Cosmic Rays I.: The cosmic ray spectrum between 10 TeV and 3 EeV

Abstract

I develop a theory to account for the cosmic ray spectrum. The essential assumption is that, due to fast convective motions, 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 use the basic concept, that the energetic Cosmic Ray particles are accelerated in a Supernova shock that travels down a stellar wind. Discussion gives a knee energy expression, which leads to a suggestion on the physical origin of the mechanical energy of Supernova explosions, the gravitational potential energy mediated by the angular momentum and the magnetic field. The spectrum below the knee is $E^{-8/3}$. At the knee the particles segregate with particle energy according to their charge. The spectrum beyond the knee is very close to $E^{-3}$. The theory has been checked successfully against air shower data in two subsequent papers (Stanev, Biermann, Gaisser, 1992 preprint; Rachen, Stanev, Biermann, 1992 preprint).