Supernova remnants and the origin of the cosmic radiation: I. SNR acceleration models and their predictions

An analysis is made of the cosmic ray energy spectrum expected from superno va remnant acceleration of cosmic rays for energies below the well known kn ee at 3 x 10(6) GeV. Two models are considered; that based on the single-sh ock acceleration model of Axford (1981 Pi-oc 17th Int. Cosmic Ray Conf. (Pa ris) 12 155) with associated diffusion and Galactic leakage is preferred. A local recent supernova, with a statistical probability as high as similar to 15-50%, is adequate to explain the features of the knee, in accord with our previous arguments (e.g. Erlykin and Wolfendale 1998 Astropart Phys. 82 65). Such a supernova needs to be closer than 500 pc to the Earth and young er than 110 kyr.