Formation of higher harmonics of the galactic cosmic-ray distribution function

We derive equations for the multipole moments of the distribution function of Galactic cosmic rays with energies 1--20 TeV that experience random scattering by turbulence with a power-law spectrum. We take into account the irregularity of the local interstellar medium (LISM) in the neighborhood of the solar system due to the presence of interstellar clouds, the interstellar wind flow around the heliomagnetosphere, and preceding supernova explosions in the local superbubble. The amplitudes of the second and third harmonics of the cosmic-ray distribution function are expressed in terms of the amplitude of the first harmonic without assuming them to be small compared to the first harmonic. Reconciling their values in magnitude and phase with the observed values requires a significant LISM irregularity, which is consistent with other observational data on the LISM structure. Our model is consistent with the assumption that supernova remnants in the Galactic disk located at distances from the Solar system much larger than the particle transport mean free path are the sources of the particles under consideration.