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O-21 - Cosmic rays above 1e17 eV strike Earth at 5e-14 per cm2 per s - 3e22 above-LHC-energy collisions over Earth's history and 1e31 universe-wide

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Properties8
type
observation
id
O-21
statement
The measured cosmic-ray spectrum extends to ~1e20 eV, and the total flux at or above 1e17 eV — the fixed-target energy whose centre-of-mass energy equals the LHC's 14 TeV — is about 5e-14 per cm2 per second; over Earth's 5e18 cm2 surface and 4.5 Gyr age this gives over 3e22 above-LHC-energy collisions, i.e. ~1e5 full LHC programmes on Earth, ~1e9 on the Sun, ~1e31 across the observable universe's stars since its origin, and ~3e13 complete LHC programmes per second ongoing.
source
S-1 - LSAG report- Review of the Safety of LHC Collisions
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§2, Fig. 1
quote
the total flux of cosmic rays with energies of 10^17 eV or more that hit each square centimeter of the Earth's surface is measured to be about 5x10^-14 per second
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Derivation chain (all arithmetic from the measured flux): a cosmic-ray proton on a fixed target reaches the LHC’s 14 TeV CM energy at E ≳ 1e17 eV; Earth surface 5e18 cm2 x 4.5 Gyr → 3e22 collisions ≈ 1e5 LHC programmes (each LHC detector expects ~1e17 pp collisions). Sun has 1e4 x Earth’s surface → ~1e9 programmes; ~1e11 Sun-like stars per galaxy x ~1e11 galaxies → ~1e31 programmes since the beginning of the universe, ~3e13 per second ongoing. Caveat (ref [6] of the paper): the counts drop by roughly a factor A if the ultra-high-energy cosmic rays are nuclei of atomic number A, since the spectrum falls like 1/E^3. The comparison assumes special relativity holds for cosmic rays at these energies (ref [4]).

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