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

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].

Fig. 1. Storage facilities in the U.S.

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):

σ θ=13.6 MeV

βpc √ xX0 (1+0.038 log x

X0 ) (1)

with , X0=

716.4( gcm2 )

ρA

Z ( Z+1 ) log 287√Z

(2)

where ρ is the material density, Z the atomic number of the material, β=u /c, 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 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.

Fig. 2. Dry cask and muon detectors

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:

λrad=∑i=1

3

(σθ2/ L)i= 1

2 N ∑i=1

3

∑k=1

N ( θx k

2 +θyk

2

L )i

(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

fully-loaded 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 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

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

Fig. 3. Geant4 simulations of dry casks fully loaded (left) and empty (right).

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. 832-

839, 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.