Cosmic ray muon tomography has been recently explored as a non-destructive technique for monitoring or imaging dense well-shielded objects, classically not achievable with traditional tomographic methods. As a recent example of technology transition from high-energy physics to real-world engineering applications, cosmic ray muon tomography has been used with various levels of success in nuclear nonproliferation. However, present muon detection systems have no momentum measurement capabilities and recently developed muon-based radiographic techniques rely only on muon tracking. This unavoidably reduces resolution and requires longer measurement times thus limiting the widespread use of cosmic ray muon tomography. Measurement of cosmic ray muon momenta has the potential to significantly improve the efficiency and resolution of cosmic ray muon tomography. In this paper, we propose and explore the use of momentum-dependent cosmic ray muon tomography using multi-layer gas Cherenkov radiators, a new concept for measuring muon momentum in the field. The muon momentum measurements are coupled with a momentum-dependent imaging algorithm (mPoCA) and image reconstructions are presented to demonstrate the benefits of measuring momentum in cosmic ray muon tomography.

Cosmic ray muons have been considered as a non-conventional radiation probe in various applications. To utilize cosmic ray muons in engineering applications, two important quantities, trajectory and momentum, must be known. The muon trajectories are easily reconstructed using two-fold detector arrays with a high spatial resolution. However, precise measurement of muon momentum is difficult to be achieved without deploying large and expensive spectrometers such as solenoid magnets. Here, we propose a new method to estimate muon momentum using multi-layer pressurized gas Cherenkov radiators. This is accurate, portable, compact (< 1m3), and easily coupled with existing muon detectors without the need of neither bulky magnetic nor time-of-flight spectrometers. The results show that not only our new muon spectrometer can measure muon momentum with a resolution of ± 0.5 GeV/c in a momentum range of 0.1–10.0 GeV/c, but also we can reconstruct cosmic muon spectrum with high accuracy (~ 90%).

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Cosmic ray muons have emerged as a non-conventional high-energy radiation probe to monitor dense and large objects. Muons are the most abundant cosmic radiation on Earth, however, their flux at sea level is approximately 10,000 min−1m−2 much less than that of induced radiation. In addition, cosmic ray muon flux depends on not only various natural conditions (e.g., zenith angle, altitude, or solar activities) but also the geometric characteristic of detectors. Since the low muon flux typically results in long measurement times, an accurate estimation of measurable muon counts is important for muon applications. Here we propose a simple and versatile semi-empirical model to improve the accuracy in muon flux estimation at all zenith angles by incorporating the geometric parameters of detectors, and we name this the “effective solid angle model”. To demonstrate the functionality, our model is compared with i) the cosine-squared, ii) PARMA model, and iii) Monte-Carlo simulations, and iv) measurements. Our results show that the muon count rate estimation capability is significantly improved resulting in increasing a mean C/E from 0.7 to 0.95. By selecting an appropriate intensity correlation, the model can be easily extended to estimate muon flux at various altitude and underground level.

Cosmic muons are highly energetic and penetrative particles and these figures are used for imaging of large and dense objects such as spent nuclear fuels in casks and special nuclear materials in cargo. Cosmic muon intensity depends on the incident angle (zenith angle, φ), and it is known that I(φ) = I0 cos2 φ at sea level. Low intensity of cosmic muon requires long measurement time to acquire statistically meaningful counts. Therefore, high-energy particle simulations e.g., GEANT4, are often used to guide measurement studies. However, the measurable cosmic muon count rate changes upon detector geometry and configuration. Here we develop an “effective solid angle” model to estimate experimental results more accurately than the simple cosine-squared model. We show that the cosine-squared model has large error at high zenith angles (φ ≥ 60°), whereas our model provides improved estimations at all zenith angles. We anticipate our model will enhance the ability to estimate actual measurable cosmic muon count rates in muon imaging applications by reducing the gap between simulation and measurement results. This will increase the value of modeling results and improve the quality of experiments and applications in muon detection and imaging.

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