Cosmic ray muons passing through matter lose energy from inelastic collisions with electrons and are deflected from nuclei due to multiple Coulomb scattering. The strong dependence of scattering on atomic number Z and the recent developments on position sensitive muon detectors indicate that multiple Coulomb scattering could be an excellent candidate for spent nuclear fuel imaging. Muons present significant advantages over existing monitoring and imaging techniques and can play a central role in monitoring nuclear waste and spent nuclear fuel stored in dense well shielded containers. The main purpose of this paper is to investigate the applicability of multiple Coulomb scattering for imaging of spent nuclear fuel dry casks stored within vertical and horizontal commercial storage dry casks. Calculations of muon scattering were performed for various scenarios, including vertical and horizontal fully loaded dry casks, half loaded dry casks, dry casks with one row of fuel assemblies missing, dry casks with one fuel assembly missing and empty dry casks. Various detector sizes (1.2 m x 1.2 m, 2.4 m x 2.4 m and 3.6 m x 3.6 m) and number of muons (10 5 , 5·10 5 , 10 6 and 10 7 ) were used to assess the effect on image resolution. The Point-of-Closest-Approach (PoCA) algorithm was used for the reconstruction of the stored contents. The results demonstrate that multiple Coulomb scattering can be used to successfully reconstruct the dry cask contents and allow identification of all scenarios with the exception of one fuel assembly missing. In this case, an indication exists that a fuel assembly is not present; however the resolution of the imaging algorithm was not enough to identify exact location.*Corresponding author: schatzid@purdue.edu I. INTRODUCTIONSince the pioneering work of E.P. George [1] and L. Alvarez [2], relativistic muons have been shown to have the ability to penetrate dense materials and by monitoring the subsequent scattering and/or attenuation of muons, a measurable signal about the structure and composition of the interrogated material can be obtained [3]. Recently, cosmic ray muons have been investigated for volcano imaging and cargo scanning applications and their use has been extended to nuclear waste imaging and determination of molten nuclear fuel location in nuclear reactors having suffered from the effects of a severe accident similar to the one happened in Fukushima [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].Earlier muon radiographic techniques were based on attenuation principles. A new promising method based on multiple Coulomb scattering was developed and demonstrated at LANL for detection of high-Z materials hidden in a large volume of low-Z materials, a situation representative of shielded material shielded hidden in a cargo container [24,25]. It was suggested that muon momentum measurement which can be achieved by indirectly measuring muon scattering in several layers of materials with known thickness could improve image resolution.This was later demonstrate...

In this study, a cosmic ray muon sampling capability using a phenomenological model that captures the main characteristics of the experimentally measured spectrum coupled with a set of statistical algorithms is developed. The "muon generator" produces muons with zenith angles in the range 0-90 o and energies in the range 1-100 GeV and is suitable for Monte Carlo simulations with emphasis on muon tomographic and monitoring applications. The muon energy distribution is described by the Smith & Duller (1959) phenomenological model. Statistical algorithms are then employed for generating random samples. The inverse transform provides a means to generate samples from the muon angular distribution, whereas the Acceptance-Rejection and Metropolis-Hastings algorithms are employed to provide the energy component. The predictions for muon energies 1 to 60 GeV and zenith angles 0-90 o are validated with a series of actual spectrum measurements and with estimates from the software library CRY. The results confirm the validity of the phenomenological model and the applicability of the statistical algorithms to generate polyenergetic-polydirectional muons. The response of the algorithms and the impact of critical parameters on computation time and computed results were investigated. Final output from the proposed "muon generator" is a look-up table that contains the sampled muon angles and energies and can be easily integrated into Monte Carlo particle simulation codes such as Geant4 and MCNP.

27The potential non-proliferation monitoring of spent nuclear fuel sealed in dry casks 28 interacting continuously with the naturally generated cosmic ray muons is investigated. 29 Treatments on the muon RMS scattering angle by Moliere, Highland and, 30 Lynch-Dahl were analyzed and compared with simplified Monte Carlo simulations. The 31Lynch-Dahl expression has the lowest error and appears to be appropriate when performing 32 conceptual calculations for high-Z, thick targets such as dry casks. The GEANT4 Monte 33 Carlo code was used to simulate dry casks with various fuel loadings and scattering variance 34 estimates for each case were obtained. The scattering variance estimation was shown to be 35 unbiased and using Chebyshev's inequality, it was found that 10 6 muons will provide 36 estimates of the scattering variances that are within 1% of the true value at a 99% confidence 37 level. These estimates were used as reference values to calculate scattering distributions and 38 evaluate the asymptotic behavior for small variations on fuel loading. It is shown that the 39 scattering distributions between a fully loaded dry cask and one with a fuel assembly missing 40 initially overlap significantly but their distance eventually increases with increasing number 41 of muons. One missing fuel assembly can be distinguished from a fully loaded cask with a 42 small overlapping between the distributions which is the case of 100,000 muons. This 43 indicates that the removal of a standard fuel assembly can be identified using muons 44 providing that enough muons are collected. A Bayesian algorithm was developed to classify 45 dry casks and provide a decision rule that minimizes the risk of making an incorrect decision. 46 The algorithm performance was evaluated and the lower detection limit was determined. 47 48

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Cosmic ray muon-computed tomography (μCT) is a new imaging modality with unique characteristics that could be particularly important for diverse applications including nuclear nonproliferation, spent nuclear fuel monitoring, cargo scanning, and volcano imaging. The strong scattering dependence of muons on atomic number Z in combination with high penetration range could offer a significant advantage over existing techniques when dense, shielded containers must be imaged. However, μCT reconstruction using conventional filtered back-projection is limited due to the overly simple assumptions that do not take into account the curved path caused by multiple Coulomb scattering prompting the need for more sophisticated approaches to be developed. In this paper, we argue that the use of improved muon tracing and scattering angle projection algorithms as well as an algebraic reconstruction technique should produce muon tomographic images with improved quality - or require fewer muons to produce the same image quality - compared to the case where conventional methods are used. We report on the development and assessment of three novel muon tracing methods and two scattering angle projection methods for μCT. Simulated dry storage casks with single and partial missing fuel assemblies were used as numerical examples to assess and compare the proposed methods. The reconstructed images showed an expected improvement in image quality when compared with conventional techniques, even without muon momentum information, which should lead to improved detection capability, even for partial defects.