Cosmic-ray pitch-angle scattering through 90°

We study the problem of cosmic-ray diffusion in the Galactic disk with particular attention paid to the problem of particle scattering through the theta = cos(-1) (v(parallel to)/v) = 90 degrees pitch angle in momentum space by wave-particle mirror interaction (here v(parallel to) is the cosmic-ray velocity parallel to the average Galactic magnetic field). We consider the case in which cosmic rays are the only source of magnetic turbulence, which originates as the relativistic particles try to stream through the interstellar plasma faster than the local Alfven speed. The wave growth rate is proportional to the cosmic-ray anisotropy, and the amplitude of hydromagnetic waves generated by this streaming instability is limited by the presence of various damping mechanisms. We study the propagation of cosmic rays in the different phases of the interstellar medium, in particular the coronal regions (where the main form of wave dissipation is nonlinear Landau damping) and the warm regions (where charge exchange between the ions and the neutral atoms gives rise to the dominant form of wave dissipation). We also account for ion-cyclotron damping of small wavelength waves. The effect of a spectrum of waves is to limit the anisotropy of the cosmic-ray distribution function and hence their drift velocity. We show that quasi-linear resonant scattering cannot account for particle diffusion everywhere in momentum space and that particles with theta similar to 90 degrees must change their pitch angle by mirror interaction with long-wavelength waves generated by the theta similar to 0 degrees particles. We match the quasi-linear scattering with the adiabatic mirroring in a small boundary layer in momentum space close to the theta similar to 90 degrees point, and then we calculate the diffusion coefficient together with the cosmic-ray drift velocity. We show that scattering through the 90 degrees point is very efficient, and we calculate the correction to the particle diffusion coefficient due to the presence of mirroring.