Cosmic Rays I . The cosmic ray spectrum between 10 4 GeV and 3 10 9 GeV

Based on a conjecture about the diffusion tensor of relativistic particles perpendicular to the magnetic field at a shock, and considering particle drifts, I develop a theory to account for the Cosmic Ray spectrum between 10 GeV and 3 10 GeV. The essential assumption is that the free mean path perpendicular to the magnetic field is independent of energy and has the scale of the thickness of the shocked layer. I then use the basic concept, that the energetic Cosmic Ray particles areaccelerated in a Supernova shock that travels down the density gradient of a stellar wind; as an example I use a Wolf Rayet star wind. Physically important ingredients beside the presence of a strong shock are diffusion, drifts, convection, adiabatic cooling, the injection history, and the topology of the magnetic field, assumed to behave similarly to the solar wind. The result is a spectrum, which for strong shocks and negligible wind speeds in a gas with adiabatic index 5/3 yields a spectrum of E. Discussion of the latitude dependence of the acceleration leads to a knee energy which is determined by an expression of which the functional form leads to a suggestion on the physical origin of the mechanical energy of Supernova explosions, namely the gravitational potential energy mediated by the angular momentum and the magnetic field. Interstellar turbulence with a Kolmogorov spectrum then leads by losses from the galactic disk to a spectrum, which is E below the knee, as observed in Cosmic Rays, and as deduced from radio observations of the nonthermal emission of our Galaxy as well as that of all other well observed galaxies. At the knee the particles segregate with particle energy according to their charge, with H dropping off first, then CNO elements, then Mg, Si etc., and finally iron nuclei. Further consideration of the energy gain due to drifts at high particle energies leads to a spectrum beyond the knee. This spectrum is E at injection, and, corrected for diffusive transport through the Galaxy, very close to E, as observed. Beyond the knee, iron and other heavy nuclei dominate out to the highest energies of galactic Cosmic Ray particles.