  In this work, we propose a new approach to cosmic ray muon momentum
measurement using multiple pressurized gaseous Cherenkov radiators. Knowledge
of cosmic ray muon momentum has the potential to significantly improve and
expand the use of a variety of recently developed muon-based radiographic
techniques. However, existing muon tomography systems rely only on muon
tracking and have no momentum measurement capabilities which reduces the image
resolution and requires longer measurement times. A fieldable cosmic ray muon
spectrometer with momentum measurement capabilities for use in muon scattering
tomography is currently missing. We address this challenge by optimally varying
the pressure of multiple gaseous Cherenkov radiators and identifying the
radiators that are triggered by muons that have momentum higher than the
Cherenkov threshold momentum. We evaluate the proposed concept through Geant4
simulations and demonstrate that the cosmic ray muon momentum spectrum can be
reconstructed with sufficient accuracy and resolution for two scenarios: (i) a
perfect Cherenkov muon spectrometer and (ii) a practical spectrometer where
noise is introduced in the form of scintillation and transition radiation
photons. To quantify the accuracy of spectrometer, the concept of true and
false classifications are introduced. The fraction of true classification is
investigated for each momentum level in a practical radiator. The average
classification rate for momentum range of 0.2 to 7.0 GeV/c with uncertainty of
1 GeV/c is approximately 85%.
