H. Partial Cross-sections in High-energy Nuclear

Reactions, and Astrophysical Applications. II. Targets Heavier than Nickel. Astro. Phys. J. Suppl. 25, 335-368 (1973)

23

14. Silberberg, R. and Tsao, C.H. Improved Cross-section Calculations for Astrophysical Applications. Astro. Phys. J. Suppl. 58, 873-881 (1985)

15. Rudstam, G., Systematics of Spallation Yields. Z. Naturforschung 21a, 1027

(1966).

16. Barbier, M. Induced Radioactivity. John Wiley and Sons Inc. (New York) (1969)

17. Furihata, S., Moritz, L. Benchmark Calculations of Cross Sections for the Production of Nuclei by the Bombardment of Uranium with Protons. TRIUMF Design Note TRI-DN-I7-3-14 (1998).

18. Prael, R.E. and Lichtenstein, H. User Guide to LCS: The LAHET Code System.

LA-UR-89-3014, Los Alamos National Laboratory (1989).

19. Schopper, H., editor. LANDOLT-BORNSTEIN: Numerical Data and Functional Relationship in Science and Technology, Group I: Production of Radionuclides at Intermediate Energies, Subvolume C: Interactions of Protons with Targets from I to Am. Springer-Verlag, (Berlin, Heidelberg) (1993)

20. Schopper, H. editor. LANDOLT-BORNSTEIN: Numerical Data and Functional

Relationship in Science and Technology, Group I: Production of Radionuclides at Intermediate Energies, Subvolume D: Interactions of Protons with Nuclei. Springer-Verlag, (Berlin, Heidelberg) (1994).

21. Roesch, W.C., editor. US-Japan Joint Reassessment of Atomic Bomb Radiation

Dosimetry. Vol. 1. Radiation Effects Research Foundation. (1986)

22. Stapleton, G.B., O’Brien, K. and Thomas, R.H. Accelerator Skyshine, Tyger, Tyger, Burning Bright. Part. Accel. 44(1), 1-15 (1994).

23. Alsmiller, R.G., Jr., Barish, J.R. and Childs, R.L. Skyshine at Neutron Energies

less than 400 MeV. Part. Accel. 11, 131-141 (1981).

24. National Council on Radiation Protection and Measurements, Screening Models for Releases of Radionuclides to Atmosphere, Surface Water, and Ground. NCRP Report No. 123 (1996).

25. International Atomic Energy Agency. Atmospheric Dispersion in Nuclear Power

Plant Siting, a Safety Guide. Safety Series No. 50-SG-S3 (Vienna) (1980)

24

TABLE CAPTIONS

Table 1: Values of parameters n0 and m for the production of neutrons (En > 100 MeV) of the form n=n0Ep

m as a function of proton energy Ep. The parameters have been obtained as best fits to the points calculated using FLUKA99 and shown in Fig. 4. The number of neutrons n is normalized to the number of interacting protons.

Table 2: The angular relaxation parameter β as a function of proton bombarding energy for a number of different target materials. The values of β have been obtained as best fits to the points calculated using FLUKA99 and shown in Fig. 5.

Table 3: The source term h0 and the attenuation length ρλ as a function of incident proton energy. These values have been obtained as best fits to equivalent dose attenuation in a concrete shield at 90o from a stopping copper target calculated using FLUKA99. Table 4: The parameters a, b, and the attenuation length λ, to be used in equation 10. These were obtained as best fits to the skyshine calculations of Stapleton et al.(16)

25

Material n0 m Be 0.66±0.02 0.71±0.01C 0.59±0.02 0.73±0.02Al 0.58±0.01 0.76±0.01Fe 0.46±0.02 0.76±0.02Cu 0.44±0.02 0.76±0.02Nb 0.46±0.02 0.80±0.02Pb 0.46±0.03 0.82±0.03

26

β Energy (GeV) Al Cu Pb

0.2 5.13±0.18 4.33±0.13 4.62±0.09 0.3 4.59±0.18 4.08±0.05 3.82±0.09 0.4 4.02±0.15 3.54±0.11 3.39±0.07 0.5 3.58±0.14 3.20±0.12 2.99±0.07 0.6 3.19±0.17 2.92±0.08 2.69±0.06 0.7 2.97±0.17 2.72±0.11 2.49±0.08 0.8 2.80±0.18 2.54±0.10 2.36±0.07 0.9 2.70±0.14 2.51±0.08 2.30±0.06 1.0 2.58±0.16 2.34±0.13 2.14±0.09

27

Energy(GeV)

h0 (pSv m2)

λ (kg m-2)

0.2 1.40±0.18 881±540.3 1.66±0.27 891±450.4 1.01±0.07 954±160.5 0.76±0.06 982±140.6 0.44±0.03 1012±90.7 0.47±0.01 1031±50.8 0.33±0.02 1046±70.9 0.32±0.01 1058±51.0 0.24±0.02 1086±7

28

Ec (MeV) a (fSv m2) b (m) λ (m) g (fSv m2)1.1 1.96±0.28 47.1±5.4 142±4 4.0 4.5 2.78±0.16 53.1±2.5 183±2 5.7 12.2 2.94±0.15 54.2±2.2 213±3 7.4 45 2.81±0.14 53.1±2.1 267±4 9.6 125 2.44±0.11 49.2±1.8 355±7 11.3 400 2.24±0.27 47.1±4.5 467±33 13.2 1000 2.24±0.18 47.3±3.0 532±28 14.1 5000 2.23±0.18 46.8±3.1 597±36 14.6

10 000 2.23±0.24 46.8±4.0 604±49 14.7 30 000 2.22±0.26 46.4±4.4 617±57 14.7

29

FIGURE CAPTIONS Figure 1: The fraction f n(Ep) of protons incident on a stopping target that participate in nuclear reactions as a function of proton energy for a number of target materials (2). Figure 2: The 56Fe(n, tot) cross-section as a function of neutron energy. The width of the gaps between 0.01 and 0.1 MeV are greater than the mean energy loss per scatter and hence neutrons with energy just above the gaps build up in iron shielding. Figure 3: The variation with energy of the attenuation length ρλ of mono-energetic neutrons in concrete of density ρ = 2400 kg m-3. The high-energy limit is 1170 kg m-2. Figure 4: The yield of neutrons with energy En > 100 MeV per interacting proton in stopping targets of a number of materials as a function of proton energy. The points are the results of calculations with FLUKA99 and the lines are best fits to these points of the relation m

pp EnEn 0)( = .

Figure 5: The angular distribution of the yield of neutrons with energy En > 100 MeV in the angular interval 60o<θ < 120o for targets of aluminum, copper and lead for incident proton energies in the range 0.2 to 1.0 GeV. The points are the results of calculations with FLUKA99 and the lines are best fits to these points of a relation of the form exp(-βθ ) . Figure 6: A vertical section through shielding experiment at TRIUMF. A 0.49 GeV proton beam is incident on a 1.2 m long graphite beam stop. The dashed lines indicate concrete shielding and the solid points indicate the location of measurements made with a moderated BF3 counter. The large open circles indicate the location of multi-sphere and 12C(n, 2n)11C measurements. Figure 7: Results of calculations and measurements on the geometry depicted in Fig. 6. The solid line indicates the calculation using Equation (5). The FLUKA99 calculations are indicated by open squares ( ) and the BF3 counter measurements by solid squares ( ). The multi-sphere results are plotted as filled circles (•). Figure 8: The measured BF3 counter response ( ) and the response calculated from the spectra generated by FLUKA folded with the detector response function (Δ). The BF3 counter response calculated from the unfolded multi-sphere spectra and the counter response function are also shown (×). Figure 9: Cross sections for the production of nuclides by bombardment with 500 MeV protons as a function of atomic mass A summed over atomic number Z for a number of targets. These cross sections have been calculated using the semi-empirical formulae of Silberberg and Tsao. The highest yield is always for products with mass very near that of the target. For heavy target nuclei, fission also contributes significantly to the mix of product activities.

30

Figure 10: The results for the calculation by Stapleton et al. of equivalent dose due to skyshine as a function of horizontal distance from the source. The dashed lines are best fit to the data points of equation 10. Figure 11: The effective attenuation length for skyshine neutrons as determined by a best fit to the data in Fig. 9 of equation 10. Figure 12: A comparison of the simple model of equation 9 with that of Stapleton et al. (equation 10). For high neutron spectrum cut-off energies and distances greater than 200 m there is very little difference. At short distances, the Stapleton model gives more realistic results. Figure 13: An example of an environmental pathway model for the release of radioactive effluents from an accelerator facility. Compartment 0 is the source and compartment 9 is the dose in a member of the critical group. Figure 14: The effect of the entrainment of the wake on the downwind atmospheric dilution factor as a function of the ratio of exhaust air speed top wind speed.

31