Ultra-high-energy galactic cosmic ray hadrons from distributed focused acceleration

Large-scale spatial variations of the galactic guide magnetic field, characterized by the focusing length L = − [ d ( ln B ( z ) ) / d z ] − 1 , together with a nonzero value of the cross helicity state of Alfvenic slab turbulence H give rise to first-order Fermi, betatron-like acceleration of energetic cosmic ray hadrons, if the product H L 0 is negative. The equilibrium momentum spectrum of accelerated particles by this focus ed acceleration mechanism is determined. Assuming a simple chemical composition of injected cosmic rays (99 percent protons and 1 percent Fe), it is shown that the ultra-high-energy Fe/p-ratio is a rapidly changing function of the total energy. The derived chemical composition of cosmic rays is first proton-dominated at low energies, then becomes Fe-dominated between 0.1 and 2.4 PeV, before becoming strongly proton-dominated between 2.4 PeV and 1100 PeV, and strongly Fe-dominated at energies beyond 1100 PeV.