Tim Jones Industry Team Project Report

PH30096 Report, Tim Jones Page | 1
Skyshine:
Development of a Radioactive Waste Store
Design and Optimisation Tool
Tim Jones, 20662
University of Bath, 20/4/2016
Abstract
It has recently become of inceasing interest to evaluate the effect known as ‘Skyshine’, a
phenominon where x-ray or gamma radiation is found to reflect off the atmosphere back
towards the ground. As this effect was not previously considered significant, radioactive waste
stores were designed with relativiely thin concrete roofs. As a result, Skyshine radiation levels,
potentially leading to harmful doses in surrounding areas, now need to be considered for future
design of waste stores. This report looks to compare a complex Monte Carlo N-Particle
(MCNP) model with an analytic method using a commonly accepted equation for Skyshine.
The results showed that the analytic model underestimated the potential dose for all input
conditions, ranging from 43.4 – 188.1 times less than that predicted by the MCNP model. This
difference was mainly attributed to the effect of scattering events both within the concrete roof
and in the air surrounding the waste store. It was therefore concluded that the analytic model
is not a suitable substitute for the specialist MCNP software and should not be used in future
waste store design until a method for accurately evaluating scattering is implemented in the
model.

Table of Contents
1. Introduction ------------------------------------------------------------------------------------------------- 3
2. Method -------------------------------------------------------------------------------------------------------- 4
2.1 Skyshine Calculation --------------------------------------------------------------------------------------------- 4
2.2 Analytic Method --------------------------------------------------------------------------------------------------- 6
2.2.1 Energy Dose Calculation------------------------------------------------------------------------------------ 7
2.2.2 Shielding and Build-Up Factors --------------------------------------------------------------------------- 7
2.3 MCNP Method ----------------------------------------------------------------------------------------------------- 9
3. Results--------------------------------------------------------------------------------------------------------11
4. Discussion ---------------------------------------------------------------------------------------------------13
5. Conclusion---------------------------------------------------------------------------------------------------17
References ------------------------------------------------------------------------------------------------------18
Appendices -----------------------------------------------------------------------------------------------------20
A.1 Complete Results for Model Comparison----------------------------------------------------------------20
A.2 Calculation of Additional Solid Angle Component Due To Reflection -------------------------22
Acknowledgements and Personal Contributions
I would like to thank the rest of my team for their support and contributions to this project.
Specifically:
 Fintan O’Brien for obtaining the dose values described in Section 2.2.1, contributing to
the analytic program and writing the majority of the paper submitted for peer review.
 Sophie Trerise and Ryan Meadows for their work on the shielding and build-up factor
calculations described in Section 2.2.2, contributions to the analytic program and
producing the poster used to present this work at the SRP annual conference 2016.
A large thanks must also go to Arcadis in their support and guidance throughout the project,
particularly Peter Bryant and Valentin Haemmerli. In addition to this, I would like to
acknowledge Valentin for writing the MCNP model, giving continuous feedback of his
progress in comparison to the analytic model and offering additional explanations for the
discrepancy between the two model’s results.
My specific personal contribution, in addition to general problem solving and overall support
to the rest of the team, was as follows:
 Writing the majority of the analytic model
 Producing the energy spectra described in Section 2.2.1
 Calculating the additional primary reflection component to the Skyshine formula
The industry project team did all other work, such as result analysis, collectively.

1. Introduction
The mechanism for which both photon and neutron emissions are scattered by the atmosphere
and reflected back down to Earth, commonly known as ‘Skyshine’, has been of great interest
in many key areas: from its effect upon infrared aircraft lock-on systems in the defence industry
[1] to its influence in the design of roof shielding above x-ray machines in laboratories [2]. It
has also been shown to interfere with radio detection systems over long distances [3],
demonstrating the issues surrounding the occurrence of Skyshine. There has been much work
conducted in assessing the contribution of neutron radiation, especially that emitted from
particle accelerators [4] [5] [6], however little work has been completed regarding the Skyshine
of photons emitted from nuclear waste stores.
Historically, waste stores have been constructed with thick concrete walls to prevent radiation
directly escaping and reaching nearby workers and/or surrounding residents. However until
recently, Skyshine was not considered to contribute to radiation dose levels and hence stores
were made with relatively thin concrete roofs with little attenuation. After fears have recently
grown regarding the potential exposure pathway, Arcadis (a leading global natural and build
asset design and consultancy company) require the quantification and mitigation of this risk. It
has been shown for medical particle accelerators, the effect of Skyshine reaches a peak at very
close distances before dropping thereafter [7] and hence Skyshine needs to be evaluated
primarily for workers and nearby residents to such waste stores.
A common way of simulating radioactive behavior is the use of specialist software Monte Carlo
N-Particle (MCNP), which works by modeling the life of each emission and determining
specific aspects of their average behavior (such as typical distances travelled, changes in energy
and direction due to scattering events etc.). This has an advantage over deterministic methods,
as the latter solves for overall average particle behavior whereas MNCP does not need to use
averaging approximations in space, energy and time [8], therefore is well suited to model
complicated, 3D systems and generate detailed information regarding all aspects of physical
data.
However, MNCP is not user friendly; it requires specialist training in order to write the input
files needed to run simulations. The cost of such training, along with costs associated with
obtaining the simulation software, makes the model expensive and requires significant
investment. In addition to this, it not a flexible model; small changes to the system’s input
conditions and/or geometries can require extensive alterations to the input files. Due to the
nature of modeling a large amount of emission paths, the computation time to run simulations
is also very large.
Although MCNP is widely recognized in the industry, it is therefore attractive to find a cheaper,
less time-consuming solution that still gives an accurate evaluation of Skyshine in order to
counteract these disadvantages. This investigation looks to create such a model, named
‘analytic’ in the report. It then compares the results obtained through MNCP to that of the
analytic method in order to determine to what extent the results match, and evaluate whether
the analytic model can serve as a suitable substitute in calculating Skyshine doses for the design
of future nuclear waste stores.

2. Method
2.1 Skyshine Calculation
To investigate the contribution of Skyshine to the dose a distance 𝑑 𝑠 away from the source, the
geometry in Figure 1 was considered. A radioactive source (contained within a standard waste
drum) was positioned in the middle of a typical waste store, external dimensions 20 x 20 x
20m. The figure emphasizes the difference in concrete thickness between the walls and roof; it
is not to scale.
Figure 1. The geometry of the simulation used for both methods. The orange dotted line
shows the potential exposure pathway to an observer via Skyshine.
The cylindrical waste drum, an example of a typical container used in industry, had a height
and diameter of 1.3m and 1.1m respectively and a lid thickness of 10cm (similar to [9]). The
drum was made from type 304 stainless steel, composing of approximately 70% iron, 18%
chromium and 12% nickel (plus other small contributions of other elements, assumed
negligible) at an overall density 8.0 g cm-3
[10]. The drum was positioned in the centre of the
store, with the density of concrete taken as 2.35 g cm-3
[11]. As the investigation was purely
interested in Skyshine, radiation transmitted through the walls of the store was not considered,
and the thickness of the walls and ceiling were assumed negligible when calculating
geometrical properties of the system.
It was proposed in NCRP 151 [12] that the dose, 𝐷, due to Skyshine a distance 𝑑 𝑠 away from
the source is given as
𝐷 =
2.5 × 10−2
𝐷0Ω1.3
(𝑑 𝑠 𝑑𝑖)2
, (1)
where 𝐷0 is the dose 1m above the top surface of the drum, 𝑑𝑖 is the distance between the top
surface of the drum and 2m above the waste store, 𝑑 𝑠 is the distance away from the source

and Ω is the solid angle subtended by the square roof. For a square aperture, the solid angle is
given by the equation proposed by [13]
Ω = 4𝑎𝑟𝑐𝑠𝑖𝑛
𝑎2
𝑎2 + 4ℎ2
, (2)
where 𝑎 is the side length of the square aperture and ℎ is the distance from the source to the
aperture (as shown in Figure 1).
To calculate 𝐷0, it is common to use a reference distance when considering the reduction in
dose with increasing distance. The MCNP model takes a reference distance 10cm above the
top surface of the drum (due to the difficulty of interpreting dose on the surface). When the
size of the source is similar in size compared to the distance (which is the case for the geometry
considered here), the dose is assumed inversely proportional to distance [14], therefore the dose
was calculated to decrease by a factor of 10 (1m is 10 times further than the reference distance
of 10cm). This assumption was used in both models to make the results more comparable.
Two sets of radioactive waste were modelled, representing typical activity levels for different
applications. The first was a mixture of PWR sludge and water filters and the second was from
the waste stream 3N02 Hinkley Point B (HPB) sludge [15] (PWR and HPB refer to two specific
nuclear power plants, with sludge a commonly used phrase to describe particular types of
nuclear waste. Both are not important for this investigation as Skyshine only depends on the
source’s emissions, therefore the names are used solely as labels for clarity in results within
this report). The waste was assumed to be intermediate: highly radioactive, yet does not
generative heat. Both inventories were supplied by Arcadis and are given in Table I.
Table I. The two inventories for the radioactive waste contained within the waste drum
evaluated in the report.
Radionuclide 1) PWR sludge initial activity
(Bq)
2) 3N02 HPB sludge initial
activity* (Bq)
58
Co 8.5E+10 3.499E+11
60
Co 3.5E+10 3.345E+08
55
Fe 9.5E+08 6.998E+11
59
Ni 1.9E+05 6.998E+08
129
I 1.5E+01 0
137
Cs 1.5E+09 2.729E+08
110m
Ag 1.7E+10 2.099E+09
* 1 Bq is equal to 1 decay per second, by definition
** Original data given in an ‘activity concentration’, therefore activity obtained by multiplying with the volume
of the 500L drum
Only the isotopes listed in Table I were considered for this investigation, due to their particular
importance to Arcadis (some have large emission energies, some have very long half-lives
etc.). Other isotopes of interest (such as 63
Ni, 90
Y and 90
Sr) were found to only emit β-radiation,
which is completed attenuated by any thickness of concrete, and hence were not included in
Table I. In order to consider all emissions of the isotopes upon decay, the decay chain was
important to be considered; a particular isotope may decay into one or more radioactive
‘intermediate’ isotopes, which can subsequently emit further radiation at different energies. In

addition to this, some isotopes decay into multiple progeny nuclei with different branching
ratios, therefore this must be considered when determining the various emissions for a given
set of initial activities. Table II shows the decay data for each of the isotopes that was used in
both models. Emissions lower than 1% were considered negligible and hence were ignored. It
is worth noting that the decay chain of 110m
Ag is extremely complex and therefore, in this
investigation, only the largest 3 emissions were considered.
Table II. Radionuclide data, taken from [16]
Radionuclide Progeny
nuclei
Half-life Photon
emission(s)
(MeV)
Branching ratio
58
Co 58
Fe 70.8 days 0.511
0.811
30%
99%
60
Co 60
Ni 5.27 years 1.173
1.333
100%
100%
55
Fe 55
Mn 2.68 years 0.006
0.007
25%
3%
59
Ni* 59
Co* 1.01E5 years* 0.0024* 100%*
129
I 129
Xe 1.57E7 years 0.029
0.034
0.04
57%
13%
8%
137
Cs 137
Ba, 137m
Ba 30.2 years 0.032
0.036
0.662
6%
1%
85%
110m
Ag 110
Ag, 110
Pd,
110
Cd
249.8 days 0.658
0.885
1.505
94%
73%
13%
*No data for 59
Ni in [16], therefore data taken from [17]
The two models were run for many different scenarios in order to assess under which conditions
(if any) results become comparable or diverge. For this reason, both models were run using 50,
75, 100, 150, 200 and 250m as the distance from the waste store wall, (𝑑 𝑠 − 10). To evaluate
how Skyshine dose changes with time, the models were set to calculate the Skyshine dose
initially and 15 years after emplacement. Finally, to investigate the effect of changing the
thickness of the concrete roof (which could be altered to see at what thickness Skyshine has
negligible contribution, therefore can be neglected), the models were run for 5 thicknesses: 10,
20, 30, 40 and 50cm.
2.2 Analytic Method
The analytic method was split into two well-defined parts. The first calculated the dose 1m
above the drum, ignoring any shielding effects. This involved taking each isotope’s activity,
calculating the number of photons emitted per second and hence finding the corresponding
dose. The second calculated the attenuation due to the drum’s lid and the concrete roof of the

waste store, so that it can be considered when calculating the Skyshine dose. Section 2.2.1 and
2.2.2 contain further details on the method of calculation.
2.2.1 Energy Dose Calculation
Using the data found in Table I and Table II, each isotope’s activity after 15 years was
calculated, using the simple relationship between half-life, 𝑡1/2, and decay constant, 𝜆,
𝜆 𝑡1/2 = ln(2), (3)
which was then used to calculate the new activity at time 𝑡, 𝐴(𝑡), based upon each individual
initial activity 𝐴0,
𝐴(𝑡) = 𝐴0 𝑒−𝜆𝑡
. (4)
Using the definition of activity, the data was turned into an emission spectrum by the
multiplication of the activity of the isotope with the branching ratio for the emission energy,
resulting in the number of emissions per second for each energy.
To convert this spectrum into a dose, the number of emissions was multiplied by the dose per
photon. The dose data was taken from Table A.21 of ICRP publication 74 [18], linearly
interpolating to obtain each individual value.
2.2.2 Shielding and Build-Up Factors
To incorporate the attenuation due to both the top surface of the drum and the concrete roof of
the waste store, the shielding factor of each material was evaluated. The intensity of radiation,
𝐼(𝑥), diminishes as it travels through a material of thickness 𝑥 is given by
𝐼(𝑥) = 𝐼0 𝐵(𝑥)𝑒
−
𝜇
𝜌
𝜌𝑥
, (5)
where 𝐼0 is the incident intensity at 𝑥 = 0, 𝐵(𝑥) is the build-up factor, 𝜇 is the linear attenuation
coefficient and 𝜌 is the density of the material [19]. Data for 𝜇 was given as the mass attenuation
coefficient 𝜇 𝜌⁄ , hence the requirement for density in Equation (5). Figure 2 shows the mass
attenuation coefficient for iron, taken from [20]. A similar set of data was used for concrete.
It was found that the differences between the mass attenuation coefficients of chromium and
nickel compared to iron were negligible, therefore the top lid of the steel drum was modelled
using the data in Figure 2, using linear interpolation to obtain attenuation coefficients for
individual photon energies. It is worth noting the sharp increase in 𝜇 𝜌⁄ at approximately
7 × 10−3
𝑀𝑒𝑉. This represents a ‘K-Edge’ transition; photon attenuation is greatly increased
as the photon energy corresponds to a transition in the K shell (1S) electron of the absorbing
material, therefore a photon with an energy slightly higher than the edge transition energy is
more likely to be absorbed than an energy slightly below [21]. The data given in [20] uses two
instances of the same photon energy (with different mass attenuation coefficients) to represent
this edge transition. Hence, to allow the linear interpolation to complete successfully, the lower
attenuation value’s energy was reduced by 1eV.

Figure 2. The mass attenuation coefficient as a function of photon energy for iron (solid line)
[20].
The build-up factor is defined as the ratio of the primary radiation and secondary radiation
(scattered) intensity compared to only the primary radiation at a given point in space [19]. For
this reason, the build-up factor increases as the thickness of the material increases, as the
amount of scattered radiation also increases. The build-up factor was calculated using the
number of mean free paths, 𝑁 𝑚𝑓𝑝, within a material of thickness 𝑙, where
𝑁 𝑚𝑓𝑝 =
𝑙
𝜇
=
𝜌
𝜇
×
𝑙
𝜌
. (6)
This was then combined with data from the Oak Ridge National Laboratory (ORNL) [22],
interpolating to give individual values. This process was completed for the 10cm drum lid and
the 5 thicknesses of concrete. Table III shows the data obtained for Iron, with similar sets of
data gathered for each thickness of concrete.
It is worth noting that the ORNL data only contained values up to 40 mean free paths yet for
some emissions, 𝑁 𝑚𝑓𝑝 was more than 40. This presented problems in obtaining a build-up
factor in these instances, however it was found that this occurred only for low energy emissions,
which are mostly attenuated by the material. This made the build-up factors negligible in
calculations and were therefore taken as 1 (in Table III, these instances are represented with
dashes to be clearly distinguishable).
The shielding factor due to iron was incorporated after calculating the dose from each emission
energy, summing to obtain a value for 𝐷0. The concrete shielding was applied after calculating
the Skyshine dose for each emission energy, again summing to obtain an overall dose due to
Skyshine.

Table III. Build up factors in iron at source emission energies.
Energy (MeV) Linear Attenuation
Coefficient Iron (m-1
)
Build-up Factor
0.511 0.083319 11.689
0.811 0.066615 7.1841
1.173 0.055502 5.0751
1.333 0.05194 4.8671
0.006 84.84 -
0.007 56.352 -
0.0024 1198.6 -
0.029 9.9264 -
0.034 6.3572 -
0.04 3.629 -
0.032 7.2666 -
0.036 5.4478 -
0.662 0.0739 9.3395
0.658 0.0741 9.3505
0.885 0.064025 7.0103
1.505 0.048739 4.646
2.3 MCNP Method
The MCNP model was completed by Arcadis independently from the analytic model. Key data,
such as the dose 1m above the drum, the solid angle subtended by the roof of the waste store
etc. was passed between the two teams to ensure both models were using the same input
parameters and was used as a check throughout the investigation; maximising the number of
consistent values minimised potential reasons for discrepancies between the results. This
section gives a brief overview of the MCNP model, highlighting key assumptions and
parameters used in creating the simulation. As previously discussed, the geometry of the
problem was as written in Section 2.1.
In order to define when the MCNP model needed to stop simulating the paths of photons, it
required an outer ‘universe size’ to be defined (past this, world-lines ceased to be modelled).
This prevents the program wasting computational time simulating activity beyond areas of
interest. The boundary was set to a hemisphere of radius 2 mean free paths of the most energetic
emission, as it can be assumed the main component of Skyshine is attributed to the ‘first
collision’ with the atmosphere [23]. This resulted in a ‘universe’ radius ~0.62 km.
One method of reducing simulation time is the introduction of ‘weight windows’ into the
model. This defines areas of importance for simulating the paths of emissions. For example,
the area immediately surrounding the waste drum is of high importance as all photons originate
from this section, whereas areas far away from the waste store at the edge of the universe will
have less impact upon the Skyshine dose and therefore will be less important. MCNP handles
this by implementing a ‘Russian Roulette’ process; when photons travel from an area of high

importance to an area of low importance, a particular fraction of photons are terminated. To
conserve energy, the remaining photons have their weight increased, which does not have a
significant effect upon the results of the simulation (the average weight remains constant) yet
avoids extensive simulation of unimportant photons. Figure 3 shows the distribution of weight
windows implemented in the MNCP model using a series of spherical segments and cone
‘shells’, following the approach described in [24].
Figure 3. A cut away of the weight windows surrounding the waste store, as defined in the
MCNP model. The rainbow of colours represents the scale of importance, with blue
representing maximum weight and the red, minimum.
The concrete walls of the waste store were modelled as 2 mean free paths thick, then giving
way to a ‘void’. This allowed photons to scatter, yet prevented direct transmission (particle
histories terminated upon reaching the void). Radiation reflected from the ground, known as
‘Groundshine’, was not considered. Although making the results less objectively accurate, it
made them more comparable to that of the analytic model. The physics settings of the model
were set to not include bremsstrahlung and coherent scattering. Doppler broadening and
photonuclear interaction were also not considered. By doing so, the computational run time of
the simulation was drastically reduced, without significantly compromising the accuracy of the
results.
The model geometry was filled with air, density 0.001225 gcm-3
(taken from the standard
library included with MCNPX). Ring detectors were positioned at distances 50 – 250m away
from the waste store, as discussed in Section 2.1, 100 cm above the ground. Details regarding
how the problem geometry was created and further initialisation parameters in the model are
not included in this report as they were not relevant to the investigation.

3. Results
Both models were run using the input parameters discussed in Section 2.1, gathering a range
of data to compare the analytic method to the MCNP model. The results obtained for 3N02
HPB sludge at 𝑡 = 0 for concrete roof thicknesses 10cm and 50cm are shown in Figure 4,
and equivalent results for PWR sludge are shown in Figure 5. The complete set of results are
shown in Appendix A.1 Complete Results for Model Comparison, however are not included
here as all data is similar and displays the same trends.
Figure 4. Results obtained from both models for the 3N02 HPB sludge set of activities at time
t = 0.
Figure 5. Results obtained from both models for the PWR sludge set of activities at time t = 0.
1.00E-12
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
0 50 100 150 200 250
Dosage[mSv/hr]
Detector distance [m]
H.C.10cm H.C. 50cm MCNP 10cm MCRP 50cm
1.00E-12
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
0 50 100 150 200 250
Dosage[mSv/hr]
H.C. 10cm H.C. 50cm MCNP 10cm MCRP 50cm
MCNP 50cmAnalytic 50cmAnalytic 10cm MCNP 10cm
MCNP 50cmAnalytic 50cmAnalytic 10cm MCNP 10cm

Both models show the same general trend: Skyshine dose was found to decrease with both
increasing distance from the waste store and roof thickness. However, the analytic model
clearly underestimates the dose compared to that obtained through the MCNP model. Typically
predicting values approximately 2 orders of magnitude smaller, the analytic gave lower doses
due to Skyshine for all input parameters used in this investigation. For the initial dose, the
factor-difference (ratio of the MCNP result compared to the analytic value) over all concrete
roof thicknesses and distances ranged from 43.4 – 141.5 for 3N02 HPB sludge and 45.9 – 167.0
for PWR sludge. Considering Skyshine after 15 years, the factor-difference range became 46.6
– 181.3 and 46.5– 188.1 respectively. Table IV shows the average factor-difference over all
distances for all conditions.
Table IV. The average factor-difference over all distances between the results obtained
through the analytic and MCNP models.
Roof Thickness / cm
10 20 30 40 50
3N02 HPB
Sludge
𝑡 = 0 115.7 108.4 80.1 65.3 69.3
𝑡 = 15 𝑦𝑒𝑎𝑟𝑠 150.6 93.6 85.9 76.9 64.1
PWR
Sludge
𝑡 = 0 138.6 97.0 82.4 72.1 62.8
𝑡 = 15 𝑦𝑒𝑎𝑟𝑠 157.6 92.1 85.2 74.1 63.2
The results show that there is no real difference in the discrepancy of the models between the
two initial sets of activities. It is worth noting however that increasing the time resulted in a
general increase in the factor difference, showing that the reason for the discrepancy between
the models becomes more prominent with increasing time.
There was also found to be a variation in the factor-difference between individual conditions.
Considering roof thicknesses, the results show the factor-difference decreased with increasing
roof thickness, indicating the analytic model was providing a more accurate evaluation of
Skyshine compared to thinner roofs. The factor-difference was found to approximately half
between the limits of roof thickness. For example, the initial Skyshine factor-difference for
PWR sludge reduced by 54.7%, when comparing the dose with a 50cm roof to that of a 10cm
roof.
Finally considering the distance from the waste store, the factor-difference was found to peak
consistently at approximately 100m. This was found for all concrete thicknesses, both initially
and after 15 years and for both inventories. For example, the dose for 3N02 HPB sludge 15
years after emplacement was found to be 67.4% higher at 100m than at 250m, in addition to
being 41.8% higher than at 50m.

4. Discussion
As Figure 4 and Figure 5 show, both sets of data follow the same general trend. This is also
observed in the rest of the data. This shows there are similarities between the two models in
their simulation of the Skyshine problem; both MCNP and the analytic model demonstrate dose
decreasing with distance. This is to be expected; as the distance increases, less radiation will
scatter in the required direction to reach the greater distance and therefore Skyshine dose will
decrease. Further work is required to assess the long-range behaviour, however Skyshine is
thought to be a short-range effect [7] therefore is not considered important in the nuclear
industry.
The results also show Skyshine dose decreasing with concrete roof thickness. This is also to be
expected; as the thickness increases, so does the shielding effect and thus less radiation escapes
and reaches the atmosphere. Although not explored here, a similar observation is expected if
the thickness of the stainless steel drum were to increase. Both models are able to explore the
effect of changing drum dimension, composition and thickness in order to determine the
optimal solution, which is suggested as further work required when designing future waste
store solutions that minimise Skyshine (it may be more cost-effective to change the thickness
of the steel rather than the concrete roof). By altering the roof thickness, and considering the
safe dose limit for workers or surrounding residents, it can also be determined what thickness
of concrete roof is required to provide safe dose levels. The analytic model is not well suited
to this due to the nature of manually calculating build up factors and shielding coefficients for
each concrete thickness. Further work on improving the analytic model would look to find an
easier, more autonomous method of determining the shielding coefficients.
However that being said, there is a clear discrepancy in the results of the two models; the
MCNP model predicts Skyshine doses much higher than the analytic model. Assuming MCNP
gives the more accurate real-world solution (Monte Carlo simulations are used as the
benchmark for validating Skyshine models and verifying their results [25]), the analytic method
grossly underestimates dose and therefore should not be used in simulations. The difference
emerges due to intrinsic differences between the two models. Given that both models use the
same underlying assumptions, agree upon the solid angle, source terms and emissions, dose
1m above the drum and build-up and shielding factors the difference must lie within the
treatment of scattering within each model.
As previously discussed, MCNP simulates the movement of each photon, including reflection
and scattering from surfaces within the waste store. The initial analytic model did not account
for this, therefore further steps were taken to investigate surface-effects as the underlying cause.
Using the same method as discussed in Sections 2.1 and 2.2, an additional reflection component
was added to the analytic model. It was assumed only radiation reflected once was emitted
from the roof (multiple internal reflections were considered negligible). The main change
occurred in the solid angle calculation; Ω was made larger to accommodate reflections from
the walls, as shown in Figure 6. Equation (2) was used to calculate the solid angle, using a
‘projected roof width’ of 60m. Appendix A.2 Calculation of Additional Solid Angle Component
Due To Reflection demonstrates how this value was calculated.

Figure 6. A diagram showing single reflection from the surface of the concrete walls of the
waste store (red dashed lines). Taking the point of contact with the wall, this can be extended
to give a projected solid angle (solid red lines) used in an improved equation for Skyshine.
All other dimensions are as shown in Figure 1, with the solid black lines representing direct
emission.
Subtracting the new solid angle from the previous ‘direct’ solid angle gave the solid angle due
to reflection, Ω′, which was then incorporated into Equation (1) to give a new estimate for
Skyshine dose 𝐷′
𝐷′
=
2.5 × 10−2
𝐷0
(𝑑 𝑠 𝑑𝑖)2
(Ω1.3
+ 𝑟Ω′1.3
) , (7)
where 𝑟 is the reflection coefficient of incident radiation on concrete. An initial estimate of 𝑟
was taken to be 0.1 [26] and all other variables were kept constant from the initial investigation.
For completeness, the model was also run assuming complete primary reflection to give a
theoretical maximum value for the analytic method, giving an indication whether reflection is
a major contributor to the difference between the models. All results obtained are included in
A.1 Complete Results for Model Comparison.
The results for initial Skyshine with a 10cm thick roof for 3N02 HPB sludge are shown in
Figure 7. Using a reflection coefficient of 0.1 increased the average Skyshine dose over all
distances by 36%, showing that primary reflection significantly changes the dose obtained
using the analytic method. Secondary reflection (i.e. radiation reflected twice before leaving
the waste store), although not considered in this report, may also give a significant contribution
and therefore should be investigated in further work.
However despite this increase, the difference between the results of the two models is still
large. The average factor-difference was reduced to 84.9, yet the results are still approximately
two orders of magnitudes lower than the MCNP data. Even assuming complete reflection, the
results remained over an order of magnitude larger; the average factor-difference was found to
be 25.0. This therefore implies that reflection is not the main reason for the discrepancy in the
results.

Figure 7. The initial Skyshine dose for 3N02 HPB sludge and a 10cm thick roof, with the
consideration of primary reflection from the waste store’s walls. The original data from the
analytic and MCNP models are included for comparison.
Although reflection has been discounted, another potential source of the difference is scattering
from the surfaces of the waste container. Due to the relatively simple nature of the analytic
model, and its dependence on photon energy, scattering cannot be modelled without the use of
specialist software. For this reason, it was not possible to include scattering events in the
analytic model. However, the MNCP model was run with the exclusion of scattering to give a
better representation of the physics simulated in the simple model. Two events were excluded:
scattering from the walls of the waste store and scattering from the sides of the drum.
The results found the dose did indeed decrease when scattering was not considered; again for
3N02 HPB sludge with a 10cm roof thickness and at 𝑡 = 0, the dose 50m from the waste store
was found to reduce from 4.69× 10−7
to 3.70× 10−7
mSv/hr. However, this reduction was not
sufficient to make the results from the two models comparable, therefore the source of the
difference lies outside of the waste store.
It is assumed that the main reason for the discrepancy between the two models is therefore
scattering both inside the concrete roof and in the air above the waste store. MCNP treats this
fundamentally differently to the analytic model, which makes no attempt to consider scattering
events due to their complex nature. Figure 8 demonstrates this; many photon paths are affected
by scattering, demonstrating its occurrence and need for consideration. Even secondary
scattering events (i.e. photons scattering for a second time), despite largely reducing the
photon’s energy, have been found to greatly affect the Skyshine dose.
To verify this, the MCNP model was changed to bring the world boundary to 2m above the
waste store roof. This minimised the number of scattering events that occurred in the air above
the store. It was found that by doing so, the dose was reduced to a comparable value to that of
the analytic model. For example, the initial Skyshine dose with a 10cm thick roof containing
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
0 50 100 150 200 250
Dosage[mSv/hr]
H.C. r = 0 H.C. r = 0.1 H.C. r = 1 MCNPMCNPAnalytic, r = 0 Analytic, r = 0.1 Analytic, r = 1

3N02 HPB sludge was found to be 7.58× 10−9
mSv/hr 50m from the store. Compared to the
original analytic result of 4.58× 10−9
mSv/hr, the values were of the same order of magnitude.
Incorporating a reflection coefficient of 0.1 brings the results to within 18% of the reduced
MCNP Skyshine dose. This demonstrates the capabilities of the analytic model to predict
correct order of magnitude estimates of Skyshine dose, however only under non-scattering
conditions.
As well as this, scattering events inside the concrete roof also have an effect. Comparing the
images shown in Figure 8, image (b) has many photon paths approximately directly upwards.
These photons are unlikely to contribute to Skyshine doses at larger distances from the store
due to the vertical nature of their paths. However, the introduction of even a 10cm roof (shown
in (a)) gives rise to more photons traveling in directions other than straight up. This in turn
contributes more to Skyshine at larger distances from the waste store, therefore can be expected
to lead to higher values for Skyshine dose compared to a model that does not consider scattering
events.
The neglect of scattering can also explain the increase in factor-difference over time. As the
activity of the source decreases, the number of photons emitted from the waste store also
increases. This means that scattering events causing photon propagation in the direction of the
observer will have a larger, more significant contribution. This increases the importance of
using specialist software to accurately predict Skyshine doses over time.
The reason for the factor-difference peaking at approximately 100m is not explored here. It
may be a result of scattering preferably focusing on a given point (dependent upon initial
conditions), hence the difference between MCNP and analytic is a maximum at this point.
Further work would be to explore this theory, determining more accurately the distance at
which the difference peaks and investigating how this changes with starting parameters.
As previously discussed, neither model evaluated reflection from the ground (Groundshine)
contributing to Skyshine. This effect can contribute as much as 20% of the dose in MCNP
simulations [23], therefore future work should look to include Groundshine in both models to
investigate its effect on the results.
(a) (b)
Figure 8. A small proportion of photon tracks exiting the waste store building with (a): a
10 cm concrete roof and (b): no roof, simulated by the MCNP model. The square shape in
the small semi-circle represents the waste store.

5. Conclusion
Skyshine (the reflection of radiation from the atmosphere, directing it back down towards the
ground) has been suggested to create a potential exposure pathway when evaluating the dose
surrounding nuclear waste stores. This report compared two methods of simulating this dose -
Monte Carlo N-Particle (MCNP) and a relatively simple analytic model - with the aim of giving
an indication as to the suitability of the analytic method for use in the design of future waste
stores.
A typical 20x20x20m waste store was modelled, containing a stainless steel waste drum in the
centre. The drum contained one of two sets of radioactive activity for a variety of isotopes of
particular interest in the nuclear safety industry: 3N02 HPB sludge, and PWR sludge. Both are
considered intermediate-level waste and are therefore do not generate heat. Skyshine was
evaluated, both initially and 15 years after emplacement, for a variety of roof thicknesses: 10,
20, 30, 40 and 50cm. The distance from the waste store was also varied between 50 – 250m.
The results showed the analytic model under-predicted the Skyshine dose for all input
conditions compared to the MCNP model, approximately two orders of magnitude lower. The
average factor-difference over all distances for initial Skyshine dose was found to range
between 43.4 – 141.5 for 3N02 HPB sludge and 45.9 – 167.0 for PWR sludge over the 5
concrete roof thicknesses. This factor-difference was found to decrease with increasing
distance from the waste store, however was found to increase when evaluated after 15 years. It
is therefore concluded that the analytic method is not a suitable substitute to the specialist
software, and should be used with caution in mitigating potential risk.
The main source of the discrepancy between the two methods was found to likely lie in the
treatment of scattering both within the concrete roof and in the air surrounding the waste store.
Due to its complex nature, the analytic model made no attempt to simulate scattering events,
which is a limit of the simulation. Changes to the MCNP model in order to minimise scattering
above the waste store were found to dramatically reduce the difference between the results,
bringing the data to within an order of magnitude and hence demonstrating the importance of
simulating scattering events when evaluating Skyshine.
A reflection component of radiation incident on the walls of the waste store was also
implemented in an attempt to improve the results of the analytic model. It was found that
although the Skyshine dose increased, the average factor-difference was still approximately
two orders of magnitude below MCNP. Further work is therefore recommended to include
scattering and/or reflection into the analytic model before it can reliably be used in the design
of nuclear waste stores.

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Appendices
A.1 Complete Results for Model Comparison
The results obtained for all input scenarios simulated by the two models, for complete
comparison. H.C. corresponds to the data obtained from the analytic model, and unless other
stated values are the dose due to Skyshine, units mSv/hr.
Table V. PWR Sludge, Time 𝒕 = 0
Detector
Distance
/m
Concrete Thickness / cm
10 20 30 40 50
H.C. MCNP H.C. MCNP H.C. MCNP H.C. MCNP H.C. MCNP
50 3.26E-09 3.85E-07 1.46E-09 1.20E-07 5.05E-10 3.53E-08 1.70E-10 1.05E-08 5.57E-11 2.98E-09
75 1.63E-09 2.47E-07 7.30E-10 7.73E-08 2.51E-10 2.27E-08 8.49E-11 6.76E-09 2.77E-11 1.92E-09
100 9.71E-10 1.62E-07 4.36E-10 5.07E-08 1.50E-10 1.48E-08 5.07E-11 4.41E-09 1.66E-11 1.25E-09
150 4.59E-10 7.37E-08 2.06E-10 2.35E-08 7.10E-11 6.80E-09 2.40E-11 2.00E-09 7.83E-12 5.73E-10
200 2.67E-10 3.46E-08 1.20E-10 1.11E-08 4.12E-11 3.27E-09 1.39E-11 9.49E-10 4.55E-12 2.70E-10
250 1.74E-10 1.82E-08 7.80E-11 5.58E-09 2.69E-11 1.62E-09 9.07E-12 4.82E-10 2.97E-12 1.36E-10
Table VI. PWR Sludge, Time 𝒕 = 15 years
Detector
Distance
/m
10 20 30 40 50
50 2.50E-10 3.28E-08 1.44E-10 1.11E-08 4.94E-11 3.53E-09 1.75E-11 1.09E-09 6.20E-12 3.29E-10
75 1.25E-10 2.12E-08 7.19E-11 7.17E-09 2.46E-11 2.28E-09 8.73E-12 7.07E-10 3.09E-12 2.13E-10
100 7.45E-11 1.40E-08 4.29E-11 4.73E-09 1.47E-11 1.50E-09 5.21E-12 4.61E-10 1.84E-12 1.40E-10
150 3.52E-11 6.51E-09 2.03E-11 2.16E-09 6.95E-12 6.86E-10 2.46E-12 2.11E-10 8.71E-13 6.39E-11
200 2.04E-11 3.13E-09 1.18E-11 1.05E-09 4.03E-12 3.31E-10 1.43E-12 1.04E-10 5.06E-13 3.09E-11
250 1.33E-11 1.58E-09 7.68E-12 5.47E-10 2.63E-12 1.69E-10 9.33E-13 5.12E-11 3.30E-13 1.53E-11
Table VII. 3N02 HPB Sludge, Time 𝒕 = 0
Detector
Distance
/m
10 20 30 40 50
50 4.58E-09 4.69E-07 1.27E-09 1.23E-07 4.19E-10 3.02E-08 1.20E-10 7.16E-09 2.72E-11 1.69E-09
75 2.28E-09 2.98E-07 6.33E-10 7.77E-08 2.09E-10 1.91E-08 6.00E-11 4.53E-09 1.35E-11 1.07E-09
100 1.36E-09 1.93E-07 3.78E-10 5.01E-08 1.25E-10 1.23E-08 3.58E-11 2.90E-09 8.08E-12 6.87E-10
150 6.43E-10 8.51E-08 1.79E-10 2.21E-08 5.89E-11 5.36E-09 1.69E-11 1.27E-09 3.82E-12 3.03E-10
200 3.74E-10 3.99E-08 1.04E-10 1.03E-08 3.42E-11 2.52E-09 9.83E-12 5.69E-10 2.22E-12 1.39E-10
250 2.44E-10 1.95E-08 6.76E-11 5.08E-09 2.23E-11 1.21E-09 6.41E-12 2.79E-10 1.45E-12 6.79E-11

Table VIII. 3N02 HPB Sludge, Time 𝒕 = 15 years
Detector
Distance
/m
10 20 30 40 50
50 3.44E-12 4.39E-10 1.73E-12 1.37E-10 5.65E-13 4.11E-11 1.86E-13 1.21E-11 6.41E-14 3.23E-12
75 1.71E-12 2.84E-10 8.60E-13 8.85E-11 2.81E-13 2.66E-11 9.24E-14 7.80E-12 3.19E-14 2.28E-12
100 1.02E-12 1.85E-10 5.14E-13 5.79E-11 1.68E-13 1.73E-11 5.52E-14 5.11E-12 1.91E-14 1.49E-12
150 4.83E-13 8.47E-11 2.43E-13 2.62E-11 7.94E-14 7.88E-12 2.61E-14 2.33E-12 9.01E-15 6.78E-13
200 2.81E-13 4.08E-11 1.41E-13 1.27E-11 4.61E-14 3.82E-12 1.51E-14 1.12E-12 5.23E-15 3.29E-13
250 1.83E-13 1.98E-11 9.19E-14 6.29E-12 3.01E-14 1.89E-12 9.88E-15 5.56E-13 3.41E-15 1.59E-13
Table IX. 3N02 HPB Sludge, 10cm thick roof, reflection coefficient 𝒓
Detector
Distance
/m
Time, 𝑡 = 0 Time, 𝑡 = 15 years
𝑟 = 0.1 𝑟 = 1 𝑟 = 0.1 𝑟 = 1
50 6.24E-09 2.12E-08 4.69E-12 1.59E-11
75 3.11E-09 1.06E-08 2.34E-12 7.94E-12
100 1.86E-09 6.31E-09 1.39E-12 4.74E-12
150 8.77E-10 2.98E-09 6.59E-13 2.24E-12
200 5.09E-10 1.73E-09 3.83E-13 1.30E-12
250 3.32E-10 1.13E-09 2.50E-13 8.48E-13

A.2 Calculation of Additional Solid Angle Component Due To Reflection
In order to calculate the projected solid angle used in evaluating the additional Skyshine
component due to primary reflection, a projected aperture width was calculated. From Figure
6, three geometrical triangles can be drawn, assuming a critical angle of incidence φ (the
minimum angle of incidence reflected radiation can have to escape within one reflection). The
construction is shown in Figure 9. Note the thickness of the roof is ignored.
Figure 9. The geometrical construction created to calculate the projected aperture width due
to primary reflection. All units are shown in meters. The dimensions of the waste store are as
shown in Figure 1. In this appendix: triangle 1 = blue, triangle 2 = red, triangle 3 = green.
Considering triangle 1, the base length is half the width of the waste store. Therefore using
trigonometry,
tanφ =
𝑥
10
. (𝐴2.1)
Now considering triangle 2, the base length is the full width of the waste store and therefore
tanφ =
20 − 𝑥 − 1.3
20
. (𝐴2.2)
Equating Equation A2.1 and A2.2, we find that
𝑥 =
18.70
3
= 6.23 , (𝐴2.3)
which substituting back into Equation A2.1 gives a value for the critical angle of incidence
𝜑 = 31.94° . (𝐴2.4)
Finally, from triangle 3 and using Equation (A2.4),
tanφ =
20 − 1.3
𝑏
= 0.623 , (𝐴2.5)
giving a projected aperture width 2𝑏 = 60m.

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