2023/07/24 by Cainã de Oliveira, de Oliveira, Cainã, Leonardo Paulo Maia +2 · 1 citation
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE) #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2307.13095
openalex publication_date 2023/07/24 · openalex created_date 2023/07/27 · openalex updated_date 2026/07/28
We present a solution to Liouville's equation for an ensemble of charged particles propagating in magnetic fields. The solution is presented using an expansion in spherical harmonics of the phase space density, allowing a direct interpretation of the distribution of arrival directions of cosmic rays. The results are found for chosen conditions of variability and source distributions. We show there are two conditions for an initially isotropic flux of particles to remain isotropic while traveling through a magnetic field: isotropy and homogeneity of the sources. In case isotropically-distributed sources inject particles continuously in time, a transient magnetic induced dipole will appear. This dipole will vanish if the system reaches a steady-state. The formalism is used to analyze the data measured by the Pierre Auger Observatory, contributing to the understanding of the dependence of the dipole amplitude with energy and predicting the energy in which the quadrupole signal should be measured.