Solving the 90° Scattering Problem in Isotropic Turbulence

A fundamental problem of cosmic-ray diffusion theory is pitch-angle scattering at 90°. For isotropic and anisotropic turbulence, the 90° problem leads to an infinitely large parallel mean free path. In this Letter, the second-order quasi-linear theory for cosmic-ray scattering parallel to a mean magnetic field is generalized for isotropic turbulence. It is shown that, in contrast to classic quasi-linear theory, the second-order theory provides nonvanishing scattering through 90° even for magnetostatic turbulence. The problem of 90° scattering is thus solved, because the comparison with simulations shows good quantitative agreement. It is also shown that the Fokker-Planck coefficient for pitch-angle scattering has its maximum at 90°.