Interaction of cosmic ray muons with spent nuclear fuel dry casks and determination of lower detection limit

The potential non-proliferation monitoring of spent nuclear fuel sealed in dry casks interacting continuously with the naturally generated cosmic ray muons is investigated. Treatments on the muon RMS scattering angle by Moliere, Rossi-Greisen, Highland and, Lynch-Dahl were analyzed and compared with simplified Monte Carlo simulations. The Lynch-Dahl expression has the lowest error and appears to be appropriate when performing conceptual calculations for high-Z, thick targets such as dry casks. The GEANT4 Monte Carlo code was used to simulate dry casks with various fuel loadings and scattering variance estimates for each case were obtained. The scattering variance estimation was shown to be unbiased and using Chebyshev's inequality, it was found that 106 muons will provide estimates of the scattering variances that are within 1% of the true value at a 99% confidence level. These estimates were used as reference values to calculate scattering distributions and evaluate the asymptotic behavior for small variations on fuel loading. It is shown that the scattering distributions between a fully loaded dry cask and one with a fuel assembly missing initially overlap significantly but their distance eventually increases with increasing number of muons. One missing fuel assembly can be distinguished from a fully loaded cask with a small overlapping between the distributions which is the case of 100,000 muons. This indicates that the removal of a standard fuel assembly can be identified using muons providing that enough muons are collected. A Bayesian algorithm was developed to classify dry casks and provide a decision rule that minimizes the risk of making an incorrect decision. The algorithm performance was evaluated and the lower detection limit was determined.