The Effect of Wave-Particle Interactions on the Propagation of Cosmic Rays

Abstract

The interaction between galactic cosmic rays and Alfvén waves in the interstellar medium is investi- gated. They may interact adiabatically through magnetic mirror scattering or non-adiabatically through gyration frequency resonance. The equations describing the latter are derived. The growth rates for the waves are given, and the Fokker-Planck equation for the diffusion of cosmic rays in velocity space is derived. These two equations are applied to a model of the cosmic rays consisting of a uniform tube of magnetic field with open ends. An equation of spatial diffusion is derived in the limit of strong wave- particle scattering, and this equation is compared with the observed properties of the galactic cosmic rays to derive a mean free path for scattering of about 10 pc. It is shown that when the interstellar damping of the Alfvén waves is included, the waves are probably marginally stable. Finally, a self- consistent model is specified in which the sources of turbulence and cosmic rays are given and the cosmic- ray densities are to be determined. This model is solved in the crude approximation where all particles have effectively the same energy and all waves the same wavelength. It is shown that the cosmic rays can have an appreciable effect on their confinement to the Galaxy. It is shown that if the inhomogeneous distribution of mass is taken into account, the confinement of cosmic rays is determined primarily by the low-density regions between the clouds. An attempt is made to evaluate the efficiency of heating of cosmic rays, and it appears that their energy changes very little during their galactic confinement. However, because there is a non-linear relation between the source and the cosmic-ray density, the observed energy spectrum does not necessarily represent the emitted spectrum