INDUCED ACTIVITY IN ACCELERATOR STRUCTURES, AIR AND...

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#SL010 INDUCED ACTIVITY IN ACCELERATOR STRUCTURES, AIR AND WATER Graham R. Stevenson European Organisation for Nuclear Physics (CERN) 1211 Geneva 23, Switzerland E-mail: [email protected] Running Title: INDUCED ACTIVITY

Transcript of INDUCED ACTIVITY IN ACCELERATOR STRUCTURES, AIR AND...

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#SL010

INDUCED ACTIVITY IN ACCELERATOR STRUCTURES, AIR AND WATER

Graham R. Stevenson

European Organisation for Nuclear Physics (CERN) 1211 Geneva 23, Switzerland

E-mail: [email protected]

Running Title: INDUCED ACTIVITY

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INDUCED ACTIVITY IN ACCELERATOR STRUCTURES, AIR AND WATER

Graham R. Stevenson

Abstract A summary is given of several Rules of Thumb which can be used to predict the formation and decay of radionuclides in the structure of accelerators together with the dose rates from the induced radioactivity. Models are also given for the activation of gases (air of the accelerator vault) and liquids (in particular cooling water), together with their transport from the activation region to the release point. Word count: 67 words

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INTRODUCTION Simulation programs such as MCNPX (1) and FLUKA (see references (2,3) and the references they contain) are now capable of giving estimates of the number and types of radionuclides created by the hadronic component of the cascades induced by high-energy particles. In assessing the problems raised by induced radioactivity, it would seem that all one has to do is run one of these programs, sum up the different isotopes produced and make the appropriate exponential corrections for the irradiation profile as a function of time and for cooling time. One can then use the spatial distribution of the concentration of these radionuclides as the source of photons in a second simulation to determine the dose-rates from this induced radioactivity.

The reality of the situation is that even with modern computers, the time taken for such a calculation is nearly prohibitive, and there is always the problem of low statistics in the regions of the cascade where one would like to determine the induced radioactivity. Simple rules of thumb still have their uses in a number of cases: 1. When making a first guess at the order of magnitude of a problem. 2. When making an estimate if a computer simulation program is not available. 3. Providing an estimate for judging if mistakes of orders of magnitude have been

made in the computer simulations.

The first part of this paper summarises the simple rules that have been proposed in order to estimate both the activity levels and dose rates from radionuclides produced by inelastic interactions in high-energy cascades in the solid materials of an accelerator structure. It leans heavily on the formalism developed by Gollon (4) and on the section on Induced Radioactivity to be found in the review by Thomas and Stevenson (5). Although mainly applicable to proton accelerators, these simple rules will enable accurate estimates to be obtained of several global quantities, such as the total inventory of radioactivity, but do not replace computer simulations of the high-energy cascade in particular elements of the structure of an accelerator where more detail may be required.

Whereas the environmental impact of radioactivity in the structure of an accelerator is readily assessed from its inventory of radionuclides, that of the radioactivity produced in air and water requires that transport models are developed which take the radioactivity from its region of production to a release point (drain or chimney). In the second part of this paper several formalisms are developed for dealing with the transport of this radioactivity.

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ACTIVATION OF METALLIC STRUCTURES Lifetime of radionuclides Sullivan has pointed out that approximately one-half of the one hundred or so radionuclides below iron in the isotope tables have half-lives in the range 10 minutes to 10 years (6). This is illustrated in Figure1 which is redrawn from an earlier work by Sullivan (7). Barbier (8) extends this argument to materials whose atomic mass is both higher and lower than that of iron. This allows one to propose the following: Rule 1: For most materials used in the construction of accelerators, about one-third to one-half of all inelastic interactions give rise to a radionuclide with a half-life between several tens of minutes and a few years. Total radioactivity at saturation The total quantity of radioactivity produced in an accelerator structure (magnets, shield and environment) will be related to the number of inelastic interactions produced by the proton and its cascade in the material of interest. Interactions of lower energy neutrons will contribute, but in equilibrium cascades their proportion of the total will be constant. The number of inelastic interactions can easily be determined from simulations of the cascade using programs such as FLUKA for example (2). Calculations of the number of inelastic interactions are summarised in Table 1. The data in this Table show that the number of interactions is not strongly dependent on the target material and is approximately proportional to the incident proton energy, as indicated by the numbers in the final column of the Table. This leads to the following: Rule 2: The total number of inelastic reactions produced by a high-energy proton is approximately equal to its kinetic energy in GeV multiplied by three. Rules 1 and 2 allow one to conclude that for an incident proton beam intensity of 1 proton per second, the saturation activity in becquerels is numerically equal to the beam energy in GeV. Photon dose-rate from small objects In simpler, older times, one could calculate the dose rate at a certain distance from a photon emitter using the formula:

CED 6=•

rad/h, (1) where that certain distance was a foot, C is the activity of the photon emitter, measured in curies, and E is the sum of the photon energies emitted per disintegration measured in MeV. Tabulations exist of radionuclide-specific values of the dose rate at a given distance from sources of defined activity. These kγ values are given in (8) for example, where the standard distance is the metre but the activity is still measured in curies. Certain of these kγ values are listed in Table 2 together with the sum of the photon

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energies weighted by their emission probability. The last column contains the kγ value divided by the energy for each radionuclide. With the knowledge that a foot is 0.305 metres, the value of kγ/E determined from the above equation is 0.55, in good agreement with the final column of Table 2

Modern tradition insists that the dose is measured in sieverts and activity in becquerels, so the best translation of the above formula into modern units that still retains some of the simplicity of the original is:

Rule 3: The dose rate in Sv/h at one metre from a photon source is equal to the sum of the photon energies in MeV weighted by their emission probability multiplied by the activity of the source in TBq and divided by 7. A value of the mean energy emitted from components in an accelerator can be obtained from the transmission measurements of photons emitted by irradiated steel components of the CERN Proton Synchrotron (CPS) made by Goebel (9). These transmission measurements are illustrated in Figure 2. Examination of this Figure shows that the transmission curves lie between those for 137Cs and 226Ra and would roughly correspond to that for photons with an energy of 800 keV. This fact, taken with Rules 1 and 3 suggest that the saturation photon dose rate in Sv/h at 1 m from a small object is 5×10-14 times the number of inelastic interactions per second in the object. Photon dose-rate from large objects Another “magic” formula, derivable from simple energy conservation, relates the dose rate at the surface of a semi-infinite slab to the concentration of a photon emitter which is uniformly distributed in the slab.

cED 7109.2 −•

×= Sv/h , (2)

where c is measured in Bq g-1 and E is in MeV as before. For iron, unit star density production rate in cm-3 s-1 corresponds to 0.12 Bq g-1 at saturation, and so, using the information that the mean photon energy is 0.8 MeV, for an infinitely long irradiation with no cooling time the surface dose rate close to a slab in which unit star density is produced per second is:

87 108.28.012.0109.2 −−•

×=×××=D Sv h-1. (3) It has been traditional to refer dose rates to an irradiation time of one month and a decay time of one day, which is lower by about a factor of three than the dose rate after an infinite irradiation and no cooling time in the case of iron. This dose rate from unit star density is referred to in the literature as the ω-factor, which as the above argument shows will have a value of 10-8 Sv h-1 for unit star-density production rate. ω-factors for other materials have been determined by Höfert (11) and are listed in Table 3.

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To summarise then: Rule 4: For iron as an irradiated material, the photon dose rate close to the material in Sv h-1 is approximately 10-8 times the density of inelastic interactions in cm-3 s-1. Rules 3 and 4 allow one to determine the photon dose rates close to targets or bulky objects intercepted by the beam. Sometimes a cascade calculation may be necessary to determine the inelastic interaction density. There are now better means available for determining the dose rates from star densities. The program FIASCO (12) FLUKA Induced Activity Shielding in Combinatorial geometry) by Huhtinen is still based on star densities and ω-factors, but considers 3 photon energies and includes photon transport (attenuation and build-up) using the FLUKA geometry. Dose-rates from thin objects There are certain circumstances when the dose rate produced by electron-emitting radionuclides can be important. One of these is the case of an irradiated thin foil. Following Sullivan (13) the β- dose rate from a thin foil may be written as:

βββ

×= −

x

END

d

d106.1 10 Sv s-1 , (4)

where Nβ is the number of β- particles emitted per cm2 per second and (dE/dx)β is the average stopping power in MeV cm2 g-1. The corresponding photon dose rate is:

γγγ µ END 10106.1 −•

×= Sv s-1, (5)

where Nγ is the number of photons emitted per cm2 per second, Eγ is the average photon energy and µ is the mass energy attenuation coefficient in cm2 g-1. The ratio of the dose rates is given by:

γγ

ββ

γ

β

µ EN

xEN

D

D )d/d(=•

, (6)

which for the case of Nβ/Nγ = 1, (dE/dx)β = 2 MeV cm2 g-1, Eγ = 1 MeV and µ = 0.03 cm2 g-1 gives:

70=•

γ

β

D

D . (7)

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The ratio is not as high as this in practice for several reasons. Self-absorption of

electrons even in very thin foils reduces this electron dose rate, electron capture is often a competing mode of decay and finally the gamma dose rate may be enhanced by positron capture and annihilation. Sullivan has reported measurements of this ratio for 0.1 mm thick foils of aluminium, steel and copper, giving values of 12, 7 and 9 respectively (14). The value of the ratio between the beta and gamma dose rates is evidently a function of the thickness of the foil. Sullivan (13) suggests that whereas the beta dose rate will increase only slowly with foil thickness, the gamma dose rate will be nearly proportional to foil thickness. He predicts that the electron and photon surface dose rates will be nearly equal for foil thicknesses of about 1 mm. Extreme caution must be used when standard survey instruments are used to assess the hazard from thin foils. The surface dose rates may be underestimated by a factor as high as 200, and dose rates at 30 cm from the foil may be 104 times lower than the surface dose rate (14). These considerations can be summarised in the following: Rule 5: For thin objects (thickness less than 0.1 mm), the beta dose rate at the surface of the object may be some 50 times higher than the gamma dose rate. Dose rates indicated by some standard survey instruments may underestimate the surface dose rate by as much as a factor of 200. Effective half-life Sullivan and Overton (7) have described an analytical method of predicting the variation of dose rate from induced radioactivity with irradiation time T and cooling time t. They showed that:

]/)ln[()( ttTBtD +=•

φ , (8) where B is a constant of proportionality and φ is the irradiating flux density.

It is interesting to explore the asymptotic values of the Sullivan-Overton formula with respect to T and t (13). When the cooling time is long compare to the irradiation time, we have:

tTBtD /)( φ=•

, (9) i.e. the dose rate is inversely proportional to the cooling time. When the irradiation time is long compared to the cooling time, then:

),ln(ln)( tTBtD −=•

φ (10)

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a relationship which gives a logarithmic decrease with cooling time.

It has long been a common assumption that the effective half-life of the dose rate from induced radioactivity is approximately equal to the cooling time. (In physical terms this means that the radionuclides with short half-lives will have already decayed and those with long half-lives will not yet be contributing to the dose rate). This common assumption was justified by Freytag (15). Differentiating the Sullivan-Overton formula we obtain:

ttTtTt

T

tD

tDd

)/1ln(

1

)/1()(

)(d2 ++

−=•

. (11)

This gives an effective half-life of:

2ln)1ln(1

2/1 xx

xtT ++= , (12)

where x = T/t. For values of x of 0.1, 1.0 and 10, T1/2 is 0.7, 1.0 and 1.7 times t respectively, showing that the common assumption has some more rigorous justification, giving: Rule 6: The effective half-life of the activity induced in most accelerator components, concrete excepted, is approximately equal to the time since the accelerator was switched off. ACTIVATION OF OTHER MATERIALS This subject was dealt with in a very comprehensive way by Barbier (8). The variation of the photon dose rate per unit mass of irradiated material as a function of atomic number is illustrated in Figure 3, based on the work of Barbier. Trends are not very dependent on the cooling time. The remanent dose rate is at its maximum for elements with an atomic number close to that of molybdenum: at lower atomic numbers there is a minimum in the region of calcium. Barbier suggested that this could be put to good effect by using marble as an external face to permanent shielding around radioactive accelerator items. Höfert's measurements summarised in Table 3 suggest that the reduction in dose rate could attain two orders of magnitude over the dose rate from iron. For irradiated aluminium the remanent dose rate after several hours cooling will come entirely from isotopes of sodium. Lower-Z materials produce mainly short-lived positron emitters: the only photon emitter of any importance is 7Be, but this does not contribute significantly to remanent dose rates.

Of the heavier elements, the dose rate from the radionuclides produced in lead is of importance since lead is often used a shield for photons and it is evidently more

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convenient to leave such shields in place during accelerator operation. Sullivan has shown that the dose rate from irradiated lead decays as t-1.4 if the irradiation time is short compared with the cooling time (16). This is somewhat faster than the t-1.0 dependence of iron in similar circumstances. The data of Table 3 would suggest that the remanent dose rate from lead should be somewhat higher than that from iron. This is in contradiction to the work of Sullivan (16) who observed that for an irradiation time of 1 year and a cooling time of 1 month, the dose rate from lead was only one-fifth of that from steel. Further evidence is provided by the calculations of Gabriel and Santoro who compared dose rates from a heavy iron cylinder used as a beam stop for 200 GeV protons (17). Calculations were also made for the iron cylinder surrounded by lead collars of different thicknesses. Figure 4 shows the results of the calculations. For all irradiation times and decay times considered, the lead collars substantially reduced the dose rate compared with that from the iron cylinder. In addition, the decay of the dose rate from the lead collar is faster than that for bare iron. However this behaviour depends critically on the presence of impurities in the lead, especially antimony. RADIOACTIVITY IN AIR AND WATER The yield, Pi, of a radionuclide i, produced by a hadronic cascade in air or water can be calculated by integrating the product of the production cross-sections with the particle track-length spectrum:

EEEnP kkjiji ji d)()(,,,Λ= ∫∑ σ , (13)

where the summation is performed over all possible parent elements j and all hadron components k in the cascade. nj is the atomic concentration of the element j in air or water per cm3 and Λk is track-length spectrum in cm of hadrons of type k and energy E, as obtained from a cascade simulation. σi,j,k is the cross-section for production of the radionuclide i in the reaction of the particle of type k and energy E on the nucleus j. The 39 radionuclides of interest in for air and water activation together with their energy-dependent production cross-sections are given in (18).

However the main problems in assessing the environmental impact of the activation of fluids lie in choosing the correct model for fluid movement during activation and in transit to the release point. The additional problem concerning the dispersion of the radionuclides after release will not be discussed here. The simplest activation model assumes that the fluid is stationary during activation and then moves directly to the release point after irradiation. Since this involves only simple exponentials, the mathematics of this model will not be considered further. More interesting are the cases firstly where the fluid passes at a uniform speed through the irradiation region without turbulence and, secondly, where there is complete mixing of the fluid in the irradiation region and a small fraction of the fluid is removed regularly. A special case of these models is when the irradiation is a function of time.

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Laminar flow model

Let the number of beam particle (protons) intercepted per second by the activating system (target) be np which is a function of time and L be the length of the accelerator tunnel or water tube. If the total volume of the air or water circuit is Virr cm3 and the flow rate of air (or water) through the circuit is Q cm3 s-1, the linear velocity of the fluid in the tunnel or pipe, v, is:

irrV

QLv = cm s-1 (14)

If the transit time of the fluid past the activating region is very short when

compared with the time variations of the proton beam intensity, one can make considerable simplifications in the following calculations of release and concentration of radioactivity. Release The number of nuclei of a given radionuclide produced during a time dt in an elemental length of the activation region dx at a distance x from the end of the activating region is np P dt dx / ", where P is the total number of nuclei of the radionuclide produced in the fluid by the loss of one proton and " is the length of the activation region. The transit time for the fluid in this elemental volume to reach the end of the activating region is x/v, and so the number of radioactive nuclei reaching the end of the activation region is np P dt dx exp(-x/vτ)/", where τ is the mean lifetime of the radionuclide. The total activity, A, produced in the time dt in the whole activation region and which reaches the end of this region is then:

[ ])/exp(1dn

d)/exp(d1

p

0

τ

ττ

irrirr

p

tt

tP

xvxtPnA

−−=

−= ∫"

" (15)

where tirr = "/v is the transit time for the fluid to traverse the activation region.

If it takes a time td for the fluid to reach the release point, the amount of radioactivity, R, produced in the time dt and which escapes to the environment is:

[ ] )/exp()/exp(1d

)/exp(

ττ

τ

dirrirr

p

d

ttt

Ptn

tAR

−−=

−= (16)

The total amount of radioactivity released during one operating period, Y, is then

simply:

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[ ] )/exp()/exp(1 ττ dirrirr

p ttt

PNY −−= , (17)

where Np is the total number of protons intercepted by the target during an operating period. Concentration The concentration of a given radionuclide in the fluid at the end of the activation region is A, taken from Equation (15), divided by the volume of the fluid flowing past in the time dt. If ttot is the duration of the operating period, the average concentration during operation, aave is then:

[ ])/exp(1 τirrtotirr

pave t

tQt

PNa −−= . (18)

Complete mixing model In this model the activity is produced in a region where there is complete mixing of the air inside the region. There is a supply of air to and an extraction of air from the region, and it is assumed that an activated nucleus has the same probability of being removed from the region no matter where it is produced. Let the volume of air cycled through the region per second be Q and the volume of the region Virr. Thus the change in the number, N, of radionuclides of a given species per unit time is the difference between the production rate and the sum of its decay and extraction rates:

+−= N

V

QNtP

t

N

irrp τ

ν )(d

d. (19)

P is the production per unit proton of the radionuclide, whose mean life-time is τ,

by the hadronic cascade in air and can be calculated by integrating the production cross-sections with the particle track-length spectrum following the usual formula. νp is the proton interaction rate which can vary with time. For the sake of convenience, in the following λ the decay constant, will be used instead of 1/τ and Q/Virr will be defined as the air-exchange rate in the cavern m. The above equation then becomes:

( ) )(d

dtPNm

t

Npνλ =++ , (20)

which has the solution

[ ] [ ]∫ +++−= ttmtPtmN p d)(exp)()(exp λνλ constant. (21)

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In the trivially simple case where N = 0 at t = 0 and the p-interaction rate is a constant ν, then after a time t the number of nuclei is given by the relation:

( )])(exp[11

tmm

PN +−−+

= λλ

ν . (22)

In the more general case where Ni radionuclei remain at the start of the i’th period

of operation from previous periods at t = 0:

[ ] [ ]

+++−= ∫t

pi ttmtPNtmN0

d)(exp)()(exp λνλ . (23)

Concentration The total activity in the volume of the region is thus λN and its concentration λN/Virr. Release The activity of a given radionuclide extracted from the activation region is mλN, where N is given by equation (22). Thus the rate of release in Bq per second of the radionuclide is:

[ ]dtNmR λλ −= exp , (24)

where td is the decay time during which the activated fluid passes through the ducts from the activation region to the outside world.

The total activity released during the i’th operation period which lasts for a time ton is obtained by integrating the above equation:

∫= ontoni tRY

0d . (25)

At the end of the operation period, the number of radionuclei in the activation

region, Ni′ is given by substituting ton into equation (23). If the time between operation periods is toff, the number remaining at the start of the next period of operation is simply:

[ ]offoffii tmNN )(exp1 +−′=+ λ , (26)

where the air-exchange rate during the down-time between operation periods, moff, could well be different from the value of m during operation because of a different ventilation rate Qoff.

The total activity vented after the i’th operation period during the time between periods is:

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[ ]∫ +−′−= offt

offioffd

offi ttmNtmY

0d)(exp)exp( λλλ ,

[ ]( )offoffioffd tmNt

m

m)(exp1)exp( +−−′−

+= λλ

λλ

. (27)

In the calculation of the total release in one year of operation the contributions from successive periods are summed up:

( )∑ +=i

offi

onitot YYY , (28)

remembering that after the final fill the integration in equation (27) has to be taken to infinity rather than to toff. ACKNOWLEDGEMENTS The author wishes to point out that the only originality in this work is in the selection and presentation of the different subjects. I have drawn on the work of my colleagues at CERN: M. Barbier, K. Goebel, M. Höfert, M. Huhtinen and A. H. Sullivan. I thank them all. REFERENCES 1. Waters, L. S., Editor, MCNPXTM User’s Manual, Los Alamos Report TPO-E83-G-

UG-X-00001 (1999). 2. Fassò, A., Ferrari, A., Ranft, J. and Sala, P. R. New developments in FLUKA modelling

of hadronic and EM interactions, in Proceedings of The Third Workshop on Simulating Accelerator Radiation Environments (SARE-3)}, KEK, Tsukuba, Japan, 1997, 32-43 (1997).

3. Ferrari, A., Rancati, T., and Sala, P. R. FLUKA applications in high-energy problems: from LHC to ICARUS and atmospheric showers, in Proceedings of The Third Workshop on Simulating Accelerator Radiation Environments (SARE-3)}, KEK, Tsukuba, Japan, 1997, 165-175 (1997).

4. Gollon, P. J. Production of radioactivity by particle accelerators, IEEE Transactions on Nuclear Science NS-23 1395-1400 (1976).

5. Thomas, R. H., and Stevenson, G. R. Radiological safety aspects of the operation of proton accelerators, Technical Report Series No. 283, IAEA Vienna (1988).

6. Sullivan, A. H. An approximate relation for the prediction of dose rate from radioactivity induced in high-energy particle accelerators, Health Physics 23 253-255 (1972).

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7. Sullivan, A. H., and Overton, T. R. Time variation of the dose rate from induced radioactivity induced in high-energy particle accelerators, Health Physics 11 1101-1105 (1965).

8. Barbier, M. Induced Radioactivity, North Holland, Amsterdam (1969), in particular pages 19-27.

9. Goebel, K. Personnel exposure from βγ radiation of induced radioactivity at high-intensity exploitation of the Proton Synchrotron, CERN Internal Report HP-47 (1967).

10. International Commission on Radiological Protection, Data for protection against ionising radiation from external sources, ICRP Publication 21, Pergamon Press, Oxford and New York (1973).

11. Höfert, M., and Bonifas, A. Measurement of radiation parameters for the prediction of dose rates from induced radioactivity, CERN Internal Report HP-75-148 (1975).

12. Huhtinen, M. Method for estimating dose rates from induced radioactivity in complicated hadron accelerator geometries - Write-up of the FIASCO code, CERN Internal Report, CERN/TIS-RP/IR/98-28 (1988).

13. Sullivan, A. H. Some ideas on radioactivity induced in high-energy particle accelerators, CERN Internal Report HS-RP/TM/83-27 (1983).

14. Sullivan, A. H. Dose rates from radioactivity induced in thin foils, CERN Internal Report HS-RP/IR/82-46 (1982).

15. Freytag, E. Halbwertzeiten der Aktivierung bei Beschleunigern, Health Physics 14 267-269 (1968).

16. Sullivan, A. H. Induced activity dose rates from steel and lead, CERN Internal Report HP-72-106 (1972).

17. Gabriel, T. A., and Santoro, R. J. Photon dose rates from the interaction of 200 GeV protons in iron and iron-lead beam stops, Particle Accelerators 4 169-186 (1972).

18. Huhtinen, M. Determination of cross-sections for assessments of air activation at LHC, CERN Internal Report CERN/TIS-RP/TM/97-29 (1997).

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Table 1

Star production in various materials as a function of incident proton energy

Proton Energy

Material Graphite Copper Tungsten

Stars Per GeV

300 MeV 0.83 0.69 0.64 2.4 1 GeV 4.8 4.2 4.1 4.4 3 GeV 14 13 12 4.3 30 GeV 85 87 87 2.9

300 GeV 580 630 640 2.1 3 TeV 4300 4600 4900 1.5

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Table 2

kγ factors in rad h-1 at 1 metre

Radionuclide kγ rad h-1 at 1 m per Ci

E MeV

kγ/E

7Be 0.029 0.049 0.59 18F 0.489 1.000 0.49

24Na 2.08 4.123 0.50 41Ar 0.645 1.293 0.50 48V 1.473 2.928 0.50

54Mn 0.424 0.835 0.51 60Co 1.264 2.505 0.50 137Cs 0.333 0.563 0.59 203Hg 0.122 0.215 0.57

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Table 3

Factors for converting star density production rate to remanent dose rate.

Material ω-factor Sv h-1/(cm-3 s-1)

Iron 1.0×10-8 Copper 1.0×10-8

Stainless steel 1.3×10-8 Aluminium 2.0×10-9

Lead 1.5×10-8 Tungsten 1.1×10-8

Normal concrete 3.0×10-9 Marble 6.0×10-10

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TABLE CAPTIONS Table 1: Star production in various materials as a function of incident proton energy Table 2: kγ factors in rad h-1 at 1 metre Table 3: Factors for converting star density production rate to remanent dose rate.

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FIGURE CAPTIONS Figure 1: Cumulative percentage of radionuclides with mass number smaller than that of iron and whose half-lives are smaller than the corresponding value on the x-axis

Figure 2: Absorption curves for photons in lead. Curves for irradiated iron objects taken from (9). a is an average of un-collimated sources, b is an un-collimated view of the short straight-section 58 and c is a collimated view of a septum in the same straight-section. Isotopic data are taken from ICRP Publication 21 (10).

Figure 3: Calculated variation of the remanent gamma dose rate at a distance of 1 m from 1 g of an irradiated element with the atomic number of the element, based on data from Barbier (8). The element was assumed to be irradiated in a 2.9 GeV proton fluence rate of 106 cm-2 s-1 for 5000 days. Solid points are for a cooling time of 1 day; open circles are for a cooling time of 30 days. Figure 4: Comparison of the average total photon dose rate from an iron cylinder surrounded by two thicknesses of lead for several irradiation times, from Gabriel and Santoro (17). A 200 GeV proton beam having an intensity of 1 cm-1 s-1 interacts along the axis of the cylinder. Case A (dashed lines) is for an iron cylinder of radius 40.64 cm; Case B (dot-dashed line) is for an iron cylinder of radius 30.48 cm surrounded by a lead collar of 5.08 cm thickness; Case C (solid lines) is for an iron cylinder of radius 30.48 cm surrounded by a lead collar of 10.16 cm thickness.

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0

0.2

0.4

0.6

0.8

1

10-4 10-3 10-2 10-1 100 101 102 103 104 105

Cum

ulat

ive

frac

tion

of is

otop

es

Half-life in days

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10-5

10-4

10-3

0 10 20 30 40 50 60 70 80 90

Gam

ma

Dos

e-ra

te in

µS

v/h

Atomic Number

Al Ca FeCu Sn W Pb

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