Project Title: Creation of a Geant4 Muon Tomography Package for Imaging of Nuclear Fuel in
Dry Cask Storage (13-5376)
Principal Investigator: Prof. Lefteri H. Tsoukalas, 765-496-9696, tsoukala@purdue.edu
1. Introduction
Monitoring spent nuclear fuel stored in dense shielded dry casks using cosmic ray muons has the
potential to allow for non-destructive assessment of nuclear material accountancy with the aim to
independently verify and identify weapons grade material, such as fuel pellets, fuel rods and fuel
assemblies stored within those sealed dense dry casks. Cosmic ray muons are charged particles,
having approximately 200 times the mass of electron, generated naturally in the atmosphere, and
rain down upon the earth. Energetic muons have the unique ability to penetrate high density
materials allowing the distribution of material within the object to be inferred from muon
measurements. High energy cosmic rays continuously entering Earth’s atmosphere generate a
cascade of secondary rays and relativistic particles. Of those that eventually reach the surface are
cosmic ray muons. Cosmic ray muons are charged particles, generated naturally in the
atmosphere, and rain down upon the earth at an approximate rate of 10.000 particles m-2 min-1
[1]. Energetic muons have the unique ability to penetrate high density materials allowing the
distribution of material within the object to be inferred from muon measurements. The
applicability of cosmic muons for a number of monitoring and imaging applications has been
investigated over the years and includes applications to archaeology, volcano imaging, material
identification and medical diagnosis. It is worth noting the pioneering work of L. Alvarez, which
measured the cosmic ray muon flux attenuation to determine the presence and location of hidden
chambers within the Egyptians pyramids [2] and that of E. P. George, which used a similar
method to infer rock depth covering underground tunnels [4]. Innovative applications of cosmic
ray muons have been proposed for medical examination of comatose patients towards bone
density monitoring and determination of the molten nuclear fuel location in nuclear reactors
having suffered from the effects of a severe accident similar to the one happened in Chernobyl
and Fukushima [4]. More recently, cosmic ray muons have been shown to have the potential to
allow for non-destructive assessment of nuclear material accountancy with the aim to
independently verify and identify weapons grade material hidden in cargo containers [5] or fuel
pellets, fuel rods and fuel assemblies stored within sealed dense dry casks [6]. The subsequent
scattering and transmission of muons can provide a measurable signal about the structural and
chemical composition of the stored materials [7].
In the U.S., we operate 104 commercial nuclear reactors, 69 Pressurized Water Reactors and 35
Boiling Water Reactors, at 64 sites in 31 states. Over the past five decades approximately 65000
metric tons of uranium (MTU) have been generated by the 100+ nuclear reactors in the U.S. A
typical reactor generates 20 MTU per year. 75% is
stored in used fuel pools while the rest 25% is under dry
storage conditions. As of today, no permanent repository
exists and all studies at Yucca Mountain have been
suspended resulting in increased used fuel accumulation
at reactor sites. The current number of dry cask storage
containers in utilities is approximately 1200 and it is
Fig. 1. Storage facilities in the U.S.
anticipated that by 2020 more than 2400 casks will be in
use by U.S. utilities.
In this project, an effort is undertaken to exploit the passive nature of muons for spent nuclear
fuel monitoring purposes. Monitoring nuclear waste and controlling nuclear material at its source
is one of the main strategies to minimize the risks of nuclear proliferation and reduce potential
homeland threats [7]. The reason to monitor nuclear waste stems from the need to investigate
whether the stored content agrees with the declared content. It is well established that since the
early 1950’s, when the first nuclear power plant began to produce electricity, vast numbers of
drums, containers and dry casks house, frequently unknown, waste that include spent nuclear
fuel, concrete and voids [8]. After the spent nuclear fuel has been placed inside the dry cask, the
cask is welded, not allowing for visual inspection [6]. This new technique can prove to have
significant advantages over the existing ones such as the utilization of the passive nature of
muons, the lack of radiological sources and consequently the absence of any artificial
radiological dose. Conventional methods for examining the interior of materials e.g., x-rays, are
limited by the fact that they cannot penetrate very dense well-shielded objects while more
sophisticated techniques such as the penetrating neutrons or the recently developed proton
radiography necessitate the use of an expensive accelerator [9].
A Brief Introduction to Cosmic Ray Muons
Cosmic ray muons are charged particles, having approximately 200 times the mass of
electron, generated naturally in the atmosphere, and rain down upon the earth at an approximate
rate of 10,000 particles m-2 min-1 (Hagiwara, 2002). This rate is low enough, ~160 Hz, to allow
for single event processing. Muon energy at sea level ranges from 0.1 GeV to 100 GeV with
mean energy 3-4 GeV, the flux is greatest at the vertical and decreases with increasing zenith
angle. When muons traverse matter they undergo multiple scattering events with the atomic
nuclei due to Coulomb interactions. Theory (Bethe, 1953) predicts that the angular distribution
of the outgoing muons has an approximately Gaussian distribution with zero mean and standard
deviation (Schultz, 2003):
𝜎𝜃 =
13.6𝑀𝑒𝑉 𝑥
𝑥
√ (1 + 0.038 log )
𝛽𝑝𝑐
𝑋0
𝑋0
𝑔
)
𝑐𝑚2
716.4 (
𝑤𝑖𝑡ℎ,
𝑋0 =
𝜌
(1)
𝐴
𝑍(𝑍 + 1) log
287
√𝑍
(2)
where ρ is the material density, Z the atomic number of the material, 𝛽 = 𝑢⁄𝑐 , A the mass
number of the material. The dependency on atomic
number has been shown to allow for material
differentiation. A system that tracks the path of muons,
including their deflection and energy loss, could serve as
a unique way to identify and scan the contents of a sealed
and shielded container. It is envisaged that the design of
an inexpensive muon monitoring system will include
placing two detector modules (Fig. 2) on mobile units
Fig. 2. Dry cask and muon detectors
which would allow for the detectors to move around the
storage facility. From this setup the detectors could be
maneuvered until they are positioned around the target cask. The detector could then be linked
back to a central computing system and the gathered data could even be monitored remotely,
where any significant deviations in scattering distribution would imply material diversion.
Preliminary Calculations
Muon monitoring takes advantage of the fact that the scattering angle, energy loss and range
of a muon are functions of cask composition. The scattering angle and energy loss of a muon
allows for the differentiation of material types (Table 1).
Table 1. Characteristics of 3 GeV muons in various materials
Material
Energy loss, MeV/cm
Range, m
Scattering, mrad/cm
Concrete
4.64
6.4
0.77
Iron
13.90
2.1
1.09
Lead
16.50
1.8
1.67
Uranium
28.51
1.1
1.72
It is interesting to note that muons will penetrate approximately 1 meter in high density
materials such as Uranium or Lead. This new information can be used to not only identify the
cask composition, e.g. iron vs uranium, but by calculating the most probable point of deflection
and using imaging reconstruction techniques it becomes possible to determine where that
material is physically located. Thus, information can be obtained not only about the composition
of interrogated materials, but also about their geometries. As an example, consider a dry cask, 3
meters in diameter and 6 m length. Placement of position sensitive, e.g., drift wire, and energy
sensitive, e.g., scintillator, detectors around the cask would provide the trajectory and energy of
the incoming and outgoing particles. After passing through the initial detector, the muons pass
through concrete, then uranium, exiting through another layer of concrete before hitting the final
detector. The detector measurements are then processed to determine the muon energy loss and
the scattering angles. These measurements are samples from independent, identically distributed
random variables (Schultz, 2003). The scattering density is estimated as:
3
𝜆𝑟𝑎𝑑
3
𝑁
2
2
𝜃𝑥_𝑘
+ 𝜃𝑦_𝑘
1
2
= ∑(𝜎𝜃 ⁄𝐿)𝑖 =
∑∑(
)
2𝑁
𝐿
𝑖
𝑖=1
𝑖=1 𝑘=1
(3)
where L is the thickness of the i-th material, θx and θy are the projected scattering angles and N is
the number of measurements. At the typical sea-level flux, about N=10,000 muons per minute
pass through a detector having an area of 1.0x1.0=1.0 m2. For a dry cask, 20,000 measurements
of scattering angles are obtained per minute. Random samples of muons were generated and two
dry cask configurations were considered. The first
one, “Case A”, requires the dry cask to be fullyloaded with fuel assemblies. In “Case B”, “one fuel
assembly is missing” and, therefore, the thickness is
reduced by ~20 cm. The process of generating
random samples of muons was repeated 5,000 times
and the results are shown in Fig. 2. The results
indicate that reducing the amount of nuclear material
Fig. 2. Scattering density distributions
for two cases.
in a dry cask leads to a meaningful change of its
scattering distribution which indicates that the
removal of a nuclear fuel assembly can be identified with a high level of confidence. Of course,
there do exist additional factors yet to be considered. Measurement errors, less than perfect
detector efficiency, and more complicated geometries are real-world considerations that will
broaden the distributions and motivate the experimental study of muon radiography in order to
identify its performance under real world conditions.
Early efforts will be directed towards the development of an integrated mathematical framework
to couple the muon scattering with the currently unutilized muon attenuation. Transport
principles will be used to describe the stochastic nature of muon particles and provide a
mathematical analysis for identification of the
primary mechanisms and features of cosmic
ray muon transport in dry casks. Building on
this
analysis,
large
scale,
high-fidelity
modeling studies will be performed using the
Monte Carlo simulator GEANT4 (Agostinelli,
2003) a well-known and tested simulation tool
Fig. 3. Geant4 simulations of dry casks fully
loaded (left) and empty (right).
developed at CERN for tracking muons and
their paths through materials. Fig. 3 depicts preliminary dry cask simulations for 4 GeV
monoenergetic muons incident upon a dry cask. One case considers a dry cask fully loaded with
the fuel assemblies while the other is empty. A muon beam is initiated above the cask and
scattering patterns are visualized. The fully loaded cask has a wider distribution of deflection
angles than its counterpart making it feasible to separate these two cases, albeit extreme for
visualization purposes, with minimal processing. The proposed effort will expand on preliminary
results and establish accurate simulations including but not limited to i) test scenarios with
missing fuel assemblies, ii) missing fuel rods, iii) measurements under differing levels of
background radiation, iv) old and new fuel, and v) non-standard behavior including damaged or
disfigured fuel elements. Detector positioning will be optimized appropriately to minimize
measurement time and improve signal resolution.
Significance:
Currently, more than 2,000 casks have been installed in the U.S. only and projections by
Electric Power Research Institute (Blue Ribbon Committee, 2012) show that eventually over
10,000 casks will be required by 2050. As worldwide nuclear capacity continues to increase it is
essential to continue verifying international spent fuel declarations in proving that the diversion
of plutonium has not occurred and help make the world safer.
Project Scope
This project focuses on advancing the mathematical framework, simulation, signal processing
and imaging technology for spent nuclear fuel monitoring applications. It outlines the
development of a simulation and analysis package to aid in the non-destructive assessment of
sealed spent nuclear fuel dry casks using cosmic ray muons. The methodology we propose to
develop will help the user to solve the inverse problem, i.e., determine presence, structure and
geometry of spent nuclear fuel assemblies from muon transport measurements. Advantages of
cosmic muon tomography include the utilization of the passive nature of muons, the lack of
radiological sources and consequently the absence of any artificial radiological dose. Such a
technique is in-line with the non-proliferation objectives of the Department of Energy (DoE),
since using radiological sources for radiography could potentially pose the security risk in the
case of source diversion.
Project Objectives
The project objectives are:

Identification of the principal mechanisms of muon-dry cask interaction

Development of a mathematical framework to allow for sound process description

Formulation, implementation and testing of Geant4 simulations

Development of intelligent algorithms for signal processing to provide information about the
contents of spent nuclear fuel dry casks

Verification and validation of results through comparison with available experiments
Once completed, the proposed muon tomography package for dry cask storage monitoring will
enable a new approach towards efficient, inexpensive and potentially remote safeguarding of
nuclear materials.
Project Schedule
The project schedule is shown below:
References
[1] Hagiwara et al., “Review of particle physics”, Physics Review D, Vol. 66, Issue 1, pp. 1-974,
2002.
[2] Alvarez et al., “Search for hidden chambers in the pyramids”, Science, Volume 167, pp. 832839, 1970.
[3] George, E. P., “Cosmic rays measure overburden of tunnel”, Commonwealth Engineer, pp.
455-457, 1955.
[4] Perry, J. O., “Advanced applications of cosmic-ray muon radiography”, Thesis dissertation,
The University of New Mexico, 2013.
[5] Borozdin, K. N. et al., “Radiographic imaging with cosmic ray muons”, Nature, Vol. 422, p.
277, 2003.
[6] Gustafsson, J., “Tomography of canisters for spent nuclear fuel using cosmic ray muons”,
Diploma thesis, UU-NF 05#08, Uppsala University, Sweden, 2005.
[7] Schultz, L. J., “Cosmic ray muon radiography”, Thesis dissertation, Portland State
University, 2003.
[8] Cox, L., “Cosmic ray muon scattering tomography for security applications”, National
Nuclear Security Division, AWE, UK, 2010.
[9] Morris, C. L. et al., “Tomographic Imaging with Cosmic Ray Muons. Science and Global
Security, Vol. 16, Issue 1-2, pp. 37-53, 2008.