Diffusive Propagation of High Energy Cosmic Rays in Galaxy: Effect of Hall Drift

TL;DR

This paper develops a phenomenological model for high energy cosmic ray propagation in the galaxy, incorporating Hall drift effects, and explains spectral variations around the knee energy.

Contribution

It extends existing diffusion models by including Hall drift and provides analytical solutions for a two-layer galactic model.

Findings

Model explains spectral index variation around the knee energy.

Solutions align with previous models in the absence of Hall drift.

Demonstrates the significance of Hall drift in cosmic ray propagation.

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 {\it et al.}(1990) and the diffusion tensor proposed by Ptuskin {\it 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 {\it et al.} (1993) to a two-dimensional two-layer (galactic disk and halo) model, and they coincide completely with the solution derived by Berezinskii {\it et al.} (1990) 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, $\gamma$, around the knee $E \approx 10^{15}$ eV.