DIFFUSIVE PROPAGATION OF HIGH ENERGY COSMIC RAYS IN GALAXY: EFFECT OF HALL DRIFT

Abstract

We phenomenologically developed a propagation model of high energy galactic cosmic rays. We derived the analytical solutions by adopting the semi-empirical diffusion equation, proposed by Berezinskii et al. (1990) and the diffusion tensor proposed by Ptuskin et al. (1993). This model takes into account both the symmetric diffusion and the antisymmetric diffusion due to the particle Hall drift. Our solutions are an extension of the model developed by Ptuskin et al. to a two-dimensional two-layer (galactic disk and halo) model, and they coincide completely with the solution derived by Berezinskii et al. in the absence of antisymmetric diffusion due to Hall drift. We showed that this relatively simple toy model can be used to explain the variation in the exponent of the cosmic ray energy spectrum, γ, around the knee E ≈1015 eV .