Second-order quasilinear theory of cosmic ray transport

The problem of pitch-angle diffusion close to 90° is well known in cosmic ray astrophysics. If the pitch-angle Fokker–Planck coefficient for pure slab geometry is calculated, the quasilinear approximation results in vanishing pitch-angle scattering. For a realistic wave spectrum with a steep dissipation range this vanishing coefficient generates an infinitely large parallel mean free path. It is well known from numerical simulations that the 90° problem is a problem of quasilinear theory and not a problem of reality. In the current paper quasilinear theory is used to calculate corrections of the unperturbed orbit. These corrections can be resubstituted into transport theory to calculate a second-order pitch-angle Fokker–Planck coefficient. The second-order quasilinear theory is an applicable theory which agrees with simulations for pitch-angle diffusion.