Revisiting the implications of Liouville's theorem to the anisotropy of cosmic rays

Understand

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.