TITLE:
Transport in Astrophysics: I. Diffusion of Solar and Galactic Cosmic Rays
AUTHORS:
Lorenzo Zaninetti
KEYWORDS:
Cosmic Rays, Particle Diffusion, Random Walks
JOURNAL NAME:
International Journal of Astronomy and Astrophysics,
Vol.12 No.1,
February
23,
2022
ABSTRACT: Some solutions for the diffusion phenomenon as a function of time and space are reviewed. Two new solutions of the homogeneous diffusion equation in 1D and 2D are derived in the presence of an existing fixed number of particles. The initial conditions which allow deriving a power law behavior for the energy of the cosmic rays (CR) are derived. The superposition of transient diffusive phenomena on an existing power law distribution for the energy of CR allows simulating the knee, the second knee, and the ankle.