Muon Tomography Transmission

Muons from Cosmic Rays

Primary cosmic rays (mostly protons, ~90%, and helium nuclei, ~9%) strike the upper atmosphere at relativistic energies (10⁹–10²⁰ eV). The collision with atmospheric nuclei produces a shower of secondary particles, including pions (π⁺, π⁻) that decay into muons:

Cosmic ray air shower:

  p (cosmic ray) + N (atmosphere) → π⁺ + π⁻ + X
  π⁺ → μ⁺ + ν_μ       (lifetime: 26 ns)
  π⁻ → μ⁻ + ν̄_μ       (lifetime: 26 ns)
  μ⁺ → e⁺ + ν_e + ν̄_μ  (lifetime: 2.2 μs)
  μ⁻ → e⁻ + ν̄_e + ν_μ  (lifetime: 2.2 μs)

Muon properties:
  Mass: 105.7 MeV/c² (207 × electron mass)
  Charge: ±1e
  Lifetime (at rest): 2.2 μs
  Lifetime (relativistic): γ × 2.2 μs
    At 1 GeV: γ ≈ 9.5 → τ_lab ≈ 21 μs
  Penetration depth: ~1 km in rock

Muon flux at Earth's surface:
  Vertical: ~1 muon/cm²/min (at sea level)
  At 30° zenith: ~0.8 muon/cm²/min
  At 60° zenith: ~0.4 muon/cm²/min
  At 90° (horizontal): ~0.003 muon/cm²/min

Altitude dependence (from sea level to 5 km):
  Increases ~2.5× per km altitude

Transmission Muon Tomography

Transmission muon tomography measures the attenuation of cosmic-ray muons as they pass through an object. Dense materials absorb more muons than low-density materials. By placing muon detectors above and below (or on opposite sides of) an object, the transmission probability maps to the integrated density along each muon's path:

Muon attenuation:

  N(x) = N₀ × e^(-x/λ)

Where:
  N₀ = incident muon flux
  x  = thickness of material (g/cm²)
  λ  = absorption mean free path

  For rock: λ ≈ 500 g/cm²
  For lead: λ ≈ 460 g/cm²
  For water: λ ≈ 1000 g/cm²

Angular resolution:
  Typical telescope: 1–3 mrad (~0.1–0.3°)
  Emulsion film: ~1 mrad
  Drift chambers: ~5 mrad

Angular acceptance:
  Ω = A × cos(θ) × dθ × dφ
  Typical: 1–5 m²·sr for large detectors

Density resolution:
  Δρ/ρ ≈ 1–5% for 1 m³ volume
  at surface muon flux, ~1 week exposure

Detector Technologies

• Nuclear emulsion film: Silver halide crystals in gelatin record individual muon tracks with sub-millimetre precision. After chemical development, tracks are read by automated microscopes. Used in the ScanPyramids project. Spatial resolution: ~1 μm. Disadvantage: slow readout (days to weeks).
• Drift tube detectors: Gas-filled tubes (Ar/CO₂) with central anode wire. Muon ionizes gas; electrons drift to wire, producing a signal. Position resolution: ~1 mm. Real-time readout. Used in MAGE and Muon Portal projects.
• Scintillator detectors: Plastic scintillator bars with photomultiplier tubes or SiPMs. Fast timing (~1 ns resolution). Good for muon tracking and energy measurement. Used in volcano monitoring and reactor inspection.
• GEM (Gas Electron Multiplier): Thin copper-clad polymer foil with holes, coated with resistive material. High-rate capability, good spatial resolution (~100 μm). Used in next-generation muon telescopes.

Archaeological Applications

ScanPyramids (2015–present): The most famous muon tomography project. Used nuclear emulsion detectors placed inside the Great Pyramid of Giza to image its internal structure. Discovered:

• Void (2017): A large anomalous region (~30 m long) above the Grand Gallery, detected by three independent muon detector sets. Confirmed in 2023 by cosmic-ray muon imaging from outside the pyramid.
• North Face Corridor (2016): A previously unknown passage behind the North Face Chevron.
• Hidden chamber (2017): A possible chamber near the North Face.

Volcano Monitoring

Muon tomography is used to image the internal density structure of volcanoes, detecting magma chambers, conduits, and density anomalies that indicate eruptive potential:

• Mount Vesuvius (2010): Muon detectors imaged the conduit and found it was partially filled with solidified material, not liquid magma.
• Mount Asama (2009): Muon imaging revealed a low-density zone beneath the crater, interpreted as a gas-rich magma pocket.
• Sakurajima (2015): Real-time muon monitoring detected density changes before and during eruption.
• Cotopaxi (2016): Muon imaging mapped the internal conduit geometry.

Nuclear Reactor Monitoring

Muon tomography can image spent fuel pools and reactor cores, verifying the presence and arrangement of fuel assemblies without physical access:

• Fukushima Daiichi (2015): Muon detectors placed outside the damaged reactor buildings imaged the melted fuel debris (corium) inside Unit 1 and Unit 3. Found that most fuel had melted through the reactor pressure vessel into the primary containment vessel.
• Rokkasho Reprocessing Plant: Muon tomography proposed for verifying spent fuel inventories in nuclear safeguards applications.