It is assumed that cosmic rays and other high-energy particles of extraterrestrial
origin can be produced by first-order Fermi diffusive shock acceleration in plasma up to
5x1019 eV, the point where they interact with the cosmic microwave background (CMB).
First-order Fermi shock acceleration is due to a supersonic shock with a Mach number
dependent on the index (or logarithmic slope) of the shock-induced power-law spectrum.
The local all-particle interstellar cosmic-ray spectrum can be obtained from the solution of a Fredholm
integral equation in rigidity, yielding both the “knee” and the “ankle” of the primary spectrum. The effect of
the maximum galactic acceleration mechanism at high energies near the ankle is to increase the relative
number of heavy nuclei relative to protons. Multiple cutoffs of heavier nuclei due to interactions with the
CMB have the opposite effect just below the Greisen-Zatsepin-Kuz’min (GZK) cutoff, resulting in fluxes
enriched in protons.
Earthward-directed supersonic coronal mass ejections are responsible for the great bulk of high-energy solarparticle
events because of diffusive shock acceleration in the heliosphere.
Keywords: Air shower data, cosmic rays, GZK cutoff, Monte Carlo solution to integral equations,
plasma, Shock acceleration, solar modulation, the local interstellar spectrum.
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