Purdue University Graduate School

Physics-based trajectory estimation algorithm for muon tomographic applications





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A physics-based muon trajectory estimation algorithm for muon tomographic applications

posted on 2023-08-04, 16:26 authored by Reshma Sanjay UghadeReshma Sanjay Ughade

Recently, the use of cosmic ray muons in critical national security applications, e.g., nuclear nonproliferation and safeguards verification, has gained attention due to unique muon properties such as high energy and low attenuation even in very dense materials. Applications where muon tomography has been demonstrated include cargo screening for detection of special nuclear materials smuggling, source localization, material identification, determination of nuclear fuel debris location in nuclear reactors, etc. However, muon image reconstruction techniques are still limited in resolution mostly due to multiple Coulombscattering (MCS) within the target object. Improving and expanding muon tomography would require development of efficient & flexible physics-based algorithms to model the MCS process and accurately estimate the most probable trajectory of a muon as it traverses the target object. The present study introduces a novel algorithmic approach that utilizes Bayesian probability theory and a Gaussian approximation of MCS to estimate the most probable path of cosmic ray muons as they traverse uniform media.

Using GEANT4, an investigation was conducted involving the trajectory of 10,000 muon particles that underwent bombardment from a point source parallel to the x-axis. The proposed algorithm was assessed through four types of simulations. In the first type, muons with energies of 1 GeV, 3 GeV, 10 GeV, and 100 GeV were utilized to evaluate the algorithms’ performance and accuracy. The second type of simulation involved the use of target cubes composed of different materials, including aluminum, iron, lead, and uranium. These simulations specifically focused on muons with an energy of 3 GeV. Next, the third type of simulation entailed employing target cubes with varying lengths, such as 10 cm, 20 cm, 40 cm, and 80 cm, specifically using muons with an energy of 3 GeV and a uranium target. Lastly, all the previous simulations were revised to accommodate a source of poly-energetic muons. This revision was undertaken to create a more realistic source scenario that aligns with the distribution of muon energies encountered in real-world situations.

The results demonstrate significant improvements in precision and muon flux utilization when comparing different algorithms. The Generalized Muon Trajectory Estimation (GMTE) algorithm shows around 50% improvement in precision compared to currently used Straight Line Path (SLP) algorithm across all test scenarios. Additionally, GMTE algorithm exhibits around 38% improvement in precision compared to the extensively used Point of Closest Approach (PoCA) algorithm. Similarly for both mono and poly energetic source of muons, the GMTE algorithm shows 10%-35% increase in muon flux utilization for high Z materials and a 10%-15% increase for medium Z materials compared to the PoCA algorithm. Similarly, it demonstrates 6%-9% increase in muon flux utilization for both medium and high Z materials compared to the SLP algorithm across all test scenarios. These results highlight the enhanced performance and efficiency of GMTE algorithm in comparison to SLP and PoCA algorithms.

Through these extensive simulations, our objective was to comprehensively evaluate the performance and effectiveness of the proposed algorithm across a range of variables, including energy levels, materials, and target geometries. The findings of our study demonstrate that the utilization of these algorithm enables improved resolution and reduced measurement time for cosmic ray muons when compared with current SLP and PoCA algorithm.


Purdue Research Foundation


Degree Type

  • Master of Science


  • Nuclear Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Stylianos Chatzidakis

Additional Committee Member 2

Lefteri H. Tsoukalas

Additional Committee Member 3

Andreas Jung