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!!!Accelerator Division !!!!!!!!!!

R. J. Barlow and A. M. Toader

Background Studies in the ESS A2T Region

21 November 2013

ESS AD Technical Note ESS/AD/0051

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Background Studies in the ESS A2T region

R. J. Barlow and A. M. ToaderUniversity of Huddersfield

Version 5, 21 Nov 2013

1 Introduction

This note presents the results of studies of radiation in the A2T (accelerator-to-target)area of the ESS High Energy Beam Transport. We have examined the extent to whichcomponents become active and require special handling (which would have implicationsfor design plans), or suffer other types of radiation damage.

2 The problem and its treatment

MCNPX [1] is used as the main simulation program, with cross-checks from GEANT4[2] where possible. MCNPX is faster, and can use existing descriptions of the geometry.The standard cross section libraries are used.

Possible isotopes to be considered are listed in Appendix 1, with a discussion on theirpotential problems. We have selected those which we believe to be most relevant:

60Co which is produced in Copper, and thus in all the magnets and the collimator.

55Fe and 54Mn, which are produced in iron and thus in all the magnets and the beampipe.

57Co, 58Co, 51Cr and 56Mn, which are produced in steel and thus (only) in the beampipe.

22Na and 24Na, from Sodium in concrete.

Numbers for production of active isotopes, given in later sections, are the number ofactivated nuclei produced per generated proton. To convert to activated nuclei producedper second of operation they must be scaled by a factor depending on the source, describedin the next section. To convert this to Bequerels one can naively multiply by the decayrate, though this gives an over-estimate as it does not allow for the effects of decay, whichrequires a more complex calculation, making assumptions about the operation cycle. Thiswill be done in a forthcoming version of this note.

1

3 Geometry

To the standard target and surroundings, as described in the deck FBM845 (FebruaryBase Master), we added components for a beam pipe, a collimator, and magnets to composea very simple model of the HEBT, as shown in Figure 1. (The outer black lines are anotional surface, not a solid component.)

.

Figure 1: The added components (plan view)

A beam pipe (Figure 2) is taken as a steel tube of inner radius 5 cm and thickness2 mm, between 60 m and 8.5 m upstream, which flares to a cone of outer radius 1 mmatching the collimator at an inner radius of 50 cm where it adjoins.

.

Figure 2: The beam pipe and collimator

The collimator is between 8.5 and 7.5 m upstream. It is modelled by a copper cy-linder, with an inner layer which may be tungsten or copper. The aperture is made of asuperposition of a cone and two planes, and narrows from a circle of radius 50 cm to a slitof half-width 3 cm and half-length 8 cm. No extra detail of material is introduced betweenthe collimator and the existing target.

. . .

Figure 3: The collimator: longitudinal section and transverse sections

There are 12 magnets. Magnets 4 and 8 (counting from the target ) are octupoles, of

2

length 120 cm. The first 3 (’long’) quadrupoles are 100 cm long, and the remaining seven(’short’) are 80 cm. Representations are shown in Figures 4 and 5. Dimensions have beenread off drawings and the exact structures of the copper windings have been smoothedover. The resulting level of detail is adequate and appropriate given the level of accuracyof the analysis, and the changing nature of the current design.

.

.

Figure 4: Magnet model: short quadrupole

Figure 5: Magnet model: octupole

The gaps between the magnets are generally left as void (or air), but we have alsoinvestigated the effect of filling them with concrete. This is a simple cylindrical shieldbeing placed wherever there is no magnet. It is not realistic or optimised, but is useful asa sign as to whether shielding of this type would reduce rates and backgrounds.

4 Sources

We considered 3 sources

Source 1 Backsplash from the spallation target, using the standard source. To convert numbersas given below to numbers produced per second at 2 mA, they should be scaled bya factor 2 × 10−3/1.6 × 10−19 = 1.25 × 1016. Simulation of 1 million particles takesaround 30 CPU hours. (Though we do this by running 200 jobs simultaneously on afarm, so high statistics can be obtained in a few hours of real time.)

3

Source 2 Losses in the main beam pipe. 2.5 GeV protons hit the beam pipe at grazing incidence,uniformly between 50 m and 20 m upstream. To normalise losses to 1 W/m, multiplyby 30/(2.5 × 109 × 1.6 × 10−19) = 7.5 × 1010. Simulation of 1 million particles takesaround 7 CPU hours. A variation of this source clumps the protons lost at themagnets.

Source 3 Losses on the collimator. We use a file of particle trajectories provided. Of the 500,000particles only 136 strike the collimator. This corresponds to a power of 136

500000 × 2.5×109e× 2×10−3

e = 1.4 kW in the collimator (assuming all the energy is absorbed there).We simulate the x and y co-ordinates of these particles repeatedly. Results should bescaled by a factor of 136

500000 , and then by 1.25× 1016, as for Source 1. Simulation of 1million particles takes around 16 CPU hours.

Results for these 3 sources are shown in the tables and figures below.

5 Results

5.1 Neutron backsplash

Figure 6 shows the neutron flux (the mean number of neutrons per proton beamparticle crossing a particular plane), binned in energy, from Source 1, at 4 positions: di-rectly behind the source window, the far (target) side of the collimator, the near (upstream)side of the collimator, and the very start of the A2T straight, 60m upstream, before thefirst magnet.

−3 −2 −1 0 1 2

0.02

0.04

0.06

0.08

At window

log10Energy(MeV)

neutrons/proton/bin

−3 −2 −1 0 1 2

0.002

0.004

0.006

0.008

Collimator: near monolith

log10Energy(MeV)

neutrons/proton/bin

−3 −2 −1 0 1 2

2e−04

6e−04

1e−03

collimator: upstream

log10Energy(MeV)

neutrons/proton/bin

−3 −2 −1 0 1 2

0e+00

2e−07

4e−07

6e−07

8e−07

start of A2T straight

log10Energy(MeV)

neutrons/proton/bin −9 −8 −7 −6 −5 −4 −3

0.000

0.001

0.002

0.003

0.004

At window

log10Energy

neutrons/proton/bin

Figure 6: Neutron flux at various positions

4

The 4 plots on the left show that the rate falls off rapidly as one gets further fromthe monolith, and also that the spectrum changes shape to some extent. The rate dropsby an order of magnitude between the window and the collimator, and another order ofmagnitude across the 1 metre copper collimator. The rate at the start of the A2T regionis extremely small. This simulation used 10M source particles. Errors on the values in thefirst plot are of order 1%.

The binning in energy is logarithmic for convenience. Each bin (this is the MCNPconvention) contains the rate from the previous bin up to the energy shown, with animplicit zero. Thus the first bin counts the rate from zero up to 1 keV, the second from 1keV to 10 keV, etc. This point is laboured a little because all the thermal neutrons are inthe first bin. The number - compared to fast neutrons - seems surprisingly low. Howeverit may well be correct - or there may be some process which has been omitted. The ploton the right shows a high-statistics sample of the first bin in the top left plot (At window).It can be seen that neutrons do occur down to energies of 0.001 eV, i.e. about 40K. Sothere are thermal neutrons present in the simulation (i.e. it does not apply an unexpectedenergy cut), but the spectrum is not thermal.

We also show comparisons with results obtained by Eric Pitcher, using a similar butdifferent geometry, including a layer of concrete on the floor. He used importance samplingand forced collisions to improve the statistical accuracy in a finite computation time. Hisresults are shown in Figures 7 and 8 for all neutrons and for “thermal” neutrons (definedas neutrons with energy below 0.625 eV, which broadly covers the thermal and epithermalrange). The simulations show a rectangular mesh tally on the yz dimensions. The neutronsbacksplash from the target down the A2T is produced by the proton beam as describedon Source 1. We also have repeated Eric’s simulations on our computers and obtained thesame results.

5

Figure 7: Neutron backsplash by Eric Pitcher.

Figure 8: Thermal neutron backsplash by Eric Pitcher.

Our results are shown on Figures 9 and 10 for our standard geometry, and Figures 11and 12 if an extra concrete wall is included: we did this using a cylindrical concrete wallof inner radius 200cm and 125cm thickness around the beam. We did not use importancesampling or other variance reduction techniques, so as to avoid possible misinterpretations

6

of the results, and as we had the necessary computer power available.

Figure 9: Neutron backsplash: standard geometry.

Figure 10: Thermal neutron backsplash: standard geometry.

7

Figure 11: Neutron backsplash with added concrete wall.

Figure 12: Thermal Neutron backsplash with added concrete wall.

As discussed below, the results of our simulations and Erics are compatible, given thedifferent assumptions, including the fact that we assume different beam energies (2.5 and2.0 GeV respectively) and thus different currents for the same 5MW beam power.

8

1 The overall shape of the neutron flux is broadly similar. The effects of the beam pipeand of the tunnel can be clearly seen. Our simulation included the collimator, from-850 cm to -750 cm, which his does not.

2 The overall normalisation agrees. A typical flux(from Fig. 9) of 2 10−6n/cm2/s, whenmultiplied by the number of protons per second at nominal current, 1.25 1016, gives2.5 1010n/cm2/s, compared to his value(Figure 7) of 3.14 1010n/cm2/s.

3 Imposing a neutron energy upper bound of .625 eV to examine “thermal” neutronsreduces the flux by about two orders of magnitude, and limits the flux outside thebeam pipe.

4 The 125 cm concrete wall acts as a very effective shield. It produces a small increasein the flux inside (in some regions), as can be seen by comparing Figures 9 and 11.Any increase in the thermal neutron flux is small.

Although the total number of neutrons “At window” ( -400 cm) of 0.2 shown inFigure 7 top left, is larger than 0.06 (obtained by taking the typical flux from Figure 9 as2 10−6n/cm2/s multiplied by the surface, π 1002) the discrepancy arises from the way theaverage surface flux is defined in MCNPX using a factor | sec θ|. We’ve chosen to outputthe same mesh tally in our simulation for a direct comparison with the simulations by E.Pitcher.

5.2 Beam losses

Figure 13 shows the flux of particles (per square cm) per Source 2 beam particle, using10M simulated particles, that emerge from a cylinder of radius 1.5 m around the beampipe. There is no sign of angular variation (as expected). The variation along z is basicallygiving back our assumptions of uniform losses between 50 and 20 m upstream.

9

φ

z

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

V11

V12

V13

V14

V15

V16

V17

V18

V19

V20

V21

V22

2 4 6 8

0.0e+00

2.0e−06

4.0e−06

6.0e−06

8.0e−06

1.0e−05

1.2e−05

1.4e−05

1.6e−05

φ

z

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

V11

V12

V13

V14

V15

V16

V17

V18

V19

V20

V21

V22

2 4 6 8

0.0e+00

5.0e−06

1.0e−05

1.5e−05

2.0e−05

φz

V1

V2

V3

V4

V5

V6

V7

V8

V9

V10

V11

V12

V13

V14

V15

V16

V17

V18

V19

V20

V21

V22

2 4 6 8

0e+00

1e−07

2e−07

3e−07

4e−07

5e−07

6e−07

7e−07

8e−07

9e−07

Figure 13: Flux produced from around the beam.The first plot is from uniform losses, the second is clumped at the magnets,the third is like the first but with concrete in the gaps between magnets

Concentrating the losses at the magnets confines the losses to that area of the beampipe.

Completely filling the gaps between and outside the magnets with concrete appearsto reduce the flux to a very small amount.

10

5.3 Induced activity

Table 1a: Activation from Source 1.60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

Collimator 8.18E-06 - - - - - -Long Quad 1 5.13E-09 7.65E-08 4.66E-08 - - - -Long Quad 2 3.98E-09 2.27E-08 1.88E-08 - - - -Long Quad 3 4.87E-11 1.56E-08 6.42E-09 - - - -Octupole 1 5.21E-15 4.29E-09 3.12E-11 - - - -Short Quad 1 0.00E+00 4.97E-09 4.50E-10 - - - -Short Quad 2 2.33E-10 9.65E-09 2.84E-09 - - - -Short Quad 3 0.00E+00 1.99E-09 8.27E-11 - - - -Octupole 2 0.00E+00 6.47E-10 0.00E+00 - - - -Short Quad 4 3.03E-10 1.89E-09 3.11E-09 - - - -Short Quad 5 2.77E-14 7.41E-09 1.79E-09 - - - -Short Quad 6 4.98E-13 1.64E-09 1.54E-09 - - - -Short Quad 7 0.00E+00 3.60E-10 4.30E-11 - - - -Beam Pipe - 3.07E-07 9.86E-07 2.32E-08 2.00E-06 1.60E-07 4.54E-07

Table 1a shows the production of unstable isotopes from Source 1. As stated earlier,this is the number per particle simulated and can be multiplied by 1.25 × 1016 to obtainthe number produced per second of nominal running.

60Co is produced in the collimator and also in the copper of the magnets, though thisfalls rapidly as one gets further from the target. 55Fe and 54Mn are produced in the ironof the magnets but at a very low level. They are also produced in the beam pipe, as are57Co,58Co,51Cr and 56Mn.58Co is the most problematic of these, produced from Nickel inthe steel beam pipe, with a half life of 71 days which is in the problem area.

This is also shown in Figure 14. Here the number of unstable nuclei produced hasbeen multiplied by the appropriate decay rate, showing the basic activity for each isotopein each component. The largest activity is from 56Mn, though with its half-life of 2.6 hthe problem disappears after a short period.

11

Collimator

Long Quad 1

Long Quad 2

Long Quad 3

Octupole 1

Short Quad 1

Short Quad 2

Short Quad 3

Octupole 2

Short Quad 4

Short Quad 5

Short Quad 6

Short Quad 7

Beam Pipe0.0

5.0x10 -7

1.0x10 -6

1.5x10 -6

2.0x10 -6

2.5x10 -6

3.0x10 -6

60Co

55Fe

54Mn

57Co

58Co

51Cr

56Mn

60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

de

cay

rate

(1

/da

ys)

Figure 14: Activity induced by Source 1.

Table 1b also shows the production of unstable isotopes from Source 1, but with extraconcrete added to the model (as described earlier).

Table 1b: Activity induced by Source 1 with modeled concrete.60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

Collimator 8.09E-06 - - - - - -Long Quad 1 4.02E-10 7.85E-08 8.04E-09 - - - -Long Quad 2 9.42E-10 4.86E-08 7.50E-09 - - - -Long Quad 3 2.78E-10 3.62E-08 6.18E-09 - - - -Octupole 1 6.14E-15 5.35E-09 9.83E-12 - - - -Short Quad 1 0.00E+00 2.58E-08 2.19E-11 - - - -Short Quad 2 8.22E-13 1.72E-08 1.51E-09 - - - -Short Quad 3 0.00E+00 1.07E-08 3.53E-12 - - - -Octupole 2 0.00E+00 2.14E-09 0.00E+00 - - - -Short Quad 4 4.00E-15 1.26E-08 1.10E-11 - - - -Short Quad 5 2.78E-14 9.07E-09 3.09E-10 - - - -Short Quad 6 3.50E-10 2.08E-09 1.53E-09 - - - -Short Quad 7 0.00E+00 1.10E-08 4.32E-11 - - - -Beam Pipe - 7.14E-06 1.09E-06 2.47E-08 2.21E-06 8.36E-06 2.08E-05

22Na 24NaConcrete 2.84E-08 4.13E-05

The main active isotopes produced in concrete are 22Na and 24Na. Our simulationspoint out that as well as the predictable appearance of these two isotopes, the production

12

of 55Fe,51Cr and 56Mn increase significatively when concrete is added to the basic A2Tgeometry. This is not well understood but presumably arises as the concrete reflectsneutrons back into the beampipe region, with reduced energies.

This is also shown in Figure 15. Here again the number of unstable nuclei producedhas been multiplied by the appropriate decay rate.

Collimator

Long Quad 1

Long Quad 2

Long Quad 3

Octupole 1

Short Quad 1

Short Quad 2

Short Quad 3

Octupole 2

Short Quad 4

Short Quad 5

Short Quad 6

Short Quad 7

Beam PipeConcrete

0.0

2.0x10 -5

4.0x10 -5

6.0x10 -5

8.0x10 -5

1.0x10 -4

1.2x10 -4

1.4x10 -4

60Co

55Fe

54Mn

57Co

58Co

51Cr

56Mn

22Na

24Na

60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn 22Na 24Na

de

cay

rate

(1

/da

ys)

Figure 15: Activity induced by Source 1 with added concrete.

Table 2a: Activation from Source 2.60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

Collimator 3.24E-03 - - - - - -Long Quad 1 1.69E-03 6.11E-03 1.05E-02 - - - -Long Quad 2 1.68E-03 6.22E-03 1.04E-02 - - - -Long Quad 3 1.56E-03 6.09E-03 9.90E-03 - - - -Octupole 1 6.00E-04 1.39E-03 1.53E-03 - - - -Short Quad 1 1.57E-03 4.96E-03 9.21E-03 - - - -Short Quad 2 1.47E-03 4.60E-03 8.61E-03 - - - -Short Quad 3 1.70E-03 5.34E-03 1.02E-02 - - - -Octupole 2 6.69E-04 1.41E-03 1.70E-03 - - - -Short Quad 4 1.58E-03 4.84E-03 9.21E-03 - - - -Short Quad 5 1.51E-03 4.65E-03 8.70E-03 - - - -Short Quad 6 1.67E-03 5.07E-03 9.50E-03 - - - -Short Quad 7 3.29E-03 9.23E-03 1.84E-02 - - - -Beam Pipe - 2.72E-04 3.70E-03 1.05E-04 7.37E-03 1.13E-04 4.39E-04

Table 2a. shows the production of isotopes for Source 2. They are distributed

13

fairly evenly between the magnets, though the first magnet is higher, as is the collim-ator, presumably because these are not shielded by other magnets. The basic activites areshown in Figure 16.

Collimator

Long Quad 1

Long Quad 2

Long Quad 3

Octupole 1

Short Quad 1

Short Quad 2

Short Quad 3

Octupole 2

Short Quad 4

Short Quad 5

Short Quad 6

Short Quad 7

Beam Pipe0.0

5.0x10 -4

1.0x10 -3

1.5x10 -3

2.0x10 -3

2.5x10 -3

3.0x10 -3

60Co

55Fe

54Mn

57Co

58Co

51Cr

56Mn

60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

de

cay

rate

(1

/da

ys)

Figure 16: Activity from Source 2.

Table 2b. shows the production of unstable isotopes from Source 2 with the modeledconcrete geometry. Again the isotope production in the beam pipe goes up greatly, at leastin some channels, whereas the activity in the collimator and magnets falls. The activitiesare shown on Figure 17.

14

Table 2b: Activation induced by Source 2 with modeled concrete60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

Collimator 4.89E-04 - - - - - -Long Quad 1 1.37E-03 1.58E-02 8.58E-03 - - - -Long Quad 2 1.37E-03 1.59E-02 8.59E-03 - - - -Long Quad 3 1.37E-03 1.66E-02 8.73E-03 - - - -Octupole 1 4.84E-04 2.66E-03 1.26E-03 - - - -Short Quad 1 1.17E-03 1.27E-02 6.96E-03 - - - -Short Quad 2 1.16E-03 1.25E-02 6.96E-03 - - - -Short Quad 3 1.17E-03 1.24E-02 6.91E-03 - - - -Octupole 2 4.83E-04 2.48E-03 1.26E-03 - - - -Short Quad 4 1.17E-03 1.23E-02 6.91E-03 - - - -Short Quad 5 1.16E-03 1.24E-02 6.94E-03 - - - -Short Quad 6 1.15E-03 1.23E-02 6.87E-03 - - - -Short Quad 7 1.12E-03 1.19E-02 6.65E-03 - - - -Beam Pipe - 6.16E-03 3.79E-03 1.02E-04 7.56E-03 7.35E-03 1.80E-02

22Na 24NaConcrete 2.13E-03 6.11E-01

Collimator

Long Quad 1

Long Quad 2

Long Quad 3

Octupole 1

Short Quad 1

Short Quad 2

Short Quad 3

Octupole 2

Short Quad 4

Short Quad 5

Short Quad 6

Short Quad 7

Beam PipeConcrete

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

60Co

55Fe

54Mn

57Co

58Co

51Cr

56Mn

22Na

24Na

60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn 22Na 24Na

de

cay

rate

(1

/da

ys)

Figure 17: Activity induced by Source 2 with added concrete.

Table 3. shows the production of unstable isotopes from Source 3 . The basic activitiesare shown on Figure 18.

15

Table 3: Activation induced by Source 3 in the collimator60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

Collimator 3.98E-02 - - - - - -Long Quad 1 9.79E-08 2.99E-06 6.49E-07 - - - -Long Quad 2 8.02E-09 3.16E-07 6.52E-08 - - - -Long Quad 3 2.25E-09 2.11E-07 1.44E-08 - - - -Octupole 1 1.53E-10 4.27E-08 1.49E-09 - - - -Short Quad 1 1.41E-14 2.66E-08 1.58E-08 - - - -Short Quad 2 1.00E-13 2.29E-08 1.09E-08 - - - -Short Quad 3 1.14E-13 3.38E-08 2.48E-08 - - - -Octupole 2 0.00E+00 1.24E-08 1.20E-11 - - - -Short Quad 4 2.85E-16 1.86E-08 4.74E-09 - - - -Short Quad 5 0.00E+00 7.30E-09 1.04E-09 - - - -Short Quad 6 0.00E+00 7.26E-09 1.97E-09 - - - -Short Quad 7 0.00E+00 1.30E-08 1.09E-09 - - - -Beam Pipe - 4.17E-04 6.35E-04 1.15E-05 1.31E-03 1.63E-04 3.93E-04

Collimator

Long Quad 1

Long Quad 2

Long Quad 3

Octupole 1

Short Quad 1

Short Quad 2

Short Quad 3

Octupole 2

Short Quad 4

Short Quad 5

Short Quad 6

Short Quad 7

BeamPipe0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

60Co

55Fe

54Mn

57Co

58Co

51Cr

56Mn

60Co 55Fe 54Mn 57Co 58Co 51Cr 56Mn

de

cay

rate

(1

/da

ys)

Figure 18: Activity induced by Source 3 in the collimator.

5.4 Induced activity in air

Activity induced in air requires a different treatment as the active nuclei producedby radiation are not fixed in the beamline and shielded by it, but are circulated by a

16

ventilation system which may be closed or may be vented to the atmosphere.

Sullivan [4] gives figures for the activity produced per metre of path length. This isan approximation in that it ignores the energy dependence of the cross sections, but willserve for guidance purposes.

We consider the volume along the beamline outside the beampipe and magnets butwithin a radius of 1.5 m. (This is an order-of-magnitude estimate. ) The path length forneutrons and for protons was found separately.

Source neutron path(cm) proton path (cm)1 0.43 ± 0.01 1.5× 10−4 ± 1.5× 10−6

2 3085.8 ± 1.5 304.1 ± 0.43 543.6 ± 0.9 0.117 ± 0.006

So for source 2, the beam losses, the number of protons in the air is smaller than thenumber of neutrons: for the other sources it is lnegligible.

Sullivan quotes figures for the production rate of positron emitters, taking some sortof average of higher energy hadrons and thermal neutrons, of 352 kBq/second per metreper 1012 particles. Thus for source 2 the figure is:

(30.858 + 3.041)× 7.5× 1010 × 10−12 = 2.5kBq/sec

for the large volume considered this appears to be a very small number.

For 41Ar,which has caused problems elsewhere (at T2K) the figure is 1.9 rather than352. kBq/sec, and the numbers even smaller

6 Discussion

So far the numbers seem small and unalarming from the point of view of safety and ofmaterial damage, though they could give backgrounds that would affect sensitive detectors.

Continual cross checks (internal and external) are needed to make the figures firmer.

17

Appendix 1 Materials

We consider the following elements in the composition of the beamline and surroundingarea, and the list of possibly relevant reactions and unstable isotopes formed is (currently)as follows:

Element Location Isotopic Products Reaction t 12

NotesComposition

N Air 14N(100%) 11C (p,α) 20 minSi Concrete 28Si(93%) 28Al (n, p) 2.2 m Small τNa Concrete 23Na(100%) 24Na (n, γ) 15 hCa Concrete 44Ca(2%) 45Ca (n, γ) 165dAr Air 40Ar(99.6%) 41Ar (n, γ) 1.8 hCr Steel 54Cr(2.4%) 55Cr (n, γ) 3.5 min Small τ

50Cr(4.3%) 51Cr (n, γ) 28 dFe Magnets and steel 54Fe(6%) 55Fe (n, γ) 2.6y

54Mn (n, p) 312 d58Fe(0.3 %) 59Fe (n, γ) 44 d Low %

Co Steel 59Co(100%) 60Co (n, γ) 5.3 yNi Steel 58Ni(68%) 57Co (n, np), (n, d) 272 d

57Ni (n, 2n) 1.5 d58Co (n, p) 71 d59Ni (n, γ) 75,000 y Large τ

62Ni(3.7%) 63Ni (n, γ) 100y64Ni(1.2%) 65Ni (n, γ) 2.5 h

Mn Steel 55Mn(100%) 56Mn (n, γ) 2.64 hMo Steel 100Mo(9.6%) 99Mo (n, 2n) 2.74 dCu Coils, Collimator 63Cu(70%) 64Cu (n, γ) 12 h

65Cu(30%) 66Cu (n, γ) 5 min60Co (n,α) 5.1 y

W Collimator 186W(30%) 187W (n, γ) 1 day

We calculate the production of 51Cr and 55Mn, even though the fraction of the parentCr and Mn isotopes in steel is small, due to their very large cross sections of 17 and 13barn, respectively.

The composition of ‘concrete’ varies according to its intended use. The one we use is(taken from Wikipedia):

Concrete (density 2.35g/cm3)Element Composition Composition Normalised

(by weight) (by number of atoms)

O 0.4983 0.0312 0.584Si 0.3158 0.01125 0.21

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Na 0.0171 0.00074 0.01394Ca 0.0826 0.00206 0.038Al 0.0456 0.00169 0.03169K 0.0192 0.00049 0.0092Fe 0.0122 0.0002184 0.004S 0.0012 0.0000374 0.0007Mg 0.0024 0.000098 0.00185H 0.0056 0.0056 0.105

Steel has a more definite specification. That used for the beam pipe is specified asSS316 steel (density 8 g/cm3)Element Composition Composition Normalised

(by weight) (by number of atoms)

Fe 0.70 1.2533 0.6962Ni 0.10 0.170 0.094Cr 0.16 0.3076 0.1708Mo 0.02 0.020 0.01Mn 0.02 0.0364 0.02K 0.045e-2 1.15e-5 6.38e-6S 0.03e-2 9.35e-6 5.19e-6N 0.1e-2 7.14e-5 3.96e5C 0.03e-2 2.5e-5 1.38e-6

We do not consider Aluminium, on the grounds that there is none present in thecurrent design. If it is present then it can produce 22Na, with a 2.6 year half life, and thismust be included. We do not consider the effect of Zinc (though there may be traces inthe Copper), or of any Aluminium, Caesium, Europium or other additives in concrete.

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7 References

[1] D B Pelowitz (Ed) The MCNPX User’s Manual, Version 2.6.0, Report numberLA-CP-07-1473 (2008)

[2] S Agostinelli et al., Geant 4 – a simulation toolkit Nucl. Instr. & Meth. A 506,p250 (2003)

[3] J D Cossair Radiation Physics for Personnel and Environmental Protection, Fer-mliab report TM-1834, Revision 9B (2007)http://www-esh.fnal.gov/TM1834 PDF Files/TM 1834 Revision 9B.pdf

[4] A H Sullivan A guide to radiation and radioactivity levels near high energy particleaccelerators, Nuclear Technology Publishing (1992)

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